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  1. biology_processes.html +13 -13
  2. chemistry_batch_01.html +380 -0
  3. chemistry_batch_02.html +381 -0
  4. chemistry_index.html +168 -0
  5. computer_science_batch_01.html +380 -0
  6. computer_science_index.html +168 -0
  7. index.html +45 -5
  8. mathematics_batch_01.html +443 -0
  9. mathematics_batch_02.html +471 -0
  10. mathematics_batch_03.html +461 -0
  11. mathematics_batch_04.html +415 -0
  12. mathematics_batch_05.html +413 -0
  13. mathematics_batch_06.html +411 -0
  14. mathematics_batch_07.html +293 -0
  15. mathematics_index.html +168 -0
  16. physics_batch_01.html +380 -0
  17. physics_index.html +168 -0
  18. style.css +51 -0
biology_processes.html CHANGED
@@ -127,7 +127,7 @@
127
 
128
  <p>This document presents representative biological 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>
129
 
130
- <h2>1. β-Galactosidase Regulation System (E. coli)</h2>
131
  <div class="figure">
132
  <div class="mermaid">
133
  graph TD
@@ -145,9 +145,9 @@ graph TD
145
  K --> L[High Glucose Status]
146
 
147
  %% Regulatory Logic Gates
148
- I --> M{Is Lactose Present?}
149
- L --> N{Is Glucose Present?}
150
- F --> O{Is Energy Low?}
151
 
152
  %% Repressor Logic
153
  M -->|No| P[Lac Repressor Active]
@@ -167,8 +167,8 @@ graph TD
167
  Y --> AA[No CAP Binding]
168
 
169
  %% Transcription Control
170
- U --> BB{Operator Free?}
171
- Z --> CC{CAP Bound?}
172
  BB -->|Yes| DD[RNA Polymerase Binding]
173
  BB -->|No| EE[Transcription Blocked]
174
  CC -->|Yes| FF[Strong Transcription]
@@ -321,9 +321,9 @@ graph TD
321
  I --> L[Damage Signal Processing]
322
 
323
  %% Decision Logic
324
- J --> M{Nutrients Sufficient?}
325
- K --> N{Size Adequate?}
326
- L --> O{DNA Intact?}
327
 
328
  %% Cell Cycle Progression
329
  M -->|Yes| P[G1 Phase Entry]
@@ -541,9 +541,9 @@ graph TD
541
  I --> L[Stress Signal Processing]
542
 
543
  %% Threshold Logic
544
- J --> M{Autoinducer Above Threshold?}
545
- K --> N{Quorum Reached?}
546
- L --> O{Stress Conditions?}
547
 
548
  %% Gene Regulation
549
  M -->|Yes| P[LuxR Activation]
@@ -642,7 +642,7 @@ graph TD
642
  %% Molecular Oscillator
643
  M --> P[CLOCK-BMAL1 Complex]
644
  N --> Q[PER-CRY Complex]
645
- O --> R[REV-ERBα/β]
646
 
647
  %% Feedback Loops
648
  P --> S[Target Gene Activation]
 
127
 
128
  <p>This document presents representative biological 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>
129
 
130
+ <h2>1. Beta-Galactosidase Regulation System (E. coli)</h2>
131
  <div class="figure">
132
  <div class="mermaid">
133
  graph TD
 
145
  K --> L[High Glucose Status]
146
 
147
  %% Regulatory Logic Gates
148
+ I --> M[Is Lactose Present Question]
149
+ L --> N[Is Glucose Present Question]
150
+ F --> O[Is Energy Low Question]
151
 
152
  %% Repressor Logic
153
  M -->|No| P[Lac Repressor Active]
 
167
  Y --> AA[No CAP Binding]
168
 
169
  %% Transcription Control
170
+ U --> BB[Operator Free Question]
171
+ Z --> CC[CAP Bound Question]
172
  BB -->|Yes| DD[RNA Polymerase Binding]
173
  BB -->|No| EE[Transcription Blocked]
174
  CC -->|Yes| FF[Strong Transcription]
 
