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  1. mathematics_batch_01.html +247 -229
  2. mathematics_batch_02.html +249 -258
  3. mathematics_batch_03.html +249 -248
  4. mathematics_batch_04.html +246 -199
  5. mathematics_batch_05.html +108 -24
  6. mathematics_batch_06.html +108 -24
  7. mathematics_batch_07.html +106 -21
mathematics_batch_01.html CHANGED
@@ -4,7 +4,97 @@
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  <meta charset="UTF-8" />
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  <meta name="viewport" content="width=device-width, initial-scale=1" />
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  <title>Mathematics Batch 01 - Number Theory - Programming Framework Analysis</title>
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- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
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  <script>
10
  mermaid.initialize({
@@ -17,66 +107,54 @@
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  nodeSpacing: 30,
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  rankSpacing: 30,
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  padding: 10
 
 
 
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  }
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  });
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  </script>
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  </head>
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  <body>
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  <div class="container">
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- <header>
27
- <h1>🔢 Mathematics Batch 01 - Number Theory</h1>
28
- <p class="subtitle">Prime Factorization, Modular Arithmetic, and Diophantine Equations</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Number Theory Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to fundamental number theory operations. Each process shows the computational logic behind prime factorization, modular arithmetic operations, and solving Diophantine equations.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Prime Factorization Algorithm Process</h2>
38
- <div class="figure">
39
- <div class="mermaid">
40
  graph TD
41
- A1[Composite Number Input] --> B1[Number Validation]
42
- C1[Prime Testing Algorithm] --> D1[Divisibility Check]
43
- E1[Factor Search Strategy] --> F1[Prime Factor Identification]
44
-
45
- B1 --> G1[Number Classification]
46
- D1 --> H1[Prime Factor Detection]
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- F1 --> I1[Factorization Method Selection]
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-
49
- G1 --> J1[Trial Division Method]
50
- H1 --> K1[Prime Factor Extraction]
51
- I1 --> L1[Recursive Factorization]
52
 
53
- J1 --> M1[Smallest Prime Factor Search]
54
- K1 --> N1[Factor Division Operation]
55
- L1 --> O1[Remaining Number Processing]
56
 
57
- M1 --> P1[Prime Factor Found]
58
- N1 --> Q1[Quotient Calculation]
59
- O1 --> R1[Recursive Factor Search]
60
 
61
- P1 --> S1[Factor Storage]
62
- Q1 --> T1[Remaining Number Update]
63
- R1 --> U1[Factorization Continuation]
64
 
65
- S1 --> V1[Prime Factorization Complete]
66
- T1 --> W1[Next Factor Search]
67
- U1 --> X1[All Factors Identified]
68
 
69
- V1 --> Y1[Prime Factorization Result]
70
- W1 --> Z1[Factorization Validation]
71
- X1 --> AA1[Result Verification]
72
 
73
- Y1 --> BB1[Prime Factorization Output]
74
- Z1 --> CC1[Factorization Completeness Check]
75
- AA1 --> DD1[Final Result Validation]
76
 
77
- BB1 --> EE1[Prime Factorization Display]
78
- CC1 --> FF1[Factorization Documentation]
79
- DD1 --> GG1[Result Confirmation]
80
 
81
  style A1 fill:#ff6b6b,color:#fff
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  style C1 fill:#ff6b6b,color:#fff
@@ -105,13 +183,6 @@ graph TD
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  style X1 fill:#ffd43b,color:#000
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  style Y1 fill:#ffd43b,color:#000
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  style Z1 fill:#ffd43b,color:#000
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- style AA1 fill:#ffd43b,color:#000
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- style BB1 fill:#ffd43b,color:#000
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- style CC1 fill:#ffd43b,color:#000
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- style DD1 fill:#ffd43b,color:#000
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- style EE1 fill:#ffd43b,color:#000
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- style FF1 fill:#ffd43b,color:#000
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- style GG1 fill:#ffd43b,color:#000
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  style M1 fill:#51cf66,color:#fff
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  style N1 fill:#51cf66,color:#fff
@@ -127,90 +198,68 @@ graph TD
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  style X1 fill:#51cf66,color:#fff
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  style Y1 fill:#51cf66,color:#fff
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  style Z1 fill:#51cf66,color:#fff
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- style AA1 fill:#51cf66,color:#fff
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- style BB1 fill:#51cf66,color:#fff
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- style CC1 fill:#51cf66,color:#fff
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- style DD1 fill:#51cf66,color:#fff
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- style EE1 fill:#51cf66,color:#fff
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- style FF1 fill:#51cf66,color:#fff
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- style GG1 fill:#51cf66,color:#fff
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-
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- style BB1 fill:#b197fc,color:#fff
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- style CC1 fill:#b197fc,color:#fff
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- style DD1 fill:#b197fc,color:#fff
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- style EE1 fill:#b197fc,color:#fff
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- style FF1 fill:#b197fc,color:#fff
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- style GG1 fill:#b197fc,color:#fff
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  </div>
145
-
146
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
147
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
148
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
149
- </div>
150
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
151
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Number Theory Methods
152
- </div>
153
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
154
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Factorization Operations
155
- </div>
156
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
157
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
160
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
161
- </div>
162
  </div>
163
-
164
- <div class="figure-caption">
165
- <strong>Figure 1.</strong> Prime Factorization Algorithm Process. This number theory process visualization demonstrates systematic decomposition of composite numbers into prime factors. The flowchart shows composite number inputs, number theory methods and algorithms, factorization operations, intermediate calculations, and final prime factorization results.
166
  </div>
 
 
 
 
 
 
 
 
 
 
167
  </div>
168
- </section>
169
 
170
- <section class="process">
171
- <h2>2. Modular Arithmetic Operations Process</h2>
172
- <div class="figure">
173
- <div class="mermaid">
174
  graph TD
175
- A2[Integer Inputs a b] --> B2[Modulus Selection]
176
- C2[Modular Operation Type] --> D2[Operation Classification]
177
- E2[Modular Arithmetic Rules] --> F2[Rule Application Strategy]
178
-
179
- B2 --> G2[Modulus Validation]
180
- D2 --> H2[Addition Subtraction Multiplication Division]
181
- F2 --> I2[Modular Arithmetic Method]
182
-
183
- G2 --> J2[Modulus Processing]
184
- H2 --> K2[Operation Selection]
185
- I2 --> L2[Modular Calculation Method]
186
 
187
- J2 --> M2[Modular Addition]
188
- K2 --> N2[Modular Subtraction]
189
- L2 --> O2[Modular Multiplication]
190
 
191
- M2 --> P2[Sum Calculation]
192
- N2 --> Q2[Difference Calculation]
193
- O2 --> R2[Product Calculation]
194
 
195
- P2 --> S2[Modular Reduction]
196
- Q2 --> T2[Modular Reduction]
197
- R2 --> U2[Modular Reduction]
198
 
199
- S2 --> V2[Modular Division]
200
- T2 --> W2[Modular Inverse]
201
- U2 --> X2[Modular Exponentiation]
202
 
203
- V2 --> Y2[Quotient Calculation]
204
- W2 --> Z2[Inverse Calculation]
205
- X2 --> AA2[Power Calculation]
206
 
207
- Y2 --> BB2[Modular Division Result]
208
- Z2 --> CC2[Modular Inverse Result]
209
- AA2 --> DD2[Modular Power Result]
210
 
211
- BB2 --> EE2[Modular Arithmetic Output]
212
- CC2 --> FF2[Modular Arithmetic Output]
213
- DD2 --> GG2[Modular Arithmetic Output]
214
 
215
  style A2 fill:#ff6b6b,color:#fff
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  style C2 fill:#ff6b6b,color:#fff
@@ -239,13 +288,6 @@ graph TD
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  style X2 fill:#ffd43b,color:#000
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  style Y2 fill:#ffd43b,color:#000
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  style Z2 fill:#ffd43b,color:#000
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- style AA2 fill:#ffd43b,color:#000
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- style BB2 fill:#ffd43b,color:#000
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- style CC2 fill:#ffd43b,color:#000
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- style DD2 fill:#ffd43b,color:#000
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- style EE2 fill:#ffd43b,color:#000
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- style FF2 fill:#ffd43b,color:#000
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- style GG2 fill:#ffd43b,color:#000
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  style M2 fill:#51cf66,color:#fff
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  style N2 fill:#51cf66,color:#fff
@@ -261,83 +303,68 @@ graph TD
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  style X2 fill:#51cf66,color:#fff
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  style Y2 fill:#51cf66,color:#fff
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  style Z2 fill:#51cf66,color:#fff
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- style AA2 fill:#51cf66,color:#fff
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- style BB2 fill:#51cf66,color:#fff
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- style CC2 fill:#51cf66,color:#fff
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- style DD2 fill:#51cf66,color:#fff
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- style EE2 fill:#51cf66,color:#fff
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- style FF2 fill:#51cf66,color:#fff
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- style GG2 fill:#51cf66,color:#fff
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-
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- style EE2 fill:#b197fc,color:#fff
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- style FF2 fill:#b197fc,color:#fff
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- style GG2 fill:#b197fc,color:#fff
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  </div>
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-
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- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Modular Arithmetic Methods
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Modular Operations
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
292
- </div>
293
  </div>
294
-
295
- <div class="figure-caption">
296
- <strong>Figure 2.</strong> Modular Arithmetic Operations Process. This number theory process visualization demonstrates clock arithmetic and congruence calculations. The flowchart shows integer inputs and modulus selection, modular arithmetic methods and rules, modular operations and calculations, intermediate results, and final modular arithmetic outputs.
297
  </div>
 
 
 
 
 
 
 
298
  </div>
299
- </section>
300
 
301
- <section class="process">
302
- <h2>3. Diophantine Equation Solving Process</h2>
303
- <div class="figure">
304
- <div class="mermaid">
305
  graph TD
306
- A3[Diophantine Equation Input] --> B3[Equation Classification]
307
- C3[Solution Strategy Selection] --> D3[Method Identification]
308
- E3[Integer Solution Requirements] --> F3[Solution Existence Check]
309
 
310
- B3 --> G3[Linear Diophantine Equation]
311
  D3 --> H3[Extended Euclidean Algorithm]
312
- F3 --> I3[GCD Condition Check]
313
 
314
- G3 --> J3[Equation Standard Form]
315
- H3 --> K3[Bezout Identity Application]
316
- I3 --> L3[Solution Existence Validation]
317
 
318
- J3 --> M3[Coefficient Analysis]
319
- K3 --> N3[Particular Solution Finding]
320
- L3 --> O3[General Solution Construction]
321
 
322
- M3 --> P3[GCD Calculation]
323
- N3 --> O3
324
- O3 --> Q3[Parametric Solution Form]
325
 
326
- P3 --> R3[Solution Verification]
327
- Q3 --> S3[Parameter Range Determination]
328
- R3 --> T3[Integer Solution Validation]
329
 
330
- S3 --> U3[Solution Set Generation]
331
- T3 --> V3[Solution Completeness Check]
332
- U3 --> W3[All Integer Solutions]
333
 
334
- V3 --> X3[Solution Documentation]
335
- W3 --> Y3[Diophantine Solution Output]
336
- X3 --> Z3[Solution Verification Complete]
337
-
338
- Y3 --> AA3[Diophantine Equation Solution]
339
- Z3 --> BB3[Solution Set Validation]
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- AA3 --> CC3[Final Solution Display]
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342
  style A3 fill:#ff6b6b,color:#fff
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  style C3 fill:#ff6b6b,color:#fff
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  style X3 fill:#ffd43b,color:#000
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  style Y3 fill:#ffd43b,color:#000
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  style Z3 fill:#ffd43b,color:#000
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- style AA3 fill:#ffd43b,color:#000
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- style BB3 fill:#ffd43b,color:#000
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- style CC3 fill:#ffd43b,color:#000
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  style M3 fill:#51cf66,color:#fff
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  style N3 fill:#51cf66,color:#fff
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  style X3 fill:#51cf66,color:#fff
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  style Y3 fill:#51cf66,color:#fff
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  style Z3 fill:#51cf66,color:#fff
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- style AA3 fill:#51cf66,color:#fff
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- style BB3 fill:#51cf66,color:#fff
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- style CC3 fill:#51cf66,color:#fff
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- style AA3 fill:#b197fc,color:#fff
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- style BB3 fill:#b197fc,color:#fff
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- style CC3 fill:#b197fc,color:#fff
 
 
 
 
 
 
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  </div>
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-
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- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Diophantine Methods
402
- </div>
403
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Solution Operations
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
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- </div>
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- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
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- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
411
- </div>
412
  </div>
413
-
414
- <div class="figure-caption">
415
- <strong>Figure 3.</strong> Diophantine Equation Solving Process. This number theory process visualization demonstrates finding integer solutions to polynomial equations. The flowchart shows Diophantine equation inputs, solution strategy methods and algorithms, solution operations and calculations, intermediate results, and final integer solution sets.
416
  </div>
 
 
 
 
 
 
 
417
  </div>
418
- </section>
419
 
420
- <section class="navigation">
421
- <h2>Navigation</h2>
422
  <div class="nav-links">
423
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
424
  <a href="mathematics_batch_02.html" class="nav-link">Next: Analysis & Calculus →</a>
425
  <a href="index.html" class="nav-link">Programming Framework Home</a>
426
  </div>
427
- </section>
428
 
429
- <footer>
430
  <p><strong>Generated using the Programming Framework methodology</strong></p>
431
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
432
  <div class="contact-info">
@@ -437,7 +455,7 @@ graph TD
437
  <p>CUNY Graduate Center (New Media Lab)</p>
438
  <p>Email: [email protected]</p>
439
  </div>
440
- </footer>
441
  </div>
442
  </body>
443
  </html>
 
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  <meta charset="UTF-8" />
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  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 01 - Number Theory - Programming Framework Analysis</title>
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+ <style>
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+ body {
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+ font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
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+ margin: 0;
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+ background: #ffffff;
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+ color: #000000;
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+ line-height: 1.6;
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+ font-size: 12pt;
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+ }
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+ .container {
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+ max-width: 1000px;
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+ margin: 0 auto;
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+ padding: 1.5rem;
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+ }
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+ h1, h2, h3 {
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+ color: #000000;
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+ margin-top: 1.5rem;
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+ margin-bottom: 0.75rem;
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+ }
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+ h1 {
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+ font-size: 18pt;
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+ text-align: center;
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+ }
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+ h2 {
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+ font-size: 16pt;
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+ border-bottom: 2px solid #000;
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+ padding-bottom: 0.5rem;
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+ }
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+ h3 {
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+ font-size: 14pt;
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+ }
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+ p {
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+ margin-bottom: 1rem;
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+ text-align: justify;
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+ }
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+ .figure {
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+ margin: 2rem 0;
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+ text-align: center;
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+ border: 1px solid #ccc;
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+ padding: 1rem;
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+ background: #f9f9f9;
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+ }
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+ .figure-caption {
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+ margin-top: 1rem;
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+ font-style: italic;
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+ text-align: left;
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+ }
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+ .mermaid {
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+ background: white;
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+ padding: 1rem;
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+ border-radius: 4px;
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+ }
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+ .navigation {
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+ margin: 3rem 0;
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+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ }
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+ .nav-links {
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+ display: flex;
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+ flex-wrap: wrap;
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+ gap: 1rem;
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+ justify-content: center;
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+ }
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+ .nav-link {
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+ color: #007bff;
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+ text-decoration: none;
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+ padding: 0.5rem 1rem;
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+ border: 1px solid #007bff;
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+ border-radius: 4px;
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+ transition: all 0.3s ease;
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+ }
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+ .nav-link:hover {
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+ background: #007bff;
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+ color: white;
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+ }
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+ .footer {
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+ margin-top: 3rem;
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+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ text-align: center;
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+ }
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+ .contact-info {
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+ margin-top: 1rem;
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+ }
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+ .contact-info p {
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+ margin: 0.25rem 0;
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+ text-align: center;
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+ }
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+ </style>
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  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
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  <script>
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  mermaid.initialize({
 