321
  I --> L[Damage Signal Processing]
322
 
323
  %% Decision Logic
324
+ J --> M[Nutrients Sufficient Question]
325
+ K --> N[Size Adequate Question]
326
+ L --> O[DNA Intact Question]
327
 
328
  %% Cell Cycle Progression
329
  M -->|Yes| P[G1 Phase Entry]
 
541
  I --> L[Stress Signal Processing]
542
 
543
  %% Threshold Logic
544
+ J --> M[Autoinducer Above Threshold Question]
545
+ K --> N[Quorum Reached Question]
546
+ L --> O[Stress Conditions Question]
547
 
548
  %% Gene Regulation
549
  M -->|Yes| P[LuxR Activation]
 
642
  %% Molecular Oscillator
643
  M --> P[CLOCK-BMAL1 Complex]
644
  N --> Q[PER-CRY Complex]
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+ O --> R[REV-ERB alpha slash beta]
646
 
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  %% Feedback Loops
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  P --> S[Target Gene Activation]
chemistry_batch_01.html ADDED
@@ -0,0 +1,380 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ <!DOCTYPE html>
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+ <html lang="en">
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+ <head>
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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>Chemistry Batch 01 - Organic Chemistry - Programming Framework Analysis</title>
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+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
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+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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+ nodeSpacing: 30,
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+ rankSpacing: 30,
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+ padding: 10
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+ }
21
+ });
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+ </script>
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+ </head>
24
+ <body>
25
+ <div class="container">
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+ <header>
27
+ <h1>🧪 Chemistry Batch 01 - Organic Chemistry</h1>
28
+ <p class="subtitle">Reaction Mechanisms, Synthesis Pathways, and Stereochemistry</p>
29
+ </header>
30
+
31
+ <section class="batch-info">
32
+ <h2>Organic Chemistry Processes</h2>
33
+ <p>This batch demonstrates the Programming Framework's application to fundamental organic chemistry operations. Each process shows the computational logic behind reaction mechanisms, synthesis strategies, and stereochemical analysis.</p>
34
+ </section>
35
+
36
+ <section class="process">
37
+ <h2>1. Organic Reaction Mechanisms Process</h2>
38
+ <div class="figure">
39
+ <div class="mermaid">
40
+ graph TD
41
+ A1[Reactant Molecules] --> B1[Reaction Type Classification]
42
+ C1[Electron Flow Analysis] --> D1[Mechanism Determination]
43
+ E1[Energy Profile] --> F1[Transition State Analysis]
44
+
45
+ B1 --> G1[Nucleophilic Substitution]
46
+ D1 --> H1[SN1 Mechanism]
47
+ F1 --> I1[SN2 Mechanism]
48
+
49
+ G1 --> J1[Electrophilic Addition]
50
+ H1 --> K1[Carbocation Formation]
51
+ I1 --> L1[Backside Attack]
52
+
53
+ J1 --> M1[Elimination Reactions]
54
+ K1 --> N1[Carbocation Stability]
55
+ L1 --> O1[Stereochemistry Analysis]
56
+
57
+ M1 --> P1[E1 Elimination]
58
+ N1 --> O1
59
+ O1 --> Q1[E2 Elimination]
60
+
61
+ P1 --> R1[Radical Reactions]
62
+ Q1 --> S1[Concerted Mechanism]
63
+ R1 --> T1[Radical Initiation]
64
+
65
+ S1 --> U1[Radical Propagation]
66
+ T1 --> V1[Radical Termination]
67
+ U1 --> W1[Organic Reaction Result]
68
+
69
+ V1 --> X1[Reaction Mechanism Analysis]
70
+ W1 --> Y1[Mechanism Validation]
71
+ X1 --> Z1[Organic Reaction Output]
72
+
73
+ Y1 --> AA1[Organic Reaction Analysis]
74
+ Z1 --> BB1[Organic Reaction Final Result]
75
+ AA1 --> CC1[Organic Reaction Analysis Complete]
76
+
77
+ style A1 fill:#ff6b6b,color:#fff
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+ style C1 fill:#ff6b6b,color:#fff
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+ style E1 fill:#ff6b6b,color:#fff
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+
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+ style B1 fill:#ffd43b,color:#000
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+ style D1 fill:#ffd43b,color:#000
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+ style F1 fill:#ffd43b,color:#000
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+ style G1 fill:#ffd43b,color:#000
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+ style H1 fill:#ffd43b,color:#000
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+ style I1 fill:#ffd43b,color:#000
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+ style J1 fill:#ffd43b,color:#000