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  nodeSpacing: 30,
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  rankSpacing: 30,
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  padding: 10
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+ },
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+ themeVariables: {
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+ fontFamily: 'Arial Unicode MS, Arial, sans-serif'
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  }
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  });
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  </script>
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  </head>
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  <body>
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  <div class="container">
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+ <h1>Mathematics Batch 01 - Number Theory - Programming Framework Analysis</h1>
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+
121
+ <p>This document presents number theory processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Prime Number Generation Process</h2>
124
+ <div class="figure">
125
+ <div class="mermaid">
 
 
 
 
 
 
126
  graph TD
127
+ A1[Range Definition] --> B1[Sieve Algorithm Selection]
128
+ C1[Upper Bound] --> D1[Memory Allocation]
129
+ E1[Optimization Strategy] --> F1[Algorithm Implementation]
 
 
 
 
 
 
 
 
130
 
131
+ B1 --> G1[Eratosthenes Sieve]
132
+ D1 --> H1[Boolean Array Creation]
133
+ F1 --> I1[Marking Strategy]
134
 
135
+ G1 --> J1[Initialize All True]
136
+ H1 --> K1[Array Size Calculation]
137
+ I1 --> L1[Prime Detection]
138
 
139
+ J1 --> M1[Mark 0 and 1 False]
140
+ K1 --> L1
141
+ L1 --> N1[Square Root Optimization]
142
 
143
+ M1 --> O1[Iterate from 2]
144
+ N1 --> P1[Stop at Square Root]
145
+ O1 --> Q1[Prime Number Process]
146
 
147
+ P1 --> R1[Mark Multiples False]
148
+ Q1 --> S1[Collect Prime Numbers]
149
+ R1 --> T1[Prime Number Result]
150
 
151
+ S1 --> U1[Prime Number Validation]
152
+ T1 --> V1[Prime Number Count]
153
+ U1 --> W1[Prime Number Output]
154
 
155
+ V1 --> X1[Prime Number Analysis]
156
+ W1 --> Y1[Prime Number Final Result]
157
+ X1 --> Z1[Prime Number Analysis Complete]
158
 
159
  style A1 fill:#ff6b6b,color:#fff
160
  style C1 fill:#ff6b6b,color:#fff
 
183
  style X1 fill:#ffd43b,color:#000
184
  style Y1 fill:#ffd43b,color:#000
185
  style Z1 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
186
 
187
  style M1 fill:#51cf66,color:#fff
188
  style N1 fill:#51cf66,color:#fff
 
198
  style X1 fill:#51cf66,color:#fff
199
  style Y1 fill:#51cf66,color:#fff
200
  style Z1 fill:#51cf66,color:#fff
201
+
202
+ style Z1 fill:#b197fc,color:#fff
203
+ </div>
204
+
205
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
206
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
207
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
 
 
 
 
 
 
 
208
  </div>
209
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
210
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Number Theory Methods
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
211
  </div>
212
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
213
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Prime Operations
 
214
  </div>
215
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
216
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
217
+ </div>
218
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
219
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
220
+ </div>
221
+ </div>
222
+
223
+ <div class="figure-caption">
224
+ <strong>Figure 1.</strong> Prime Number Generation Process. This number theory process visualization demonstrates the Sieve of Eratosthenes algorithm. The flowchart shows range inputs and optimization strategies, number theory methods and sieve algorithms, prime operations and marking strategies, intermediate results, and final prime number outputs.
225
  </div>
226
+ </div>
227
 
228
+ <h2>2. Modular Arithmetic Process</h2>
229
+ <div class="figure">
230
+ <div class="mermaid">
 
231
  graph TD
232
+ A2[Integer a] --> B2[Modulus m]
233
+ C2[Operation Type] --> D2[Modular Arithmetic]
234
+ E2[Congruence Analysis] --> F2[Residue Calculation]
 
 
 
 
 
 
 
 
235
 
236
+ B2 --> G2[Modulo Operation]
237
+ D2 --> H2[Addition Modulo m]
238
+ F2 --> I2[Multiplication Modulo m]
239
 
240
+ G2 --> J2[Division Modulo m]
241
+ H2 --> K2[Subtraction Modulo m]
242
+ I2 --> L2[Exponentiation Modulo m]
243
 
244
+ J2 --> M2[Multiplicative Inverse]
245
+ K2 --> L2
246
+ L2 --> N2[Fermat Little Theorem]
247
 
248
+ M2 --> O2[Extended Euclidean Algorithm]
249
+ N2 --> P2[Euler Totient Function]
250
+ O2 --> Q2[Modular Arithmetic Process]
251
 
252
+ P2 --> R2[Chinese Remainder Theorem]
253
+ Q2 --> S2[Modular Arithmetic Validation]
254
+ R2 --> T2[Modular Arithmetic Result]
255
 
256
+ S2 --> U2[Modular Arithmetic Analysis]
257
+ T2 --> V2[Modular Arithmetic Parameters]
258
+ U2 --> W2[Modular Arithmetic Output]
259
 
260
+ V2 --> X2[Modular Arithmetic Analysis]
261
+ W2 --> Y2[Modular Arithmetic Final Result]
262
+ X2 --> Z2[Modular Arithmetic Analysis Complete]
263
 
264
  style A2 fill:#ff6b6b,color:#fff
265
  style C2 fill:#ff6b6b,color:#fff
 
288
  style X2 fill:#ffd43b,color:#000
289
  style Y2 fill:#ffd43b,color:#000
290
  style Z2 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
291
 
292
  style M2 fill:#51cf66,color:#fff
293
  style N2 fill:#51cf66,color:#fff
 
303
  style X2 fill:#51cf66,color:#fff
304
  style Y2 fill:#51cf66,color:#fff
305
  style Z2 fill:#51cf66,color:#fff
306
+
307
+ style Z2 fill:#b197fc,color:#fff
308
+ </div>
309
+
310
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
311
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
312
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
313
+ </div>
314
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
315
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Modular Methods
 
316
  </div>
317
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
318
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Modular Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
319
  </div>
320
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
321
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
322
  </div>
323
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
324
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
325
+ </div>
326
+ </div>
327
+
328
+ <div class="figure-caption">
329
+ <strong>Figure 2.</strong> Modular Arithmetic Process. This number theory process visualization demonstrates modular arithmetic operations and congruence analysis. The flowchart shows integer inputs and operation types, modular methods and arithmetic operations, modular operations and residue calculations, intermediate results, and final modular arithmetic outputs.
330
  </div>
331
+ </div>
332
 
333
+ <h2>3. Diophantine Equations Process</h2>
334
+ <div class="figure">
335
+ <div class="mermaid">
 
336
  graph TD
337
+ A3[Linear Equation] --> B3[Variable Analysis]
338
+ C3[Coefficient Analysis] --> D3[Solution Strategy]
339
+ E3[Integer Constraints] --> F3[Existence Check]
340
 
341
+ B3 --> G3[Two Variable Equation]
342
  D3 --> H3[Extended Euclidean Algorithm]
343
+ F3 --> I3[GCD Analysis]
344
 
345
+ G3 --> J3[General Solution]
346
+ H3 --> K3[Particular Solution]
347
+ I3 --> L3[Parametric Form]
348
 
349
+ J3 --> M3[Solution Verification]
350
+ K3 --> L3
351
+ L3 --> N3[Solution Validation]
352
 
353
+ M3 --> O3[Integer Solutions]
354
+ N3 --> P3[Solution Bounds]
355
+ O3 --> Q3[Diophantine Equations Process]
356
 
357
+ P3 --> R3[Solution Enumeration]
358
+ Q3 --> S3[Diophantine Equations Validation]
359
+ R3 --> T3[Diophantine Equations Result]
360
 
361
+ S3 --> U3[Diophantine Equations Analysis]
362
+ T3 --> V3[Diophantine Equations Parameters]
363
+ U3 --> W3[Diophantine Equations Output]
364
 
365
+ V3 --> X3[Diophantine Equations Analysis]
366
+ W3 --> Y3[Diophantine Equations Final Result]
367
+ X3 --> Z3[Diophantine Equations Analysis Complete]
 
 
 
 
368
 
369
  style A3 fill:#ff6b6b,color:#fff
370
  style C3 fill:#ff6b6b,color:#fff
 
393
  style X3 fill:#ffd43b,color:#000
394
  style Y3 fill:#ffd43b,color:#000
395
  style Z3 fill:#ffd43b,color:#000
 
 
 
396
 
397
  style M3 fill:#51cf66,color:#fff
398
  style N3 fill:#51cf66,color:#fff
 
408
  style X3 fill:#51cf66,color:#fff
409
  style Y3 fill:#51cf66,color:#fff
410
  style Z3 fill:#51cf66,color:#fff
 
 
 
411
 
412
+ style Z3 fill:#b197fc,color:#fff
413
+ </div>
414
+
415
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
416
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
417
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
418
+ </div>
419
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
420
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Diophantine Methods
421
  </div>
422
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
423
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Solution Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
424
  </div>
425
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
426
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
427
  </div>
428
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
429
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
430
+ </div>
431
+ </div>
432
+
433
+ <div class="figure-caption">
434
+ <strong>Figure 3.</strong> Diophantine Equations Process. This number theory process visualization demonstrates integer solution finding for linear equations. The flowchart shows equation inputs and coefficient analysis, Diophantine methods and solution strategies, solution operations and verification, intermediate results, and final Diophantine equation outputs.
435
  </div>
436
+ </div>
437
 
438
+ <div class="navigation">
439
+ <h3>Navigation</h3>
440
  <div class="nav-links">
441
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
442
  <a href="mathematics_batch_02.html" class="nav-link">Next: Analysis & Calculus →</a>
443
  <a href="index.html" class="nav-link">Programming Framework Home</a>
444
  </div>
445
+ </div>
446
 
447
+ <div class="footer">
448
  <p><strong>Generated using the Programming Framework methodology</strong></p>
449
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
450
  <div class="contact-info">
 
455
  <p>CUNY Graduate Center (New Media Lab)</p>
456
  <p>Email: [email protected]</p>
457
  </div>
458
+ </div>
459
  </div>
460
  </body>
461
  </html>
mathematics_batch_02.html CHANGED
@@ -4,7 +4,97 @@
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 02 - Analysis & Calculus - Programming Framework Analysis</title>
7
- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
9
  <script>
10
  mermaid.initialize({
@@ -17,70 +107,54 @@
17
  nodeSpacing: 30,
18
  rankSpacing: 30,
19
  padding: 10
 
 
 
20
  }
21
  });
22
  </script>
23
  </head>
24
  <body>
25
  <div class="container">
26
- <header>
27
- <h1>📊 Mathematics Batch 02 - Analysis & Calculus</h1>
28
- <p class="subtitle">Taylor Series Expansion, Differential Equations, and Optimization</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Analysis & Calculus Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to fundamental calculus and analysis operations. Each process shows the computational logic behind function approximation, differential equation solving, and optimization techniques.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Taylor Series Expansion Process</h2>
38
- <div class="figure">
39
- <div class="mermaid">
40
  graph TD
41
- A1[Function Input f of x] --> B1[Expansion Point Selection]
42
- C1[Order of Approximation] --> D1[Series Type Determination]
43
- E1[Convergence Analysis] --> F1[Radius of Convergence]
44
-
45
- B1 --> G1[Center Point a Selection]
46
- D1 --> H1[Taylor Series Formula]
47
- F1 --> I1[Convergence Testing]
48
-
49
- G1 --> J1[Function Evaluation at a]
50
- H1 --> K1[Derivative Calculation]
51
- I1 --> L1[Ratio Test Application]
52
-
53
- J1 --> M1[Zeroth Term Calculation]
54
- K1 --> N1[First Derivative f prime of a]
55
- L1 --> O1[Convergence Radius R]
56
 
57
- M1 --> P1[First Term f of a]
58
- N1 --> Q1[Second Derivative f double prime of a]
59
- O1 --> R1[Interval of Convergence]
60
 
61
- P1 --> S1[Linear Term x minus a]
62
- Q1 --> T1[Third Derivative f triple prime of a]
63
- R1 --> U1[Series Validity Check]
64
 
65
- S1 --> V1[Quadratic Term x minus a squared]
66
- T1 --> W1[Higher Order Derivatives]
67
- U1 --> X1[Truncation Error Estimation]
68
 
69
- V1 --> Y1[Cubic Term x minus a cubed]
70
- W1 --> Z1[Nth Derivative f nth of a]
71
- X1 --> AA1[Error Bound Calculation]
72
 
73
- Y1 --> BB1[Taylor Polynomial Construction]
74
- Z1 --> CC1[Factorial Division]
75
- AA1 --> DD1[Remainder Term R sub n]
76
 
77
- BB1 --> EE1[Series Summation]
78
- CC1 --> DD1
79
- DD1 --> FF1[Taylor Series Result]
80
 
81
- EE1 --> GG1[Taylor Series Approximation]
82
- FF1 --> HH1[Approximation Accuracy]
83
- GG1 --> II1[Function Approximation Output]
84
 
85
  style A1 fill:#ff6b6b,color:#fff
86
  style C1 fill:#ff6b6b,color:#fff
@@ -109,15 +183,6 @@ graph TD
109
  style X1 fill:#ffd43b,color:#000
110
  style Y1 fill:#ffd43b,color:#000
111
  style Z1 fill:#ffd43b,color:#000
112
- style AA1 fill:#ffd43b,color:#000
113
- style BB1 fill:#ffd43b,color:#000
114
- style CC1 fill:#ffd43b,color:#000
115
- style DD1 fill:#ffd43b,color:#000
116
- style EE1 fill:#ffd43b,color:#000
117
- style FF1 fill:#ffd43b,color:#000
118
- style GG1 fill:#ffd43b,color:#000
119
- style HH1 fill:#ffd43b,color:#000
120
- style II1 fill:#ffd43b,color:#000
121
 
122
  style M1 fill:#51cf66,color:#fff
123
  style N1 fill:#51cf66,color:#fff
@@ -133,91 +198,68 @@ graph TD
133
  style X1 fill:#51cf66,color:#fff
134
  style Y1 fill:#51cf66,color:#fff
135
  style Z1 fill:#51cf66,color:#fff
136
- style AA1 fill:#51cf66,color:#fff
137
- style BB1 fill:#51cf66,color:#fff
138
- style CC1 fill:#51cf66,color:#fff
139
- style DD1 fill:#51cf66,color:#fff
140
- style EE1 fill:#51cf66,color:#fff
141
- style FF1 fill:#51cf66,color:#fff
142
- style GG1 fill:#51cf66,color:#fff
143
- style HH1 fill:#51cf66,color:#fff
144
- style II1 fill:#51cf66,color:#fff
145
-
146
- style II1 fill:#b197fc,color:#fff
147
  </div>
148
-
149
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
150
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
151
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
152
- </div>
153
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
154
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Series Methods
155
- </div>
156
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
157
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Expansion Operations
158
- </div>
159
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
160
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
161
- </div>
162
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
163
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
164
- </div>
165
  </div>
166
-
167
- <div class="figure-caption">
168
- <strong>Figure 1.</strong> Taylor Series Expansion Process. This calculus process visualization demonstrates function approximation using polynomial series. The flowchart shows function inputs and expansion parameters, series methods and formulas, expansion operations and calculations, intermediate terms, and final function approximation results.
169
  </div>
 
 
 
 
 
 
 
170
  </div>
171
- </section>
172
 
173
- <section class="process">
174
- <h2>2. Differential Equation Solving Process</h2>
175
- <div class="figure">
176
- <div class="mermaid">
177
  graph TD
178
- A2[Differential Equation Input] --> B2[Equation Classification]
179
- C2[Solution Method Selection] --> D2[Method Identification]
180
- E2[Initial Conditions] --> F2[Boundary Conditions]
181
-
182
- B2 --> G2[First Order Linear]
183
- D2 --> H2[Separation of Variables]
184
- F2 --> I2[Initial Value Problem]
185
 
186
- G2 --> J2[Standard Form dy dx plus P of x y equals Q of x]
187
- H2 --> K2[Integrating Factor Method]
188
- I2 --> L2[Cauchy Problem Setup]
189
 
190
- J2 --> M2[Coefficient Analysis]
191
- K2 --> N2[Integrating Factor Calculation]
192
- L2 --> O2[Initial Condition Application]
193
 
194
- M2 --> P2[Integrating Factor mu of x]
195
- N2 --> Q2[Product Rule Application]
196
- O2 --> R2[Particular Solution Finding]
197
 
198
- P2 --> S2[Exponential Integration]
199
- Q2 --> T2[General Solution Form]
200
- R2 --> U2[Solution Verification]
201
 
202
- S2 --> V2[Integrating Factor Result]
203
- T2 --> W2[Arbitrary Constant C]
204
- U2 --> X2[Solution Validation]
205
 
206
- V2 --> Y2[Multiplication by Integrating Factor]
207
- W2 --> Z2[Initial Condition Substitution]
208
- X2 --> AA2[Solution Completeness Check]
209
 
210
- Y2 --> BB2[Left Side Simplification]
211
- Z2 --> CC2[Constant C Determination]
212
- AA2 --> DD2[Solution Documentation]
213
-
214
- BB2 --> EE2[Integration of Right Side]
215
- CC2 --> FF2[Particular Solution]
216
- DD2 --> GG2[Differential Equation Solution]
217
-
218
- EE2 --> HH2[General Solution]
219
- FF2 --> GG2
220
- GG2 --> II2[Final Solution Display]
221
 
222
  style A2 fill:#ff6b6b,color:#fff
223
  style C2 fill:#ff6b6b,color:#fff
@@ -246,15 +288,6 @@ graph TD
246
  style X2 fill:#ffd43b,color:#000
247
  style Y2 fill:#ffd43b,color:#000
248
  style Z2 fill:#ffd43b,color:#000
249
- style AA2 fill:#ffd43b,color:#000
250
- style BB2 fill:#ffd43b,color:#000
251
- style CC2 fill:#ffd43b,color:#000
252
- style DD2 fill:#ffd43b,color:#000
253
- style EE2 fill:#ffd43b,color:#000
254
- style FF2 fill:#ffd43b,color:#000
255
- style GG2 fill:#ffd43b,color:#000
256
- style HH2 fill:#ffd43b,color:#000
257
- style II2 fill:#ffd43b,color:#000
258
 
259
  style M2 fill:#51cf66,color:#fff
260
  style N2 fill:#51cf66,color:#fff
@@ -270,91 +303,68 @@ graph TD
270
  style X2 fill:#51cf66,color:#fff
271
  style Y2 fill:#51cf66,color:#fff
272
  style Z2 fill:#51cf66,color:#fff
273
- style AA2 fill:#51cf66,color:#fff
274
- style BB2 fill:#51cf66,color:#fff
275
- style CC2 fill:#51cf66,color:#fff
276
- style DD2 fill:#51cf66,color:#fff
277
- style EE2 fill:#51cf66,color:#fff
278
- style FF2 fill:#51cf66,color:#fff
279
- style GG2 fill:#51cf66,color:#fff
280
- style HH2 fill:#51cf66,color:#fff
281
- style II2 fill:#51cf66,color:#fff
282
-
283
- style II2 fill:#b197fc,color:#fff
 
 
284
  </div>
285
-
286
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
287
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
288
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
289
- </div>
290
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
291
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Differential Methods
292
- </div>
293
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
294
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Solution Operations
295
- </div>
296
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
297
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
298
- </div>
299
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
300
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
301
- </div>
302
  </div>
303
-
304
- <div class="figure-caption">
305
- <strong>Figure 2.</strong> Differential Equation Solving Process. This calculus process visualization demonstrates solving first-order linear differential equations. The flowchart shows differential equation inputs and conditions, solution methods and algorithms, solution operations and calculations, intermediate results, and final differential equation solutions.
306
  </div>
307
  </div>
308
- </section>
 
 
 
 
309
 
310
- <section class="process">
311
- <h2>3. Optimization Problems Process</h2>
312
- <div class="figure">
313
- <div class="mermaid">
314
  graph TD
315
- A3[Objective Function f of x] --> B3[Optimization Type]
316
- C3[Constraint Functions] --> D3[Constraint Analysis]
317
- E3[Domain Specification] --> F3[Feasible Region]
318
-
319
- B3 --> G3[Maximization Problem]
320
- D3 --> H3[Equality Constraints g of x equals 0]
321
- F3 --> I3[Inequality Constraints h of x less than or equal to 0]
322
-
323
- G3 --> J3[Minimization Problem]
324
- H3 --> K3[Lagrange Multiplier Method]
325
- I3 --> L3[Karush Kuhn Tucker Conditions]
326
 
327
- J3 --> M3[Critical Point Analysis]
328
- K3 --> N3[Lagrangian Function L]
329
- L3 --> O3[KKT Conditions Application]
330
 
331
- M3 --> P3[First Derivative Test]
332
- N3 --> Q3[Partial Derivatives]
333
- O3 --> R3[Stationary Point Finding]
334
 
335
- P3 --> S3[Second Derivative Test]
336
- Q3 --> T3[Gradient Vector nabla f]
337
- R3 --> U3[Hessian Matrix H]
338
 
339
- S3 --> V3[Concavity Convexity Analysis]
340
- T3 --> W3[Critical Point Identification]
341
- U3 --> X3[Eigenvalue Analysis]
342
 
343
- V3 --> Y3[Local Maximum Minimum]
344
- W3 --> Z3[Global Optimum Check]
345
- X3 --> AA3[Definiteness Test]
346
 
347
- Y3 --> BB3[Boundary Point Analysis]
348
- Z3 --> CC3[Feasible Region Search]
349
- AA3 --> DD3[Optimal Solution]
350
 
351
- BB3 --> EE3[Constraint Satisfaction]
352
- CC3 --> DD3
353
- DD3 --> FF3[Optimization Result]
354
-
355
- EE3 --> GG3[Optimal Value Calculation]
356
- FF3 --> HH3[Solution Verification]
357
- GG3 --> II3[Optimization Output]
358
 
359
  style A3 fill:#ff6b6b,color:#fff
360
  style C3 fill:#ff6b6b,color:#fff
@@ -383,15 +393,6 @@ graph TD
383
  style X3 fill:#ffd43b,color:#000
384
  style Y3 fill:#ffd43b,color:#000
385
  style Z3 fill:#ffd43b,color:#000
386
- style AA3 fill:#ffd43b,color:#000
387
- style BB3 fill:#ffd43b,color:#000
388
- style CC3 fill:#ffd43b,color:#000
389
- style DD3 fill:#ffd43b,color:#000
390
- style EE3 fill:#ffd43b,color:#000
391
- style FF3 fill:#ffd43b,color:#000
392
- style GG3 fill:#ffd43b,color:#000
393
- style HH3 fill:#ffd43b,color:#000
394
- style II3 fill:#ffd43b,color:#000
395
 
396
  style M3 fill:#51cf66,color:#fff
397
  style N3 fill:#51cf66,color:#fff
@@ -407,54 +408,44 @@ graph TD
407
  style X3 fill:#51cf66,color:#fff
408
  style Y3 fill:#51cf66,color:#fff
409
  style Z3 fill:#51cf66,color:#fff
410
- style AA3 fill:#51cf66,color:#fff
411
- style BB3 fill:#51cf66,color:#fff
412
- style CC3 fill:#51cf66,color:#fff
413
- style DD3 fill:#51cf66,color:#fff
414
- style EE3 fill:#51cf66,color:#fff
415
- style FF3 fill:#51cf66,color:#fff
416
- style GG3 fill:#51cf66,color:#fff
417
- style HH3 fill:#51cf66,color:#fff
418
- style II3 fill:#51cf66,color:#fff
419
-
420
- style II3 fill:#b197fc,color:#fff
421
  </div>
422
-
423
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
424
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
425
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
426
- </div>
427
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
428
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Optimization Methods
429
- </div>
430
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
431
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Optimization Operations
432
- </div>
433
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
434
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
435
- </div>
436
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
437
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
438
- </div>
439
  </div>
440
-
441
- <div class="figure-caption">
442
- <strong>Figure 3.</strong> Optimization Problems Process. This calculus process visualization demonstrates finding maxima and minima using calculus methods. The flowchart shows objective function inputs and constraints, optimization methods and algorithms, optimization operations and calculations, intermediate results, and final optimal solutions.
443
  </div>
 
 
 
 
 
 
 
 
 
 
444
  </div>
445
- </section>
446
 
447
- <section class="navigation">
448
- <h2>Navigation</h2>
449
  <div class="nav-links">
450
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
451
  <a href="mathematics_batch_01.html" class="nav-link">← Previous: Number Theory</a>
452
  <a href="mathematics_batch_03.html" class="nav-link">Next: Abstract Algebra →</a>
453
  <a href="index.html" class="nav-link">Programming Framework Home</a>
454
  </div>
455
- </section>
456
 
457
- <footer>
458
  <p><strong>Generated using the Programming Framework methodology</strong></p>
459
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
460
  <div class="contact-info">
@@ -465,7 +456,7 @@ graph TD
465
  <p>CUNY Graduate Center (New Media Lab)</p>
466
  <p>Email: [email protected]</p>
467
  </div>
468
- </footer>
469
  </div>
470
  </body>
471
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 02 - Analysis & Calculus - Programming Framework Analysis</title>
7
+ <style>
8
+ body {
9
+ font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
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+ margin: 0;
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+ background: #ffffff;
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+ color: #000000;
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+ line-height: 1.6;
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+ font-size: 12pt;
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+ }
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+ .container {
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+ max-width: 1000px;
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+ margin: 0 auto;
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+ padding: 1.5rem;
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+ }
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+ h1, h2, h3 {
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+ color: #000000;
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+ margin-top: 1.5rem;
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+ }
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+ h1 {
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+ font-size: 18pt;
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+ text-align: center;
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+ }
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+ h2 {
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+ font-size: 16pt;
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+ border-bottom: 2px solid #000;
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+ padding-bottom: 0.5rem;
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+ }
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+ h3 {
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+ font-size: 14pt;
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+ }
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+ p {
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+ margin-bottom: 1rem;
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+ text-align: justify;
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+ }
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+ .figure {
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+ margin: 2rem 0;
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+ text-align: center;
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+ border: 1px solid #ccc;
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+ padding: 1rem;
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+ background: #f9f9f9;
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+ }
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+ .figure-caption {
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+ margin-top: 1rem;
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+ font-style: italic;
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+ text-align: left;
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+ }
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+ .mermaid {
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+ background: white;
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+ padding: 1rem;
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+ border-radius: 4px;
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+ }
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+ .navigation {
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+ margin: 3rem 0;
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+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ }
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+ .nav-links {
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+ display: flex;
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+ flex-wrap: wrap;
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+ gap: 1rem;
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+ justify-content: center;
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+ }
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+ .nav-link {
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+ text-decoration: none;
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+ padding: 0.5rem 1rem;
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+ border: 1px solid #007bff;
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+ border-radius: 4px;
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+ transition: all 0.3s ease;
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+ }
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+ .nav-link:hover {
80
+ background: #007bff;
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+ color: white;
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+ }
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+ .footer {
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+ margin-top: 3rem;
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+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ text-align: center;
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+ }
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+ .contact-info {
91
+ margin-top: 1rem;
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+ }
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+ .contact-info p {
94
+ margin: 0.25rem 0;
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+ text-align: center;
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+ }
97
+ </style>
98
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
99
  <script>
100
  mermaid.initialize({
 
107
  nodeSpacing: 30,
108
  rankSpacing: 30,
109
  padding: 10
110
+ },
111
+ themeVariables: {
112
+ fontFamily: 'Arial Unicode MS, Arial, sans-serif'
113
  }
114
  });
115
  </script>
116
  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 02 - Analysis & Calculus - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents analysis and calculus processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Limit Calculation Process</h2>
124
+ <div class="figure">
125
+ <div class="mermaid">
 
 
 
 
 
 
126
  graph TD
127
+ A1[Function f of x] --> B1[Point of Interest]
128
+ C1[Approach Direction] --> D1[Limit Analysis]
129
+ E1[Indeterminate Forms] --> F1[L'Hopital Rule]
 
 
 
 
 
 
 
 
 
 
 
 
130
 
131
+ B1 --> G1[Direct Substitution]
132
+ D1 --> H1[Left Hand Limit]
133
+ F1 --> I1[Right Hand Limit]
134
 
135
+ G1 --> J1[Limit Evaluation]
136
+ H1 --> K1[Limit from Below]
137
+ I1 --> L1[Limit from Above]
138
 
139
+ J1 --> M1[Limit Exists Question]
140
+ K1 --> L1
141
+ L1 --> N1[Limit Comparison]
142
 
143
+ M1 --> O1[Limit Value]
144
+ N1 --> P1[One Sided Limits]
145
+ O1 --> Q1[Limit Calculation Process]
146
 
147
+ P1 --> R1[Limit Validation]
148
+ Q1 --> S1[Limit Verification]
149
+ R1 --> T1[Limit Calculation Result]
150
 
151
+ S1 --> U1[Limit Calculation Validation]
152
+ T1 --> V1[Limit Calculation Parameters]
153
+ U1 --> W1[Limit Calculation Output]
154
 
155
+ V1 --> X1[Limit Calculation Analysis]
156
+ W1 --> Y1[Limit Calculation Final Result]
157
+ X1 --> Z1[Limit Calculation Analysis Complete]
158
 
159
  style A1 fill:#ff6b6b,color:#fff
160
  style C1 fill:#ff6b6b,color:#fff
 
183
  style X1 fill:#ffd43b,color:#000
184
  style Y1 fill:#ffd43b,color:#000
185
  style Z1 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
 
 
186
 
187
  style M1 fill:#51cf66,color:#fff
188
  style N1 fill:#51cf66,color:#fff
 
198
  style X1 fill:#51cf66,color:#fff
199
  style Y1 fill:#51cf66,color:#fff
200
  style Z1 fill:#51cf66,color:#fff
201
+
202
+ style Z1 fill:#b197fc,color:#fff
203
+ </div>
204
+
205
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
206
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
207
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
208
+ </div>
209
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
210
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Limit Methods
 