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+ style K1 fill:#ffd43b,color:#000
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+ style L1 fill:#ffd43b,color:#000
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+ style M1 fill:#ffd43b,color:#000
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+ style N1 fill:#ffd43b,color:#000
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+ style O1 fill:#ffd43b,color:#000
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+ style P1 fill:#ffd43b,color:#000
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+ style Q1 fill:#ffd43b,color:#000
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+ style R1 fill:#ffd43b,color:#000
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+ style S1 fill:#ffd43b,color:#000
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+ style T1 fill:#ffd43b,color:#000
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+ style U1 fill:#ffd43b,color:#000
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+ style V1 fill:#ffd43b,color:#000
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+ style W1 fill:#ffd43b,color:#000
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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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+
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+ style M1 fill:#51cf66,color:#fff
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+ style N1 fill:#51cf66,color:#fff
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+ style O1 fill:#51cf66,color:#fff
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+ style P1 fill:#51cf66,color:#fff
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+ style Q1 fill:#51cf66,color:#fff
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+ style R1 fill:#51cf66,color:#fff
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+ style S1 fill:#51cf66,color:#fff
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+ style T1 fill:#51cf66,color:#fff
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+ style U1 fill:#51cf66,color:#fff
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+ style V1 fill:#51cf66,color:#fff
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+ style W1 fill:#51cf66,color:#fff
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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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+
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+ style CC1 fill:#b197fc,color:#fff
127
+ </div>
128
+
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+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
130
+ <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;">
131
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
132
+ </div>
133
+ <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;">
134
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Reaction Methods
135
+ </div>
136
+ <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;">
137
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Mechanism Operations
138
+ </div>
139
+ <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;">
140
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
141
+ </div>
142
+ <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;">
143
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
144
+ </div>
145
+ </div>
146
+
147
+ <div class="figure-caption">
148
+ <strong>Figure 1.</strong> Organic Reaction Mechanisms Process. This organic chemistry process visualization demonstrates nucleophilic substitution, elimination, and radical reactions. The flowchart shows reactant inputs and energy profiles, reaction methods and mechanisms, mechanism operations and analysis, intermediate results, and final organic reaction outputs.
149
+ </div>
150
+ </div>
151
+ </section>
152
+
153
+ <section class="process">
154
+ <h2>2. Organic Synthesis Pathways Process</h2>
155
+ <div class="figure">
156
+ <div class="mermaid">
157
+ graph TD
158
+ A2[Starting Materials] --> B2[Target Molecule Analysis]
159
+ C2[Retrosynthetic Analysis] --> D2[Disconnection Strategy]
160
+ E2[Functional Group Analysis] --> F2[Protection Strategy]
161
+
162
+ B2 --> G2[Retrosynthetic Disconnection]
163
+ D2 --> H2[Key Bond Identification]
164
+ F2 --> I2[Protecting Group Selection]
165
+
166
+ G2 --> J2[Synthon Generation]
167
+ H2 --> K2[Reaction Selection]
168
+ I2 --> L2[Protection Reaction]
169
+
170
+ J2 --> M2[Reagent Selection]
171
+ K2 --> L2
172
+ L2 --> N2[Deprotection Strategy]
173
+
174
+ M2 --> O2[Reaction Sequence]
175
+ N2 --> P2[Purification Methods]
176
+ O2 --> Q2[Yield Optimization]
177
+
178
+ P2 --> R2[Chromatography]
179
+ Q2 --> S2[Recrystallization]
180