211
  </div>
212
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
213
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Limit Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
214
  </div>
215
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
216
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
217
  </div>
218
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
219
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
220
+ </div>
221
+ </div>
222
+
223
+ <div class="figure-caption">
224
+ <strong>Figure 1.</strong> Limit Calculation Process. This analysis process visualization demonstrates limit evaluation and convergence analysis. The flowchart shows function inputs and approach directions, limit methods and evaluation strategies, limit operations and comparisons, intermediate results, and final limit calculation outputs.
225
  </div>
226
+ </div>
227
 
228
+ <h2>2. Derivative Calculation Process</h2>
229
+ <div class="figure">
230
+ <div class="mermaid">
 
231
  graph TD
232
+ A2[Function f of x] --> B2[Differentiation Method]
233
+ C2[Point of Evaluation] --> D2[Derivative Analysis]
234
+ E2[Chain Rule] --> F2[Product Rule]
 
 
 
 
235
 
236
+ B2 --> G2[Power Rule]
237
+ D2 --> H2[Quotient Rule]
238
+ F2 --> I2[Implicit Differentiation]
239
 
240
+ G2 --> J2[Constant Rule]
241
+ H2 --> K2[Trigonometric Derivatives]
242
+ I2 --> L2[Logarithmic Derivatives]
243
 
244
+ J2 --> M2[Sum Rule]
245
+ K2 --> L2
246
+ L2 --> N2[Exponential Derivatives]
247
 
248
+ M2 --> O2[Difference Rule]
249
+ N2 --> P2[Inverse Function Derivatives]
250
+ O2 --> Q2[Derivative Calculation Process]
251
 
252
+ P2 --> R2[Derivative Validation]
253
+ Q2 --> S2[Derivative Verification]
254
+ R2 --> T2[Derivative Calculation Result]
255
 
256
+ S2 --> U2[Derivative Calculation Validation]
257
+ T2 --> V2[Derivative Calculation Parameters]
258
+ U2 --> W2[Derivative Calculation Output]
259
 
260
+ V2 --> X2[Derivative Calculation Analysis]
261
+ W2 --> Y2[Derivative Calculation Final Result]
262
+ X2 --> Z2[Derivative Calculation Analysis Complete]
 
 
 
 
 
 
 
 
263
 
264
  style A2 fill:#ff6b6b,color:#fff
265
  style C2 fill:#ff6b6b,color:#fff
 
288
  style X2 fill:#ffd43b,color:#000
289
  style Y2 fill:#ffd43b,color:#000
290
  style Z2 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
 
 
291
 
292
  style M2 fill:#51cf66,color:#fff
293
  style N2 fill:#51cf66,color:#fff
 
303
  style X2 fill:#51cf66,color:#fff
304
  style Y2 fill:#51cf66,color:#fff
305
  style Z2 fill:#51cf66,color:#fff
306
+
307
+ style Z2 fill:#b197fc,color:#fff
308
+ </div>
309
+
310
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
311
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
312
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
313
+ </div>
314
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
315
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Differentiation Methods
316
+ </div>
317
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
318
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Derivative Operations
319
  </div>
320
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
321
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
322
  </div>
323
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
324
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
 
325
  </div>
326
  </div>
327
+
328
+ <div class="figure-caption">
329
+ <strong>Figure 2.</strong> Derivative Calculation Process. This analysis process visualization demonstrates differentiation techniques and rate of change analysis. The flowchart shows function inputs and differentiation methods, differentiation methods and rules, derivative operations and calculations, intermediate results, and final derivative calculation outputs.
330
+ </div>
331
+ </div>
332
 
333
+ <h2>3. Integral Calculation Process</h2>
334
+ <div class="figure">
335
+ <div class="mermaid">
 
336
  graph TD
337
+ A3[Function f of x] --> B3[Integration Method]
338
+ C3[Integration Limits] --> D3[Integral Analysis]
339
+ E3[Substitution Method] --> F3[Integration by Parts]
 
 
 
 
 
 
 
 
340
 
341
+ B3 --> G3[Power Rule Integration]
342
+ D3 --> H3[Trigonometric Integration]
343
+ F3 --> I3[Partial Fractions]
344
 
345
+ G3 --> J3[Exponential Integration]
346
+ H3 --> I3
347
+ I3 --> K3[Logarithmic Integration]
348
 
349
+ J3 --> L3[Definite Integral]
350
+ K3 --> M3[Indefinite Integral]
351
+ L3 --> N3[Area Calculation]
352
 
353
+ M3 --> O3[Antiderivative]
354
+ N3 --> P3[Fundamental Theorem]
355
+ O3 --> Q3[Integral Calculation Process]
356
 
357
+ P3 --> R3[Integral Validation]
358
+ Q3 --> S3[Integral Verification]
359
+ R3 --> T3[Integral Calculation Result]
360
 
361
+ S3 --> U3[Integral Calculation Validation]
362
+ T3 --> V3[Integral Calculation Parameters]
363
+ U3 --> W3[Integral Calculation Output]
364
 
365
+ V3 --> X3[Integral Calculation Analysis]
366
+ W3 --> Y3[Integral Calculation Final Result]
367
+ X3 --> Z3[Integral Calculation Analysis Complete]
 
 
 
 
368
 
369
  style A3 fill:#ff6b6b,color:#fff
370
  style C3 fill:#ff6b6b,color:#fff
 
393
  style X3 fill:#ffd43b,color:#000
394
  style Y3 fill:#ffd43b,color:#000
395
  style Z3 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
 
 
396
 
397
  style M3 fill:#51cf66,color:#fff
398
  style N3 fill:#51cf66,color:#fff
 
408
  style X3 fill:#51cf66,color:#fff
409
  style Y3 fill:#51cf66,color:#fff
410
  style Z3 fill:#51cf66,color:#fff
411
+
412
+ style Z3 fill:#b197fc,color:#fff
413
+ </div>
414
+
415
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
416
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
417
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
 
 
 
 
418
  </div>
419
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
420
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Integration Methods
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
421
  </div>
422
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
423
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Integral Operations
 
424
  </div>
425
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
426
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
427
+ </div>
428
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
429
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
430
+ </div>
431
+ </div>
432
+
433
+ <div class="figure-caption">
434
+ <strong>Figure 3.</strong> Integral Calculation Process. This analysis process visualization demonstrates integration techniques and area calculation. The flowchart shows function inputs and integration methods, integration methods and techniques, integral operations and calculations, intermediate results, and final integral calculation outputs.
435
  </div>
436
+ </div>
437
 
438
+ <div class="navigation">
439
+ <h3>Navigation</h3>
440
  <div class="nav-links">
441
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
442
  <a href="mathematics_batch_01.html" class="nav-link">← Previous: Number Theory</a>
443
  <a href="mathematics_batch_03.html" class="nav-link">Next: Abstract Algebra →</a>
444
  <a href="index.html" class="nav-link">Programming Framework Home</a>
445
  </div>
446
+ </div>
447
 
448
+ <div class="footer">
449
  <p><strong>Generated using the Programming Framework methodology</strong></p>
450
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
451
  <div class="contact-info">
 
456
  <p>CUNY Graduate Center (New Media Lab)</p>
457
  <p>Email: [email protected]</p>
458
  </div>
459
+ </div>
460
  </div>
461
  </body>
462
  </html>
mathematics_batch_03.html CHANGED
@@ -4,7 +4,97 @@
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 03 - Abstract Algebra - Programming Framework Analysis</title>
7
- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
9
  <script>
10
  mermaid.initialize({
@@ -17,70 +107,54 @@
17
  nodeSpacing: 30,
18
  rankSpacing: 30,
19
  padding: 10
 
 
 
20
  }
21
  });
22
  </script>
23
  </head>
24
  <body>
25
  <div class="container">
26
- <header>
27
- <h1>🔗 Mathematics Batch 03 - Abstract Algebra</h1>
28
- <p class="subtitle">Group Theory, Ring Theory, and Field Theory</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Abstract Algebra Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to fundamental abstract algebra operations. Each process shows the computational logic behind group properties, ring operations, and field extensions.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Group Theory Operations Process</h2>
38
- <div class="figure">
39
- <div class="mermaid">
40
  graph TD
41
- A1[Group Elements Set G] --> B1[Binary Operation Definition]
42
- C1[Group Axioms] --> D1[Axiom Verification]
43
- E1[Group Properties] --> F1[Property Analysis]
44
-
45
- B1 --> G1[Closure Property]
46
- D1 --> H1[Associativity Check]
47
- F1 --> I1[Identity Element]
48
-
49
- G1 --> J1[Operation Table Construction]
50
- H1 --> K1[Associative Law Verification]
51
- I1 --> L1[Identity Element e]
52
 
53
- J1 --> M1[Group Table Analysis]
54
- K1 --> N1[Triple Product Verification]
55
- L1 --> O1[Identity Property Check]
56
 
57
- M1 --> P1[Inverse Elements]
58
- N1 --> Q1[Associativity Confirmation]
59
- O1 --> R1[Inverse Element a inverse]
60
 
61
- P1 --> S1[Inverse Property Verification]
62
- Q1 --> T1[Group Structure Validation]
63
- R1 --> U1[Inverse Property Check]
64
 
65
- S1 --> V1[Subgroup Analysis]
66
- T1 --> W1[Group Order Determination]
67
- U1 --> X1[Group Homomorphism]
68
 
69
- V1 --> Y1[Subgroup Properties]
70
- W1 --> Z1[Group Classification]
71
- X1 --> AA1[Homomorphism Properties]
72
 
73
- Y1 --> BB1[Coset Analysis]
74
- Z1 --> CC1[Group Isomorphism]
75
- AA1 --> DD1[Kernel and Image]
76
 
77
- BB1 --> EE1[Lagrange Theorem]
78
- CC1 --> FF1[Group Structure Output]
79
- DD1 --> GG1[Group Theory Result]
80
-
81
- EE1 --> HH1[Group Theory Analysis]
82
- FF1 --> GG1
83
- GG1 --> II1[Group Theory Output]
84
 
85
  style A1 fill:#ff6b6b,color:#fff
86
  style C1 fill:#ff6b6b,color:#fff
@@ -109,15 +183,6 @@ graph TD
109
  style X1 fill:#ffd43b,color:#000
110
  style Y1 fill:#ffd43b,color:#000
111
  style Z1 fill:#ffd43b,color:#000
112
- style AA1 fill:#ffd43b,color:#000
113
- style BB1 fill:#ffd43b,color:#000
114
- style CC1 fill:#ffd43b,color:#000
115
- style DD1 fill:#ffd43b,color:#000
116
- style EE1 fill:#ffd43b,color:#000
117
- style FF1 fill:#ffd43b,color:#000
118
- style GG1 fill:#ffd43b,color:#000
119
- style HH1 fill:#ffd43b,color:#000
120
- style II1 fill:#ffd43b,color:#000
121
 
122
  style M1 fill:#51cf66,color:#fff
123
  style N1 fill:#51cf66,color:#fff
@@ -133,91 +198,68 @@ graph TD
133
  style X1 fill:#51cf66,color:#fff
134
  style Y1 fill:#51cf66,color:#fff
135
  style Z1 fill:#51cf66,color:#fff
136
- style AA1 fill:#51cf66,color:#fff
137
- style BB1 fill:#51cf66,color:#fff
138
- style CC1 fill:#51cf66,color:#fff
139
- style DD1 fill:#51cf66,color:#fff
140
- style EE1 fill:#51cf66,color:#fff
141
- style FF1 fill:#51cf66,color:#fff
142
- style GG1 fill:#51cf66,color:#fff
143
- style HH1 fill:#51cf66,color:#fff
144
- style II1 fill:#51cf66,color:#fff
145
-
146
- style II1 fill:#b197fc,color:#fff
147
  </div>
148
-
149
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
150
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
151
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
152
- </div>
153
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
154
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Group Theory Methods
155
- </div>
156
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
157
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Group Operations
158
- </div>
159
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
160
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
161
- </div>
162
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
163
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
164
- </div>
165
  </div>
166
-
167
- <div class="figure-caption">
168
- <strong>Figure 1.</strong> Group Theory Operations Process. This abstract algebra process visualization demonstrates group properties and operations. The flowchart shows group elements and axioms, group theory methods and algorithms, group operations and verifications, intermediate results, and final group theory analysis.
169
  </div>
 
 
 
 
 
 
 
 
 
 
170
  </div>
171
- </section>
172
 
173
- <section class="process">
174
- <h2>2. Ring Theory Processes</h2>
175
- <div class="figure">
176
- <div class="mermaid">
177
  graph TD
178
- A2[Ring Elements Set R] --> B2[Ring Operations Definition]
179
- C2[Ring Axioms] --> D2[Axiom Verification]
180
- E2[Ring Properties] --> F2[Property Analysis]
181
-
182
- B2 --> G2[Addition Operation]
183
- D2 --> H2[Additive Group Properties]
184
- F2 --> I2[Multiplication Operation]
185
-
186
- G2 --> J2[Additive Identity Zero]
187
- H2 --> K2[Additive Inverses]
188
- I2 --> L2[Multiplicative Identity One]
189
-
190
- J2 --> M2[Additive Commutativity]
191
- K2 --> N2[Additive Associativity]
192
- L2 --> O2[Multiplicative Associativity]
193
 
194
- M2 --> P2[Distributive Laws]
195
- N2 --> Q2[Additive Group Structure]
196
- O2 --> R2[Multiplicative Semigroup]
197
 
198
- P2 --> S2[Left Distributivity]
199
- Q2 --> T2[Right Distributivity]
200
- R2 --> U2[Ring Structure Validation]
201
 
202
- S2 --> V2[Ideal Analysis]
203
- T2 --> W2[Subring Properties]
204
- U2 --> X2[Ring Homomorphism]
205
 
206
- V2 --> Y2[Principal Ideals]
207
- W2 --> Z2[Ring Classification]
208
- X2 --> AA2[Homomorphism Properties]
209
 
210
- Y2 --> BB2[Factor Ring Construction]
211
- Z2 --> CC2[Ring Isomorphism]
212
- AA2 --> DD2[Kernel and Image]
213
 
214
- BB2 --> EE2[Quotient Ring]
215
- CC2 --> FF2[Ring Structure Output]
216
- DD2 --> GG2[Ring Theory Result]
217
 
218
- EE2 --> HH2[Ring Theory Analysis]
219
- FF2 --> GG2
220
- GG2 --> II2[Ring Theory Output]
221
 
222
  style A2 fill:#ff6b6b,color:#fff
223
  style C2 fill:#ff6b6b,color:#fff
@@ -246,15 +288,6 @@ graph TD
246
  style X2 fill:#ffd43b,color:#000
247
  style Y2 fill:#ffd43b,color:#000
248
  style Z2 fill:#ffd43b,color:#000
249
- style AA2 fill:#ffd43b,color:#000
250
- style BB2 fill:#ffd43b,color:#000
251
- style CC2 fill:#ffd43b,color:#000
252
- style DD2 fill:#ffd43b,color:#000
253
- style EE2 fill:#ffd43b,color:#000
254
- style FF2 fill:#ffd43b,color:#000
255
- style GG2 fill:#ffd43b,color:#000
256
- style HH2 fill:#ffd43b,color:#000
257
- style II2 fill:#ffd43b,color:#000
258
 
259
  style M2 fill:#51cf66,color:#fff
260
  style N2 fill:#51cf66,color:#fff
@@ -270,87 +303,68 @@ graph TD
270
  style X2 fill:#51cf66,color:#fff
271
  style Y2 fill:#51cf66,color:#fff
272
  style Z2 fill:#51cf66,color:#fff
273
- style AA2 fill:#51cf66,color:#fff
274
- style BB2 fill:#51cf66,color:#fff
275
- style CC2 fill:#51cf66,color:#fff
276
- style DD2 fill:#51cf66,color:#fff
277
- style EE2 fill:#51cf66,color:#fff
278
- style FF2 fill:#51cf66,color:#fff
279
- style GG2 fill:#51cf66,color:#fff
280
- style HH2 fill:#51cf66,color:#fff
281
- style II2 fill:#51cf66,color:#fff
282
-
283
- style II2 fill:#b197fc,color:#fff
284
  </div>
285
-
286
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
287
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
288
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
289
- </div>
290
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
291
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Ring Theory Methods
292
- </div>
293
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
294
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Ring Operations
295
- </div>
296
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
297
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
298
- </div>
299
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
300
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
301
- </div>
302
  </div>
303
-
304
- <div class="figure-caption">
305
- <strong>Figure 2.</strong> Ring Theory Processes. This abstract algebra process visualization demonstrates ring operations and properties. The flowchart shows ring elements and axioms, ring theory methods and algorithms, ring operations and verifications, intermediate results, and final ring theory analysis.
306
  </div>
 
 
 
 
 
 
 
307
  </div>
308
- </section>
309
 
310
- <section class="process">
311
- <h2>3. Field Theory Extensions Process</h2>
312
- <div class="figure">
313
- <div class="mermaid">
314
  graph TD
315
- A3[Base Field F] --> B3[Field Extension Definition]
316
- C3[Extension Elements] --> D3[Extension Degree]
317
- E3[Field Properties] --> F3[Property Analysis]
318
-
319
- B3 --> G3[Extension Field E]
320
- D3 --> H3[Degree of Extension]
321
- F3 --> I3[Algebraic Elements]
322
 
323
- G3 --> J3[Field Extension E over F]
324
- H3 --> K3[Finite Extension]
325
- I3 --> L3[Transcendental Elements]
326
 
327
- J3 --> M3[Minimal Polynomial]
328
- K3 --> N3[Extension Basis]
329
- L3 --> O3[Algebraic Closure]
330
 
331
- M3 --> P3[Irreducible Polynomial]
332
- N3 --> O3
333
- O3 --> Q3[Field Automorphism]
334
 
335
- P3 --> R3[Root Adjoining]
336
- Q3 --> S3[Galois Group]
337
- R3 --> T3[Simple Extension]
338
 
339
- S3 --> U3[Galois Theory]
340
- T3 --> V3[Primitive Element]
341
- U3 --> W3[Galois Extension]
342
 
343
- V3 --> X3[Primitive Element Theorem]
344
- W3 --> Y3[Galois Correspondence]
345
- X3 --> Z3[Field Extension Result]
346
 
347
- Y3 --> AA3[Galois Theory Analysis]
348
- Z3 --> BB3[Field Extension Output]
349
- AA3 --> CC3[Field Theory Result]
350
-
351
- BB3 --> DD3[Field Theory Analysis]
352
- CC3 --> EE3[Field Theory Output]
353
- DD3 --> FF3[Field Theory Final Result]
354
 
355
  style A3 fill:#ff6b6b,color:#fff
356
  style C3 fill:#ff6b6b,color:#fff
@@ -379,12 +393,6 @@ graph TD
379
  style X3 fill:#ffd43b,color:#000
380
  style Y3 fill:#ffd43b,color:#000
381
  style Z3 fill:#ffd43b,color:#000
382
- style AA3 fill:#ffd43b,color:#000
383
- style BB3 fill:#ffd43b,color:#000
384
- style CC3 fill:#ffd43b,color:#000
385
- style DD3 fill:#ffd43b,color:#000
386
- style EE3 fill:#ffd43b,color:#000
387
- style FF3 fill:#ffd43b,color:#000
388
 
389
  style M3 fill:#51cf66,color:#fff
390
  style N3 fill:#51cf66,color:#fff
@@ -400,51 +408,44 @@ graph TD
400
  style X3 fill:#51cf66,color:#fff
401
  style Y3 fill:#51cf66,color:#fff
402
  style Z3 fill:#51cf66,color:#fff
403
- style AA3 fill:#51cf66,color:#fff
404
- style BB3 fill:#51cf66,color:#fff
405
- style CC3 fill:#51cf66,color:#fff
406
- style DD3 fill:#51cf66,color:#fff
407
- style EE3 fill:#51cf66,color:#fff
408
- style FF3 fill:#51cf66,color:#fff
409
-
410
- style FF3 fill:#b197fc,color:#fff
411
  </div>
412
-
413
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
414
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
415
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
416
- </div>
417
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
418
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Field Theory Methods
419
- </div>
420
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
421
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Extension Operations
422
- </div>
423
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
424
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
425
- </div>
426
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
427
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
428
- </div>
429
  </div>
430
-
431
- <div class="figure-caption">
432
- <strong>Figure 3.</strong> Field Theory Extensions Process. This abstract algebra process visualization demonstrates field extensions and Galois theory. The flowchart shows base field and extension elements, field theory methods and algorithms, extension operations and calculations, intermediate results, and final field theory analysis.
433
  </div>
 
 
 
 
 
 
 
 
 
 
434
  </div>
435
- </section>
436
 
437
- <section class="navigation">
438
- <h2>Navigation</h2>
439
  <div class="nav-links">
440
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
441
  <a href="mathematics_batch_02.html" class="nav-link">← Previous: Analysis & Calculus</a>
442
  <a href="mathematics_batch_04.html" class="nav-link">Next: Geometry & Topology →</a>
443
  <a href="index.html" class="nav-link">Programming Framework Home</a>
444
  </div>
445
- </section>
446
 
447
- <footer>
448
  <p><strong>Generated using the Programming Framework methodology</strong></p>
449
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
450
  <div class="contact-info">
@@ -455,7 +456,7 @@ graph TD
455
  <p>CUNY Graduate Center (New Media Lab)</p>
456
  <p>Email: [email protected]</p>
457
  </div>
458
- </footer>
459
  </div>
460
  </body>
461
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 03 - Abstract Algebra - Programming Framework Analysis</title>
7
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+ margin: 2rem 0;
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+ text-align: center;
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+ border: 1px solid #ccc;
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+ .contact-info {
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+ }
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+ .contact-info p {
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+ margin: 0.25rem 0;
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+ text-align: center;
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+ }
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+ </style>
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  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
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  <script>
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  mermaid.initialize({
 
107
  nodeSpacing: 30,
108
  rankSpacing: 30,
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  padding: 10
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+ },
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+ themeVariables: {
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+ fontFamily: 'Arial Unicode MS, Arial, sans-serif'
113
  }
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  });
115
  </script>
116
  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 03 - Abstract Algebra - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents abstract algebra processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Group Theory Process</h2>
124
+ <div class="figure">
125
+ <div class="mermaid">
 
 
 
 
 
 
126
  graph TD
127
+ A1[Set G] --> B1[Binary Operation]
128
+ C1[Group Axioms] --> D1[Closure Property]
129
+ E1[Associativity] --> F1[Identity Element]
 
 
 
 
 
 
 
 
130
 
131
+ B1 --> G1[Inverse Elements]
132
+ D1 --> H1[Group Verification]
133
+ F1 --> I1[Group Structure]
134
 
135
+ G1 --> J1[Subgroup Analysis]
136
+ H1 --> K1[Order of Group]
137
+ I1 --> L1[Group Properties]
138
 
139
+ J1 --> M1[Cyclic Groups]
140
+ K1 --> L1
141
+ L1 --> N1[Abelian Groups]
142
 
143
+ M1 --> O1[Group Homomorphisms]
144
+ N1 --> P1[Group Isomorphisms]
145
+ O1 --> Q1[Group Theory Process]
146
 
147
+ P1 --> R1[Group Theory Validation]
148
+ Q1 --> S1[Group Theory Verification]
149
+ R1 --> T1[Group Theory Result]
150
 
151
+ S1 --> U1[Group Theory Analysis]
152
+ T1 --> V1[Group Theory Parameters]
153
+ U1 --> W1[Group Theory Output]
154
 
155
+ V1 --> X1[Group Theory Analysis]
156
+ W1 --> Y1[Group Theory Final Result]
157
+ X1 --> Z1[Group Theory Analysis Complete]
 
 
 
 
158
 
159
  style A1 fill:#ff6b6b,color:#fff
160
  style C1 fill:#ff6b6b,color:#fff
 
183
  style X1 fill:#ffd43b,color:#000
184
  style Y1 fill:#ffd43b,color:#000
185
  style Z1 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
 
 
186
 
187
  style M1 fill:#51cf66,color:#fff
188
  style N1 fill:#51cf66,color:#fff
 
198
  style X1 fill:#51cf66,color:#fff
199
  style Y1 fill:#51cf66,color:#fff
200
  style Z1 fill:#51cf66,color:#fff
201
+
202
+ style Z1 fill:#b197fc,color:#fff
203
+ </div>
204
+
205
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
206
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
207
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
 
 
 
 
208
  </div>
209
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
210
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Group Methods
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
211
  </div>
212
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
213
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Group Operations
 
214
  </div>
215
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
216
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
217
+ </div>
218
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
219
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
220
+ </div>
221
+ </div>
222
+
223
+ <div class="figure-caption">
224
+ <strong>Figure 1.</strong> Group Theory Process. This abstract algebra process visualization demonstrates group structure analysis and verification. The flowchart shows set inputs and binary operations, group methods and axioms, group operations and properties, intermediate results, and final group theory outputs.
225
  </div>
226
+ </div>
227
 
228
+ <h2>2. Ring Theory Process</h2>
229
+ <div class="figure">
230
+ <div class="mermaid">
 
231
  graph TD
232
+ A2[Set R] --> B2[Two Binary Operations]
233
+ C2[Ring Axioms] --> D2[Additive Group]
234
+ E2[Multiplicative Semigroup] --> F2[Distributive Laws]
 
 
 
 
 
 
 
 
 
 
 
 
235
 
236
+ B2 --> G2[Ring Verification]
237
+ D2 --> H2[Commutative Ring]
238
+ F2 --> I2[Ring with Unity]
239
 
240
+ G2 --> J2[Integral Domain]
241
+ H2 --> K2[Field Analysis]
242
+ I2 --> L2[Division Ring]
243
 
244
+ J2 --> M2[Ring Homomorphisms]
245
+ K2 --> L2
246
+ L2 --> N2[Ring Isomorphisms]
247
 
248
+ M2 --> O2[Ideals Analysis]
249
+ N2 --> P2[Quotient Rings]
250
+ O2 --> Q2[Ring Theory Process]
251
 
252
+ P2 --> R2[Ring Theory Validation]
253
+ Q2 --> S2[Ring Theory Verification]
254
+ R2 --> T2[Ring Theory Result]
255
 
256
+ S2 --> U2[Ring Theory Analysis]
257
+ T2 --> V2[Ring Theory Parameters]
258
+ U2 --> W2[Ring Theory Output]
259
 
260
+ V2 --> X2[Ring Theory Analysis]
261
+ W2 --> Y2[Ring Theory Final Result]
262
+ X2 --> Z2[Ring Theory Analysis Complete]
263
 
264
  style A2 fill:#ff6b6b,color:#fff
265
  style C2 fill:#ff6b6b,color:#fff
 
288
  style X2 fill:#ffd43b,color:#000
289
  style Y2 fill:#ffd43b,color:#000
290
  style Z2 fill:#ffd43b,color:#000
 
 
 
 
 
 
 
 
 
291
 
292
  style M2 fill:#51cf66,color:#fff
293
  style N2 fill:#51cf66,color:#fff
 
303
  style X2 fill:#51cf66,color:#fff
304
  style Y2 fill:#51cf66,color:#fff
305
  style Z2 fill:#51cf66,color:#fff
306
+
307
+ style Z2 fill:#b197fc,color:#fff
308
+ </div>
309
+
310
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
311
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
312
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
313
+ </div>
314
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
315
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Ring Methods
 
316
  </div>
317
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
318
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Ring Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
319
  </div>
320
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
321
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
322
  </div>
323
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
324
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
325
+ </div>
326
+ </div>
327
+
328
+ <div class="figure-caption">
329
+ <strong>Figure 2.</strong> Ring Theory Process. This abstract algebra process visualization demonstrates ring structure analysis and verification. The flowchart shows set inputs and binary operations, ring methods and axioms, ring operations and properties, intermediate results, and final ring theory outputs.
330
  </div>
331
+ </div>
332
 
333
+ <h2>3. Field Theory Process</h2>
334
+ <div class="figure">
335
+ <div class="mermaid">
 
336
  graph TD
337
+ A3[Set F] --> B3[Field Axioms]
338
+ C3[Additive Group] --> D3[Multiplicative Group]
339
+ E3[Distributive Laws] --> F3[Field Verification]
 
 
 
 
340
 
341
+ B3 --> G3[Commutative Field]
342
+ D3 --> H3[Field Extensions]
343
+ F3 --> I3[Algebraic Extensions]
344
 
345
+ G3 --> J3[Transcendental Extensions]
346
+ H3 --> K3[Finite Fields]
347
+ I3 --> L3[Galois Theory]
348
 
349
+ J3 --> M3[Field Homomorphisms]
350
+ K3 --> L3
351
+ L3 --> N3[Field Isomorphisms]
352
 
353
+ M3 --> O3[Field Theory Analysis]
354
+ N3 --> P3[Field Theory Validation]
355
+ O3 --> Q3[Field Theory Process]
356
 
357
+ P3 --> R3[Field Theory Verification]
358
+ Q3 --> S3[Field Theory Result]
359
+ R3 --> T3[Field Theory Output]
360
 
361
+ S3 --> U3[Field Theory Analysis]
362
+ T3 --> V3[Field Theory Parameters]
363
+ U3 --> W3[Field Theory Final Result]
364
 
365
+ V3 --> X3[Field Theory Analysis]
366
+ W3 --> Y3[Field Theory Analysis Complete]
367
+ X3 --> Z3[Field Theory Analysis Complete]
 
 
 
 
368
 
369
  style A3 fill:#ff6b6b,color:#fff
370
  style C3 fill:#ff6b6b,color:#fff
 
393
  style X3 fill:#ffd43b,color:#000
394
  style Y3 fill:#ffd43b,color:#000
395
  style Z3 fill:#ffd43b,color:#000
 
 
 
 
 
 
396
 
397
  style M3 fill:#51cf66,color:#fff
398
  style N3 fill:#51cf66,color:#fff
 
408
  style X3 fill:#51cf66,color:#fff
409
  style Y3 fill:#51cf66,color:#fff
410
  style Z3 fill:#51cf66,color:#fff
411
+
412
+ style Z3 fill:#b197fc,color:#fff
413
+ </div>
414
+
415
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
416
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
417
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
 
418
  </div>
419
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
420
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Field Methods
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
421
  </div>
422
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
423
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Field Operations
 