+ R2 --> T2[Organic Synthesis Result]
181
+
182
+ S2 --> U2[Synthesis Validation]
183
+ T2 --> V2[Product Characterization]
184
+ U2 --> W2[Organic Synthesis Output]
185
+
186
+ V2 --> X2[Organic Synthesis Analysis]
187
+ W2 --> Y2[Organic Synthesis Final Result]
188
+ X2 --> Z2[Organic Synthesis Analysis Complete]
189
+
190
+ style A2 fill:#ff6b6b,color:#fff
191
+ style C2 fill:#ff6b6b,color:#fff
192
+ style E2 fill:#ff6b6b,color:#fff
193
+
194
+ style B2 fill:#ffd43b,color:#000
195
+ style D2 fill:#ffd43b,color:#000
196
+ style F2 fill:#ffd43b,color:#000
197
+ style G2 fill:#ffd43b,color:#000
198
+ style H2 fill:#ffd43b,color:#000
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+ style I2 fill:#ffd43b,color:#000
200
+ style J2 fill:#ffd43b,color:#000
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+ style K2 fill:#ffd43b,color:#000
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+ style L2 fill:#ffd43b,color:#000
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+ style M2 fill:#ffd43b,color:#000
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+ style N2 fill:#ffd43b,color:#000
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+ style O2 fill:#ffd43b,color:#000
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+ style P2 fill:#ffd43b,color:#000
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+ style Q2 fill:#ffd43b,color:#000
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+ style R2 fill:#ffd43b,color:#000
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+ style S2 fill:#ffd43b,color:#000
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+ style T2 fill:#ffd43b,color:#000
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+ style U2 fill:#ffd43b,color:#000
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+ style V2 fill:#ffd43b,color:#000
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+ style W2 fill:#ffd43b,color:#000
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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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+
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+ style M2 fill:#51cf66,color:#fff
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+ style N2 fill:#51cf66,color:#fff
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+ style O2 fill:#51cf66,color:#fff
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+ style P2 fill:#51cf66,color:#fff
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+ style Q2 fill:#51cf66,color:#fff
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+ style R2 fill:#51cf66,color:#fff
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+ style S2 fill:#51cf66,color:#fff
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+ style T2 fill:#51cf66,color:#fff
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+ style U2 fill:#51cf66,color:#fff
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+ style V2 fill:#51cf66,color:#fff
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+ style W2 fill:#51cf66,color:#fff
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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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+
233
+ style Z2 fill:#b197fc,color:#fff
234
+ </div>
235
+
236
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
237
+ <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;">
238
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
239
+ </div>
240
+ <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;">
241
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Synthesis Methods
242
+ </div>
243
+ <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;">
244
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Synthesis Operations
245
+ </div>
246
+ <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;">
247
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
248
+ </div>
249
+ <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;">
250
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
251
+ </div>
252
+ </div>
253
+
254
+ <div class="figure-caption">
255
+ <strong>Figure 2.</strong> Organic Synthesis Pathways Process. This organic chemistry process visualization demonstrates retrosynthetic analysis and synthesis strategies. The flowchart shows starting material inputs and target analysis, synthesis methods and strategies, synthesis operations and purification, intermediate results, and final organic synthesis outputs.
256
+ </div>
257
+ </div>
258
+ </section>
259
+
260
+ <section class="process">
261
+ <h2>3. Stereochemistry Analysis Process</h2>
262
+ <div class="figure">
263
+ <div class="mermaid">
264
+ graph TD
265
+ A3[Molecular Structure] --> B3[Stereocenter Identification]