424
  </div>
425
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
426
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
427
+ </div>
428
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
429
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
430
+ </div>
431
+ </div>
432
+
433
+ <div class="figure-caption">
434
+ <strong>Figure 3.</strong> Field Theory Process. This abstract algebra process visualization demonstrates field structure analysis and verification. The flowchart shows set inputs and field axioms, field methods and properties, field operations and extensions, intermediate results, and final field theory outputs.
435
  </div>
436
+ </div>
437
 
438
+ <div class="navigation">
439
+ <h3>Navigation</h3>
440
  <div class="nav-links">
441
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
442
  <a href="mathematics_batch_02.html" class="nav-link">← Previous: Analysis & Calculus</a>
443
  <a href="mathematics_batch_04.html" class="nav-link">Next: Geometry & Topology →</a>
444
  <a href="index.html" class="nav-link">Programming Framework Home</a>
445
  </div>
446
+ </div>
447
 
448
+ <div class="footer">
449
  <p><strong>Generated using the Programming Framework methodology</strong></p>
450
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
451
  <div class="contact-info">
 
456
  <p>CUNY Graduate Center (New Media Lab)</p>
457
  <p>Email: [email protected]</p>
458
  </div>
459
+ </div>
460
  </div>
461
  </body>
462
  </html>
mathematics_batch_04.html CHANGED
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4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 04 - Geometry & Topology - Programming Framework Analysis</title>
7
- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
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  <script>
10
  mermaid.initialize({
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17
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18
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19
  padding: 10
 
 
 
20
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21
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22
  </script>
23
  </head>
24
  <body>
25
  <div class="container">
26
- <header>
27
- <h1>📐 Mathematics Batch 04 - Geometry & Topology</h1>
28
- <p class="subtitle">Geometric Constructions, Topological Transformations, and Manifold Analysis</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Geometry & Topology Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to geometric and topological operations. Each process shows the computational logic behind geometric constructions, topological transformations, and differential geometry.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Geometric Constructions Process</h2>
38
- <div class="figure">
39
- <div class="mermaid">
40
  graph TD
41
- A1[Geometric Problem Input] --> B1[Construction Tools Selection]
42
- C1[Euclidean Axioms] --> D1[Axiom Application]
43
- E1[Construction Strategy] --> F1[Method Selection]
44
-
45
- B1 --> G1[Compass and Straightedge]
46
- D1 --> H1[Postulate Application]
47
- F1 --> I1[Construction Algorithm]
48
 
49
- G1 --> J1[Point Construction]
50
- H1 --> K1[Line Construction]
51
- I1 --> L1[Circle Construction]
52
 
53
- J1 --> M1[Intersection Points]
54
- K1 --> N1[Parallel Lines]
55
- L1 --> O1[Tangent Circles]
56
 
57
- M1 --> P1[Perpendicular Bisector]
58
- N1 --> Q1[Angle Bisector]
59
- O1 --> R1[Circumscribed Circle]
60
 
61
- P1 --> S1[Inscribed Circle]
62
- Q1 --> T1[Geometric Locus]
63
- R1 --> U1[Geometric Construction]
64
 
65
- S1 --> V1[Construction Verification]
66
- T1 --> W1[Geometric Properties]
67
- U1 --> X1[Construction Result]
68
 
69
- V1 --> Y1[Geometric Proof]
70
- W1 --> Z1[Construction Analysis]
71
- X1 --> AA1[Geometric Output]
72
 
73
- Y1 --> BB1[Construction Validation]
74
- Z1 --> CC1[Geometric Result]
75
- AA1 --> DD1[Geometric Construction Output]
76
 
77
  style A1 fill:#ff6b6b,color:#fff
78
  style C1 fill:#ff6b6b,color:#fff
@@ -101,10 +183,6 @@ graph TD
101
  style X1 fill:#ffd43b,color:#000
102
  style Y1 fill:#ffd43b,color:#000
103
  style Z1 fill:#ffd43b,color:#000
104
- style AA1 fill:#ffd43b,color:#000
105
- style BB1 fill:#ffd43b,color:#000
106
- style CC1 fill:#ffd43b,color:#000
107
- style DD1 fill:#ffd43b,color:#000
108
 
109
  style M1 fill:#51cf66,color:#fff
110
  style N1 fill:#51cf66,color:#fff
@@ -120,78 +198,68 @@ graph TD
120
  style X1 fill:#51cf66,color:#fff
121
  style Y1 fill:#51cf66,color:#fff
122
  style Z1 fill:#51cf66,color:#fff
123
- style AA1 fill:#51cf66,color:#fff
124
- style BB1 fill:#51cf66,color:#fff
125
- style CC1 fill:#51cf66,color:#fff
126
- style DD1 fill:#51cf66,color:#fff
127
 
128
- style DD1 fill:#b197fc,color:#fff
 
 
 
 
 
 
 
 
129
  </div>
130
-
131
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
132
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
133
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
134
- </div>
135
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
136
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Geometric Methods
137
- </div>
138
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
139
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Construction Operations
140
- </div>
141
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
142
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
143
- </div>
144
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
145
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
146
- </div>
147
  </div>
148
-
149
- <div class="figure-caption">
150
- <strong>Figure 1.</strong> Geometric Constructions Process. This geometry process visualization demonstrates compass and straightedge constructions. The flowchart shows geometric problem inputs and axioms, geometric methods and algorithms, construction operations and verifications, intermediate results, and final geometric construction outputs.
151
  </div>
 
 
 
 
 
 
 
152
  </div>
153
- </section>
154
 
155
- <section class="process">
156
- <h2>2. Topological Transformations Process</h2>
157
- <div class="figure">
158
- <div class="mermaid">
159
  graph TD
160
- A2[Topological Space X] --> B2[Transformation Definition]
161
- C2[Homeomorphism Properties] --> D2[Property Verification]
162
- E2[Topological Invariants] --> F2[Invariant Analysis]
163
 
164
- B2 --> G2[Continuous Function f]
165
- D2 --> H2[Bijective Mapping]
166
- F2 --> I2[Topological Properties]
167
 
168
- G2 --> J2[Inverse Function f inverse]
169
- H2 --> K2[Homeomorphism Check]
170
- I2 --> L2[Connectedness]
171
 
172
- J2 --> M2[Continuity Verification]
173
- K2 --> N2[Topological Equivalence]
174
- L2 --> O2[Compactness]
175
 
176
- M2 --> P2[Open Set Preservation]
177
- N2 --> Q2[Topological Invariants]
178
- O2 --> R2[Hausdorff Property]
179
 
180
- P2 --> S2[Closed Set Preservation]
181
- Q2 --> T2[Euler Characteristic]
182
- R2 --> U2[Topological Classification]
183
 
184
- S2 --> V2[Neighborhood Preservation]
185
- T2 --> W2[Fundamental Group]
186
- U2 --> X2[Topological Result]
187
 
188
- V2 --> Y2[Topological Transformation]
189
- W2 --> Z2[Topological Analysis]
190
- X2 --> AA2[Topological Output]
191
-
192
- Y2 --> BB2[Transformation Validation]
193
- Z2 --> CC2[Topological Result]
194
- AA2 --> DD2[Topological Transformation Output]
195
 
196
  style A2 fill:#ff6b6b,color:#fff
197
  style C2 fill:#ff6b6b,color:#fff
@@ -220,10 +288,6 @@ graph TD
220
  style X2 fill:#ffd43b,color:#000
221
  style Y2 fill:#ffd43b,color:#000
222
  style Z2 fill:#ffd43b,color:#000
223
- style AA2 fill:#ffd43b,color:#000
224
- style BB2 fill:#ffd43b,color:#000
225
- style CC2 fill:#ffd43b,color:#000
226
- style DD2 fill:#ffd43b,color:#000
227
 
228
  style M2 fill:#51cf66,color:#fff
229
  style N2 fill:#51cf66,color:#fff
@@ -239,78 +303,68 @@ graph TD
239
  style X2 fill:#51cf66,color:#fff
240
  style Y2 fill:#51cf66,color:#fff
241
  style Z2 fill:#51cf66,color:#fff
242
- style AA2 fill:#51cf66,color:#fff
243
- style BB2 fill:#51cf66,color:#fff
244
- style CC2 fill:#51cf66,color:#fff
245
- style DD2 fill:#51cf66,color:#fff
246
 
247
- style DD2 fill:#b197fc,color:#fff
 
 
 
 
 
248
  </div>
249
-
250
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
251
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
252
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
253
- </div>
254
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
255
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Topological Methods
256
- </div>
257
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
258
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Transformation Operations
259
- </div>
260
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
261
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
262
- </div>
263
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
264
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
265
- </div>
266
  </div>
267
-
268
- <div class="figure-caption">
269
- <strong>Figure 2.</strong> Topological Transformations Process. This topology process visualization demonstrates homeomorphisms and topological invariants. The flowchart shows topological space inputs and properties, topological methods and algorithms, transformation operations and verifications, intermediate results, and final topological transformation outputs.
 
 
 
 
 
270
  </div>
271
  </div>
272
- </section>
 
 
 
 
273
 
274
- <section class="process">
275
- <h2>3. Manifold Analysis Process</h2>
276
- <div class="figure">
277
- <div class="mermaid">
278
  graph TD
279
- A3[Manifold M] --> B3[Differential Structure]
280
- C3[Tangent Space] --> D3[Vector Field Analysis]
281
- E3[Curvature Properties] --> F3[Curvature Calculation]
282
-
283
- B3 --> G3[Coordinate Charts]
284
- D3 --> H3[Tangent Bundle TM]
285
- F3 --> I3[Riemannian Metric]
286
 
287
- G3 --> J3[Atlas Construction]
288
- H3 --> K3[Vector Field X]
289
- I3 --> L3[Metric Tensor g]
290
 
291
- J3 --> M3[Transition Functions]
292
- K3 --> N3[Lie Bracket Operation]
293
- L3 --> O3[Christoffel Symbols]
294
 
295
- M3 --> P3[Manifold Structure]
296
- N3 --> O3
297
- O3 --> Q3[Riemann Curvature Tensor]
298
 
299
- P3 --> R3[Differential Forms]
300
- Q3 --> S3[Ricci Curvature]
301
- R3 --> T3[Exterior Derivative]
302
 
303
- S3 --> U3[Scalar Curvature]
304
- T3 --> V3[De Rham Cohomology]
305
- U3 --> W3[Manifold Classification]
306
 
307
- V3 --> X3[Manifold Analysis]
308
- W3 --> Y3[Manifold Result]
309
- X3 --> Z3[Manifold Output]
310
 
311
- Y3 --> AA3[Manifold Analysis Output]
312
- Z3 --> BB3[Manifold Analysis Final Result]
313
- AA3 --> CC3[Manifold Analysis Complete]
314
 
315
  style A3 fill:#ff6b6b,color:#fff
316
  style C3 fill:#ff6b6b,color:#fff
@@ -339,9 +393,6 @@ graph TD
339
  style X3 fill:#ffd43b,color:#000
340
  style Y3 fill:#ffd43b,color:#000
341
  style Z3 fill:#ffd43b,color:#000
342
- style AA3 fill:#ffd43b,color:#000
343
- style BB3 fill:#ffd43b,color:#000
344
- style CC3 fill:#ffd43b,color:#000
345
 
346
  style M3 fill:#51cf66,color:#fff
347
  style N3 fill:#51cf66,color:#fff
@@ -357,48 +408,44 @@ graph TD
357
  style X3 fill:#51cf66,color:#fff
358
  style Y3 fill:#51cf66,color:#fff
359
  style Z3 fill:#51cf66,color:#fff
360
- style AA3 fill:#51cf66,color:#fff
361
- style BB3 fill:#51cf66,color:#fff
362
- style CC3 fill:#51cf66,color:#fff
363
 
364
- style CC3 fill:#b197fc,color:#fff
 
 
 
 
 
 
 
 
365
  </div>
366
-
367
- <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
368
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
369
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
370
- </div>
371
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
372
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Manifold Methods
373
- </div>
374
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
375
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Analysis Operations
376
- </div>
377
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
378
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
379
- </div>
380
- <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
381
- <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
382
- </div>
383
  </div>
384
-
385
- <div class="figure-caption">
386
- <strong>Figure 3.</strong> Manifold Analysis Process. This differential geometry process visualization demonstrates manifold analysis and curvature calculations. The flowchart shows manifold inputs and differential structures, manifold methods and algorithms, analysis operations and calculations, intermediate results, and final manifold analysis outputs.
387
  </div>
 
 
 
 
 
 
 
388
  </div>
389
- </section>
390
 
391
- <section class="navigation">
392
- <h2>Navigation</h2>
393
  <div class="nav-links">
394
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
395
  <a href="mathematics_batch_03.html" class="nav-link">← Previous: Abstract Algebra</a>
396
  <a href="mathematics_batch_05.html" class="nav-link">Next: Applied Mathematics →</a>
397
  <a href="index.html" class="nav-link">Programming Framework Home</a>
398
  </div>
399
- </section>
400
 
401
- <footer>
402
  <p><strong>Generated using the Programming Framework methodology</strong></p>
403
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
404
  <div class="contact-info">
@@ -409,7 +456,7 @@ graph TD
409
  <p>CUNY Graduate Center (New Media Lab)</p>
410
  <p>Email: [email protected]</p>
411
  </div>
412
- </footer>
413
  </div>
414
  </body>
415
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 04 - Geometry & Topology - Programming Framework Analysis</title>
7
+ <style>
8
+ body {
9
+ font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
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+ margin: 0;
11
+ background: #ffffff;
12
+ color: #000000;
13
+ line-height: 1.6;
14
+ font-size: 12pt;
15
+ }
16
+ .container {
17
+ max-width: 1000px;
18
+ margin: 0 auto;
19
+ padding: 1.5rem;
20
+ }
21
+ h1, h2, h3 {
22
+ color: #000000;
23
+ margin-top: 1.5rem;
24
+ margin-bottom: 0.75rem;
25
+ }
26
+ h1 {
27
+ font-size: 18pt;
28
+ text-align: center;
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+ }
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+ h2 {
31
+ font-size: 16pt;
32
+ border-bottom: 2px solid #000;
33
+ padding-bottom: 0.5rem;
34
+ }
35
+ h3 {
36
+ font-size: 14pt;
37
+ }
38
+ p {
39
+ margin-bottom: 1rem;
40
+ text-align: justify;
41
+ }
42
+ .figure {
43
+ margin: 2rem 0;
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+ text-align: center;
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+ border: 1px solid #ccc;
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+ padding: 1rem;
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+ background: #f9f9f9;
48
+ }
49
+ .figure-caption {
50
+ margin-top: 1rem;
51
+ font-style: italic;
52
+ text-align: left;
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+ }
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+ .mermaid {
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+ background: white;
56
+ padding: 1rem;
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+ border-radius: 4px;
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+ }
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+ .navigation {
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+ margin: 3rem 0;
61
+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ }
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+ .nav-links {
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+ display: flex;
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+ flex-wrap: wrap;
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+ gap: 1rem;
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+ justify-content: center;
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+ }
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+ .nav-link {
72
+ color: #007bff;
73
+ text-decoration: none;
74
+ padding: 0.5rem 1rem;
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+ border: 1px solid #007bff;
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+ border-radius: 4px;
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+ transition: all 0.3s ease;
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+ .nav-link:hover {
80
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+ .footer {
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+ margin-top: 3rem;
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+ padding: 1rem;
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+ background: #f8f9fa;
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+ border-radius: 8px;
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+ text-align: center;
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+ }
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+ .contact-info {
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+ margin-top: 1rem;
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+ }
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+ .contact-info p {
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+ margin: 0.25rem 0;
95
+ text-align: center;
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+ }
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+ </style>
98
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
99
  <script>
100
  mermaid.initialize({
 
107
  nodeSpacing: 30,
108
  rankSpacing: 30,
109
  padding: 10
110
+ },
111
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112
+ fontFamily: 'Arial Unicode MS, Arial, sans-serif'
113
  }
114
  });
115
  </script>
116
  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 04 - Geometry & Topology - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents geometry and topology processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Euclidean Geometry Process</h2>
124
+ <div class="figure">
125
+ <div class="mermaid">
 
 
 
 
 
 
126
  graph TD
127
+ A1[Geometric Objects] --> B1[Euclidean Axioms]
128
+ C1[Point Line Plane] --> D1[Distance Measurement]
129
+ E1[Angle Measurement] --> F1[Geometric Constructions]
 
 
 
 
130
 
131
+ B1 --> G1[Parallel Postulate]
132
+ D1 --> H1[Pythagorean Theorem]
133
+ F1 --> I1[Circle Constructions]
134
 
135
+ G1 --> J1[Triangle Properties]
136
+ H1 --> K1[Area Calculations]
137
+ I1 --> L1[Geometric Proofs]
138
 
139
+ J1 --> M1[Congruence Theorems]
140
+ K1 --> L1
141
+ L1 --> N1[Similarity Theorems]
142
 
143
+ M1 --> O1[Geometric Transformations]
144
+ N1 --> P1[Coordinate Geometry]
145
+ O1 --> Q1[Euclidean Geometry Process]
146
 
147
+ P1 --> R1[Euclidean Geometry Validation]
148
+ Q1 --> S1[Euclidean Geometry Verification]
149
+ R1 --> T1[Euclidean Geometry Result]
150
 
151
+ S1 --> U1[Euclidean Geometry Analysis]
152
+ T1 --> V1[Euclidean Geometry Parameters]
153
+ U1 --> W1[Euclidean Geometry Output]
154
 
155
+ V1 --> X1[Euclidean Geometry Analysis]
156
+ W1 --> Y1[Euclidean Geometry Final Result]
157
+ X1 --> Z1[Euclidean Geometry Analysis Complete]
158
 
159
  style A1 fill:#ff6b6b,color:#fff
160
  style C1 fill:#ff6b6b,color:#fff
 
183
  style X1 fill:#ffd43b,color:#000
184
  style Y1 fill:#ffd43b,color:#000
185
  style Z1 fill:#ffd43b,color:#000
 
 
 
 
186
 
187
  style M1 fill:#51cf66,color:#fff
188
  style N1 fill:#51cf66,color:#fff
 
198
  style X1 fill:#51cf66,color:#fff
199
  style Y1 fill:#51cf66,color:#fff
200
  style Z1 fill:#51cf66,color:#fff
 
 
 
 
201
 
202
+ style Z1 fill:#b197fc,color:#fff
203
+ </div>
204
+
205
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
206
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
207
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
208
+ </div>
209
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
210
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Geometric Methods
211
  </div>
212
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
213
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Geometric Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
214
  </div>
215
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
216
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
217
  </div>
218
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
219
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
220
+ </div>
221
+ </div>
222
+
223
+ <div class="figure-caption">
224
+ <strong>Figure 1.</strong> Euclidean Geometry Process. This geometry process visualization demonstrates Euclidean geometric constructions and proofs. The flowchart shows geometric object inputs and axioms, geometric methods and theorems, geometric operations and constructions, intermediate results, and final Euclidean geometry outputs.
225
  </div>
226
+ </div>
227
 
228
+ <h2>2. Topology Process</h2>
229
+ <div class="figure">
230
+ <div class="mermaid">
 
231
  graph TD
232
+ A2[Topological Space] --> B2[Open Sets]
233
+ C2[Topology Definition] --> D2[Neighborhood Analysis]
234
+ E2[Continuity Analysis] --> F2[Homeomorphism]
235
 
236
+ B2 --> G2[Topology Verification]
237
+ D2 --> H2[Connectedness]
238
+ F2 --> I2[Compactness]
239
 
240
+ G2 --> J2[Separation Axioms]
241
+ H2 --> K2[Homotopy Theory]
242
+ I2 --> L2[Fundamental Group]
243
 
244
+ J2 --> M2[Topological Invariants]
245
+ K2 --> L2
246
+ L2 --> N2[Covering Spaces]
247
 
248
+ M2 --> O2[Topology Analysis]
249
+ N2 --> P2[Topology Validation]
250
+ O2 --> Q2[Topology Process]
251
 
252
+ P2 --> R2[Topology Verification]
253
+ Q2 --> S2[Topology Result]
254
+ R2 --> T2[Topology Output]
255
 
256
+ S2 --> U2[Topology Analysis]
257
+ T2 --> V2[Topology Parameters]
258
+ U2 --> W2[Topology Final Result]
259
 
260
+ V2 --> X2[Topology Analysis]
261
+ W2 --> Y2[Topology Analysis Complete]
262
+ X2 --> Z2[Topology Analysis Complete]
 
 
 
 
263
 
264
  style A2 fill:#ff6b6b,color:#fff
265
  style C2 fill:#ff6b6b,color:#fff
 
288
  style X2 fill:#ffd43b,color:#000
289
  style Y2 fill:#ffd43b,color:#000
290
  style Z2 fill:#ffd43b,color:#000
 
 
 
 
291
 
292
  style M2 fill:#51cf66,color:#fff
293
  style N2 fill:#51cf66,color:#fff
 
303
  style X2 fill:#51cf66,color:#fff
304
  style Y2 fill:#51cf66,color:#fff
305
  style Z2 fill:#51cf66,color:#fff
 
 
 
 
306
 
307
+ style Z2 fill:#b197fc,color:#fff
308
+ </div>
309
+
310
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
311
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
312
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
313
  </div>
314
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
315
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Topology Methods
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
316
  </div>
317
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
318
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Topology Operations
319
+ </div>
320
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
321
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
322
+ </div>
323
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
324
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
325
  </div>
326
  </div>
327
+
328
+ <div class="figure-caption">
329
+ <strong>Figure 2.</strong> Topology Process. This topology process visualization demonstrates topological space analysis and invariants. The flowchart shows topological space inputs and definitions, topology methods and properties, topology operations and analysis, intermediate results, and final topology outputs.
330
+ </div>
331
+ </div>
332
 
333
+ <h2>3. Differential Geometry Process</h2>
334
+ <div class="figure">
335
+ <div class="mermaid">
 
336
  graph TD
337
+ A3[Manifold] --> B3[Tangent Space]
338
+ C3[Metric Tensor] --> D3[Curvature Analysis]
339
+ E3[Geodesic Equations] --> F3[Parallel Transport]
 
 
 
 
340
 
341
+ B3 --> G3[Vector Fields]
342
+ D3 --> H3[Riemann Curvature]
343
+ F3 --> I3[Levi Civita Connection]
344
 
345
+ G3 --> J3[Lie Derivatives]
346
+ H3 --> K3[Ricci Curvature]
347
+ I3 --> L3[Scalar Curvature]
348
 
349
+ J3 --> M3[Differential Forms]
350
+ K3 --> L3
351
+ L3 --> N3[Exterior Derivatives]
352
 
353
+ M3 --> O3[Differential Geometry Analysis]
354
+ N3 --> P3[Differential Geometry Validation]
355
+ O3 --> Q3[Differential Geometry Process]
356
 
357
+ P3 --> R3[Differential Geometry Verification]
358
+ Q3 --> S3[Differential Geometry Result]
359
+ R3 --> T3[Differential Geometry Output]
360
 
361
+ S3 --> U3[Differential Geometry Analysis]
362
+ T3 --> V3[Differential Geometry Parameters]
363
+ U3 --> W3[Differential Geometry Final Result]
364
 
365
+ V3 --> X3[Differential Geometry Analysis]
366
+ W3 --> Y3[Differential Geometry Analysis Complete]
367
+ X3 --> Z3[Differential Geometry Analysis Complete]
368
 
369
  style A3 fill:#ff6b6b,color:#fff
370
  style C3 fill:#ff6b6b,color:#fff
 
393
  style X3 fill:#ffd43b,color:#000
394
  style Y3 fill:#ffd43b,color:#000
395
  style Z3 fill:#ffd43b,color:#000
 
 
 
396
 
397
  style M3 fill:#51cf66,color:#fff
398
  style N3 fill:#51cf66,color:#fff
 
408
  style X3 fill:#51cf66,color:#fff
409
  style Y3 fill:#51cf66,color:#fff
410
  style Z3 fill:#51cf66,color:#fff
 
 
 
411
 
412
+ style Z3 fill:#b197fc,color:#fff
413
+ </div>
414
+
415
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
416
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
417
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
418
+ </div>
419
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
420
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Differential Methods
421
  </div>
422
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
423
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Differential Operations
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
424
  </div>
425
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
426
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
 
427
  </div>
428
+ <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
429
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
430
+ </div>
431
+ </div>
432
+
433
+ <div class="figure-caption">
434
+ <strong>Figure 3.</strong> Differential Geometry Process. This differential geometry process visualization demonstrates manifold analysis and curvature calculations. The flowchart shows manifold inputs and metric tensors, differential methods and connections, differential operations and curvature analysis, intermediate results, and final differential geometry outputs.
435
  </div>
436
+ </div>
437
 
438
+ <div class="navigation">
439
+ <h3>Navigation</h3>
440
  <div class="nav-links">
441
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
442
  <a href="mathematics_batch_03.html" class="nav-link">← Previous: Abstract Algebra</a>
443
  <a href="mathematics_batch_05.html" class="nav-link">Next: Applied Mathematics →</a>
444
  <a href="index.html" class="nav-link">Programming Framework Home</a>
445
  </div>
446
+ </div>
447
 
448
+ <div class="footer">
449
  <p><strong>Generated using the Programming Framework methodology</strong></p>
450
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
451
  <div class="contact-info">
 
456
  <p>CUNY Graduate Center (New Media Lab)</p>
457
  <p>Email: [email protected]</p>
458
  </div>
459
+ </div>
460
  </div>
461
  </body>
462
  </html>
mathematics_batch_05.html CHANGED
@@ -4,7 +4,97 @@
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 05 - Applied Mathematics - Programming Framework Analysis</title>
7
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  }
21
  });
22
  </script>
23
  </head>
24
  <body>
25
  <div class="container">
26
- <header>
27
- <h1>⚙️ Mathematics Batch 05 - Applied Mathematics</h1>
28
- <p class="subtitle">Numerical Methods, Statistical Analysis, and Cryptographic Algorithms</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Applied Mathematics Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to practical mathematical operations. Each process shows the computational logic behind numerical methods, statistical analysis, and cryptographic algorithms.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Numerical Methods Process</h2>
38
  <div class="figure">
39
  <div class="mermaid">
40
  graph TD
@@ -150,10 +236,9 @@ graph TD
150
  <strong>Figure 1.</strong> Numerical Methods Process. This applied mathematics process visualization demonstrates root finding and integration methods. The flowchart shows numerical problem inputs and error analysis, numerical methods and algorithms, numerical operations and calculations, intermediate results, and final numerical solutions.
151
  </div>
152
  </div>
153
- </section>
154
 
155
- <section class="process">
156
- <h2>2. Statistical Analysis Process</h2>
157
  <div class="figure">
158
  <div class="mermaid">
159
  graph TD
@@ -267,10 +352,9 @@ graph TD
267
  <strong>Figure 2.</strong> Statistical Analysis Process. This applied mathematics process visualization demonstrates hypothesis testing and regression analysis. The flowchart shows data set inputs and hypothesis testing, statistical methods and algorithms, statistical operations and calculations, intermediate results, and final statistical analysis outputs.
268
  </div>
269
  </div>
270
- </section>
271
 
272
- <section class="process">
273
- <h2>3. Cryptographic Algorithms Process</h2>
274
  <div class="figure">
275
  <div class="mermaid">
276
  graph TD
@@ -384,19 +468,19 @@ graph TD
384
  <strong>Figure 3.</strong> Cryptographic Algorithms Process. This applied mathematics process visualization demonstrates RSA, elliptic curve cryptography, and hash functions. The flowchart shows plaintext inputs and key generation, cryptographic methods and algorithms, cryptographic operations and calculations, intermediate results, and final cryptographic analysis outputs.
385
  </div>
386
  </div>
387
- </section>
388
 
389
- <section class="navigation">
390
- <h2>Navigation</h2>
391
  <div class="nav-links">
392
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
393
  <a href="mathematics_batch_04.html" class="nav-link">← Previous: Geometry & Topology</a>
394
  <a href="mathematics_batch_06.html" class="nav-link">Next: Discrete Mathematics →</a>
395
  <a href="index.html" class="nav-link">Programming Framework Home</a>
396
  </div>
397
- </section>
398
 
399
- <footer>
400
  <p><strong>Generated using the Programming Framework methodology</strong></p>
401
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
402
  <div class="contact-info">
@@ -407,7 +491,7 @@ graph TD
407
  <p>CUNY Graduate Center (New Media Lab)</p>
408
  <p>Email: [email protected]</p>
409
  </div>
410
- </footer>
411
  </div>
412
  </body>
413
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 05 - Applied Mathematics - Programming Framework Analysis</title>
7
+ <style>
8
+ body {
9
+ font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
10
+ margin: 0;
11
+ background: #ffffff;
12
+ color: #000000;
13
+ line-height: 1.6;
14
+ font-size: 12pt;
15
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16
+ .container {
17
+ max-width: 1000px;
18
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20
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22
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23
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24
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27
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28
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30
+ h2 {
31
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32
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33
+ padding-bottom: 0.5rem;
34
+ }
35
+ h3 {
36
+ font-size: 14pt;
37
+ }
38
+ p {
39
+ margin-bottom: 1rem;
40
+ text-align: justify;
41
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42
+ .figure {
43
+ margin: 2rem 0;
44
+ text-align: center;
45
+ border: 1px solid #ccc;
46
+ padding: 1rem;
47
+ background: #f9f9f9;
48
+ }
49
+ .figure-caption {
50
+ margin-top: 1rem;
51
+ font-style: italic;
52
+ text-align: left;
53
+ }
54
+ .mermaid {
55
+ background: white;
56
+ padding: 1rem;
57
+ border-radius: 4px;
58
+ }
59
+ .navigation {
60
+ margin: 3rem 0;
61
+ padding: 1rem;
62
+ background: #f8f9fa;
63
+ border-radius: 8px;
64
+ }
65
+ .nav-links {
66
+ display: flex;
67
+ flex-wrap: wrap;
68
+ gap: 1rem;
69
+ justify-content: center;
70
+ }
71
+ .nav-link {
72
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73
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74
+ padding: 0.5rem 1rem;
75
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76
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77
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78
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79
+ .nav-link:hover {
80
+ background: #007bff;
81
+ color: white;
82
+ }
83
+ .footer {
84
+ margin-top: 3rem;
85
+ padding: 1rem;
86
+ background: #f8f9fa;
87
+ border-radius: 8px;
88
+ text-align: center;
89
+ }
90
+ .contact-info {
91
+ margin-top: 1rem;
92
+ }
93
+ .contact-info p {
94
+ margin: 0.25rem 0;
95
+ text-align: center;
96
+ }
97
+ </style>
98
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
99
  <script>
100
  mermaid.initialize({
 
107
  nodeSpacing: 30,
108
  rankSpacing: 30,
109
  padding: 10
110
+ },
111
+ themeVariables: {
112
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113
  }
114
  });
115
  </script>
116
  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 05 - Applied Mathematics - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents applied mathematics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Numerical Methods Process</h2>
 
 
 
 
 
 
124
  <div class="figure">
125
  <div class="mermaid">
126
  graph TD
 
236
  <strong>Figure 1.</strong> Numerical Methods Process. This applied mathematics process visualization demonstrates root finding and integration methods. The flowchart shows numerical problem inputs and error analysis, numerical methods and algorithms, numerical operations and calculations, intermediate results, and final numerical solutions.
237
  </div>
238
  </div>
239
+ </div>
240
 
241
+ <h2>2. Statistical Analysis Process</h2>
 
242
  <div class="figure">
243
  <div class="mermaid">
244
  graph TD
 
352
  <strong>Figure 2.</strong> Statistical Analysis Process. This applied mathematics process visualization demonstrates hypothesis testing and regression analysis. The flowchart shows data set inputs and hypothesis testing, statistical methods and algorithms, statistical operations and calculations, intermediate results, and final statistical analysis outputs.
353
  </div>
354
  </div>
355
+ </div>
356
 
357
+ <h2>3. Cryptographic Algorithms Process</h2>
 
358
  <div class="figure">
359
  <div class="mermaid">
360
  graph TD
 
468
  <strong>Figure 3.</strong> Cryptographic Algorithms Process. This applied mathematics process visualization demonstrates RSA, elliptic curve cryptography, and hash functions. The flowchart shows plaintext inputs and key generation, cryptographic methods and algorithms, cryptographic operations and calculations, intermediate results, and final cryptographic analysis outputs.
469
  </div>
470
  </div>
471
+ </div>
472
 
473
+ <div class="navigation">
474
+ <h3>Navigation</h3>
475
  <div class="nav-links">
476
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
477
  <a href="mathematics_batch_04.html" class="nav-link">← Previous: Geometry & Topology</a>
478
  <a href="mathematics_batch_06.html" class="nav-link">Next: Discrete Mathematics →</a>
479
  <a href="index.html" class="nav-link">Programming Framework Home</a>
480
  </div>
481
+ </div>
482
 
483
+ <div class="footer">
484
  <p><strong>Generated using the Programming Framework methodology</strong></p>
485
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
486
  <div class="contact-info">
 
491
  <p>CUNY Graduate Center (New Media Lab)</p>
492
  <p>Email: [email protected]</p>
493
  </div>
494
+ </div>
495
  </div>
496
  </body>
497
  </html>
mathematics_batch_06.html CHANGED
@@ -4,7 +4,97 @@
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 06 - Discrete Mathematics - Programming Framework Analysis</title>
7
- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
9
  <script>
10
  mermaid.initialize({
@@ -17,24 +107,20 @@
17
  nodeSpacing: 30,
18
  rankSpacing: 30,
19
  padding: 10
 
 
 
20
  }
21
  });
22
  </script>
23
  </head>
24
  <body>
25
  <div class="container">
26
- <header>
27
- <h1>🕸️ Mathematics Batch 06 - Discrete Mathematics</h1>
28
- <p class="subtitle">Graph Theory, Combinatorics, and Logic & Set Theory</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Discrete Mathematics Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to discrete mathematical operations. Each process shows the computational logic behind graph algorithms, combinatorial counting, and logical reasoning.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Graph Theory Algorithms Process</h2>
38
  <div class="figure">
39
  <div class="mermaid">
40
  graph TD
@@ -148,10 +234,9 @@ graph TD
148
  <strong>Figure 1.</strong> Graph Theory Algorithms Process. This discrete mathematics process visualization demonstrates shortest path, minimum spanning tree, and network flow algorithms. The flowchart shows graph inputs and properties, graph theory methods and algorithms, graph operations and calculations, intermediate results, and final graph theory outputs.
149
  </div>
150
  </div>
151
- </section>
152
 
153
- <section class="process">
154
- <h2>2. Combinatorics Process</h2>
155
  <div class="figure">
156
  <div class="mermaid">
157
  graph TD
@@ -265,10 +350,9 @@ graph TD
265
  <strong>Figure 2.</strong> Combinatorics Process. This discrete mathematics process visualization demonstrates permutations, combinations, and counting principles. The flowchart shows combinatorial problem inputs and principles, combinatorial methods and formulas, counting operations and calculations, intermediate results, and final combinatorial analysis outputs.
266
  </div>
267
  </div>
268
- </section>
269
 
270
- <section class="process">
271
- <h2>3. Logic & Set Theory Process</h2>
272
  <div class="figure">
273
  <div class="mermaid">
274
  graph TD
@@ -382,19 +466,19 @@ graph TD
382
  <strong>Figure 3.</strong> Logic & Set Theory Process. This discrete mathematics process visualization demonstrates boolean algebra, set operations, and proof techniques. The flowchart shows logical statement inputs and proof techniques, logic and set theory methods and algorithms, proof operations and calculations, intermediate results, and final logic and set theory analysis outputs.
383
  </div>
384
  </div>
385
- </section>
386
 
387
- <section class="navigation">
388
- <h2>Navigation</h2>
389
  <div class="nav-links">
390
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
391
  <a href="mathematics_batch_05.html" class="nav-link">← Previous: Applied Mathematics</a>
392
  <a href="mathematics_batch_07.html" class="nav-link">Next: Historical & Educational →</a>
393
  <a href="index.html" class="nav-link">Programming Framework Home</a>
394
  </div>
395
- </section>
396
 
397
- <footer>
398
  <p><strong>Generated using the Programming Framework methodology</strong></p>
399
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
400
  <div class="contact-info">
@@ -405,7 +489,7 @@ graph TD
405
  <p>CUNY Graduate Center (New Media Lab)</p>
406
  <p>Email: [email protected]</p>
407
  </div>
408
- </footer>
409
  </div>
410
  </body>
411
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
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  <title>Mathematics Batch 06 - Discrete Mathematics - Programming Framework Analysis</title>
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  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
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  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 06 - Discrete Mathematics - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents discrete mathematics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Graph Theory Algorithms Process</h2>
 
 
 
 
 
 
124
  <div class="figure">
125
  <div class="mermaid">
126
  graph TD
 
234
  <strong>Figure 1.</strong> Graph Theory Algorithms Process. This discrete mathematics process visualization demonstrates shortest path, minimum spanning tree, and network flow algorithms. The flowchart shows graph inputs and properties, graph theory methods and algorithms, graph operations and calculations, intermediate results, and final graph theory outputs.
235
  </div>
236
  </div>
237
+ </div>
238
 
239
+ <h2>2. Combinatorics Process</h2>
 
240
  <div class="figure">
241
  <div class="mermaid">
242
  graph TD
 
350
  <strong>Figure 2.</strong> Combinatorics Process. This discrete mathematics process visualization demonstrates permutations, combinations, and counting principles. The flowchart shows combinatorial problem inputs and principles, combinatorial methods and formulas, counting operations and calculations, intermediate results, and final combinatorial analysis outputs.
351
  </div>
352
  </div>
353
+ </div>
354
 
355
+ <h2>3. Logic & Set Theory Process</h2>
 
356
  <div class="figure">
357
  <div class="mermaid">
358
  graph TD
 
466
  <strong>Figure 3.</strong> Logic & Set Theory Process. This discrete mathematics process visualization demonstrates boolean algebra, set operations, and proof techniques. The flowchart shows logical statement inputs and proof techniques, logic and set theory methods and algorithms, proof operations and calculations, intermediate results, and final logic and set theory analysis outputs.
467
  </div>
468
  </div>
469
+ </div>
470
 
471
+ <div class="navigation">
472
+ <h3>Navigation</h3>
473
  <div class="nav-links">
474
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
475
  <a href="mathematics_batch_05.html" class="nav-link">← Previous: Applied Mathematics</a>
476
  <a href="mathematics_batch_07.html" class="nav-link">Next: Historical & Educational →</a>
477
  <a href="index.html" class="nav-link">Programming Framework Home</a>
478
  </div>
479
+ </div>
480
 
481
+ <div class="footer">
482
  <p><strong>Generated using the Programming Framework methodology</strong></p>
483
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
484
  <div class="contact-info">
 
489
  <p>CUNY Graduate Center (New Media Lab)</p>
490
  <p>Email: [email protected]</p>
491
  </div>
492
+ </div>
493
  </div>
494
  </body>
495
  </html>
mathematics_batch_07.html CHANGED
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4
  <meta charset="UTF-8" />
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  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis</title>
7
- <link rel="stylesheet" href="style.css">
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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  <body>
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  <div class="container">
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- <header>
27
- <h1>🏛️ Mathematics Batch 07 - Historical & Educational</h1>
28
- <p class="subtitle">Euclid's Geometry and Aristotle's Syllogism</p>
29
- </header>
30
 
31
- <section class="batch-info">
32
- <h2>Historical & Educational Processes</h2>
33
- <p>This batch demonstrates the Programming Framework's application to historically significant mathematical and logical systems. Each process shows the computational logic behind Euclid's geometric method and Aristotle's syllogistic reasoning.</p>
34
- </section>
35
-
36
- <section class="process">
37
- <h2>1. Euclid's Geometry Process</h2>
38
  <div class="figure">
39
  <div class="mermaid">
40
  graph TD
@@ -148,10 +234,9 @@ graph TD
148
  <strong>Figure 1.</strong> Euclid's Geometry Process. This historical mathematics process visualization demonstrates the axiomatic method of Euclidean geometry. The flowchart shows geometric problem inputs and postulates, Euclidean methods and axioms, geometric operations and proofs, intermediate results, and final Euclidean geometry outputs.
149
  </div>
150
  </div>
151
- </section>
152
 
153
- <section class="process">
154
- <h2>2. Aristotle's Syllogism Process</h2>
155
  <div class="figure">
156
  <div class="mermaid">
157
  graph TD
@@ -265,18 +350,18 @@ graph TD
265
  <strong>Figure 2.</strong> Aristotle's Syllogism Process. This historical logic process visualization demonstrates syllogistic reasoning and logical deduction. The flowchart shows logical premise inputs and syllogistic forms, syllogistic methods and figures, logical operations and validity checks, intermediate results, and final Aristotelian logic outputs.
266
  </div>
267
  </div>
268
- </section>
269
 
270
- <section class="navigation">
271
- <h2>Navigation</h2>
272
  <div class="nav-links">
273
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
274
  <a href="mathematics_batch_06.html" class="nav-link">← Previous: Discrete Mathematics</a>
275
  <a href="index.html" class="nav-link">Programming Framework Home</a>
276
  </div>
277
- </section>
278
 
279
- <footer>
280
  <p><strong>Generated using the Programming Framework methodology</strong></p>
281
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
282
  <div class="contact-info">
@@ -287,7 +372,7 @@ graph TD
287
  <p>CUNY Graduate Center (New Media Lab)</p>
288
  <p>Email: [email protected]</p>
289
  </div>
290
- </footer>
291
  </div>
292
  </body>
293
  </html>
 
4
  <meta charset="UTF-8" />
5
  <meta name="viewport" content="width=device-width, initial-scale=1" />
6
  <title>Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis</title>
7
+ <style>
8
+ body {
9
+ font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
10
+ margin: 0;
11
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13
+ line-height: 1.6;
14
+ font-size: 12pt;
15
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16
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17
+ max-width: 1000px;
18
+ margin: 0 auto;
19
+ padding: 1.5rem;
20
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21
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22
+ color: #000000;
23
+ margin-top: 1.5rem;
24
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25
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26
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27
+ font-size: 18pt;
28
+ text-align: center;
29
+ }
30
+ h2 {
31
+ font-size: 16pt;
32
+ border-bottom: 2px solid #000;
33
+ padding-bottom: 0.5rem;
34
+ }
35
+ h3 {
36
+ font-size: 14pt;
37
+ }
38
+ p {
39
+ margin-bottom: 1rem;
40
+ text-align: justify;
41
+ }
42
+ .figure {
43
+ margin: 2rem 0;
44
+ text-align: center;
45
+ border: 1px solid #ccc;
46
+ padding: 1rem;
47
+ background: #f9f9f9;
48
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49
+ .figure-caption {
50
+ margin-top: 1rem;
51
+ font-style: italic;
52
+ text-align: left;
53
+ }
54
+ .mermaid {
55
+ background: white;
56
+ padding: 1rem;
57
+ border-radius: 4px;
58
+ }
59
+ .navigation {
60
+ margin: 3rem 0;
61
+ padding: 1rem;
62
+ background: #f8f9fa;
63
+ border-radius: 8px;
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+ }
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+ .nav-links {
66
+ display: flex;
67
+ flex-wrap: wrap;
68
+ gap: 1rem;
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+ justify-content: center;
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+ .nav-link {
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+ color: #007bff;
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+ text-decoration: none;
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90
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91
+ margin-top: 1rem;
92
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95
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96
+ }
97
+ </style>
98
  <script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/mermaid.min.js"></script>
99
  <script>
100
  mermaid.initialize({
 
107
  nodeSpacing: 30,
108
  rankSpacing: 30,
109
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110
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111
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112
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113
  }
114
  });
115
  </script>
116
  </head>
117
  <body>
118
  <div class="container">
119
+ <h1>Mathematics Batch 07 - Historical & Educational - Programming Framework Analysis</h1>
120
+
121
+ <p>This document presents historical and educational mathematics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>
 
122
 
123
+ <h2>1. Euclid's Geometry Process</h2>
 
 
 
 
 
 
124
  <div class="figure">
125
  <div class="mermaid">
126
  graph TD
 
234
  <strong>Figure 1.</strong> Euclid's Geometry Process. This historical mathematics process visualization demonstrates the axiomatic method of Euclidean geometry. The flowchart shows geometric problem inputs and postulates, Euclidean methods and axioms, geometric operations and proofs, intermediate results, and final Euclidean geometry outputs.
235
  </div>
236
  </div>
237
+ </div>
238
 
239
+ <h2>2. Aristotle's Syllogism Process</h2>
 
240
  <div class="figure">
241
  <div class="mermaid">
242
  graph TD
 
350
  <strong>Figure 2.</strong> Aristotle's Syllogism Process. This historical logic process visualization demonstrates syllogistic reasoning and logical deduction. The flowchart shows logical premise inputs and syllogistic forms, syllogistic methods and figures, logical operations and validity checks, intermediate results, and final Aristotelian logic outputs.
351
  </div>
352
  </div>
353
+ </div>
354
 
355
+ <div class="navigation">
356
+ <h3>Navigation</h3>
357
  <div class="nav-links">
358
  <a href="mathematics_index.html" class="nav-link">← Back to Mathematics Index</a>
359
  <a href="mathematics_batch_06.html" class="nav-link">← Previous: Discrete Mathematics</a>
360
  <a href="index.html" class="nav-link">Programming Framework Home</a>
361
  </div>
362
+ </div>
363
 
364
+ <div class="footer">
365
  <p><strong>Generated using the Programming Framework methodology</strong></p>
366
  <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
367
  <div class="contact-info">
 
372
  <p>CUNY Graduate Center (New Media Lab)</p>
373
  <p>Email: [email protected]</p>
374
  </div>
375
+ </div>
376
  </div>
377
  </body>
378
  </html>