266
+ C3[Chirality Analysis] --> D3[Configuration Assignment]
267
+ E3[Optical Activity] --> F3[Stereoisomer Analysis]
268
+
269
+ B3 --> G3[Chiral Centers]
270
+ D3 --> H3[R S Configuration]
271
+ F3 --> I3[Enantiomer Analysis]
272
+
273
+ G3 --> J3[Diastereomer Analysis]
274
+ H3 --> K3[Absolute Configuration]
275
+ I3 --> L3[Optical Rotation]
276
+
277
+ J3 --> M3[Conformational Analysis]
278
+ K3 --> L3
279
+ L3 --> N3[Racemic Mixtures]
280
+
281
+ M3 --> O3[Conformational Isomers]
282
+ N3 --> P3[Resolution Methods]
283
+ O3 --> Q3[Stereochemistry Result]
284
+
285
+ P3 --> R3[Chiral Resolution]
286
+ Q3 --> S3[Stereochemistry Validation]
287
+ R3 --> T3[Stereochemistry Output]
288
+
289
+ S3 --> U3[Stereochemistry Analysis]
290
+ T3 --> V3[Stereochemistry Final Result]
291
+ U3 --> W3[Stereochemistry Analysis Complete]
292
+
293
+ style A3 fill:#ff6b6b,color:#fff
294
+ style C3 fill:#ff6b6b,color:#fff
295
+ style E3 fill:#ff6b6b,color:#fff
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+
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+ style B3 fill:#ffd43b,color:#000
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+ style D3 fill:#ffd43b,color:#000
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+ style F3 fill:#ffd43b,color:#000
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+ style G3 fill:#ffd43b,color:#000
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+ style H3 fill:#ffd43b,color:#000
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+ style I3 fill:#ffd43b,color:#000
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+ style J3 fill:#ffd43b,color:#000
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+ style K3 fill:#ffd43b,color:#000
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+ style L3 fill:#ffd43b,color:#000
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+ style M3 fill:#ffd43b,color:#000
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+ style N3 fill:#ffd43b,color:#000
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+ style O3 fill:#ffd43b,color:#000
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+ style P3 fill:#ffd43b,color:#000
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+ style Q3 fill:#ffd43b,color:#000
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+ style R3 fill:#ffd43b,color:#000
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+ style S3 fill:#ffd43b,color:#000
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+ style T3 fill:#ffd43b,color:#000
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+ style U3 fill:#ffd43b,color:#000
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+ style V3 fill:#ffd43b,color:#000
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+ style W3 fill:#ffd43b,color:#000
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+
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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 O3 fill:#51cf66,color:#fff
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+ style P3 fill:#51cf66,color:#fff
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+ style Q3 fill:#51cf66,color:#fff
323
+ style R3 fill:#51cf66,color:#fff
324
+ style S3 fill:#51cf66,color:#fff
325
+ style T3 fill:#51cf66,color:#fff
326
+ style U3 fill:#51cf66,color:#fff
327
+ style V3 fill:#51cf66,color:#fff
328
+ style W3 fill:#51cf66,color:#fff
329
+
330
+ style W3 fill:#b197fc,color:#fff
331
+ </div>
332
+
333
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
334
+ <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;">
335
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
336
+ </div>
337
+ <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;">
338
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Stereochemistry Methods
339
+ </div>
340
+ <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;">
341
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Stereochemistry Operations
342
+ </div>
343
+ <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;">
344
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
345
+ </div>
346
+ <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;">
347
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
348
+ </div>
349
+ </div>
350
+
351
+ <div class="figure-caption">
352
+ <strong>Figure 3.</strong> Stereochemistry Analysis Process. This organic chemistry process visualization demonstrates chiral center analysis and stereoisomer identification. The flowchart shows molecular structure inputs and chirality analysis, stereochemistry methods and configurations, stereochemistry operations and resolution, intermediate results, and final stereochemistry analysis outputs.
353
+ </div>
354
+ </div>
355
+ </section>
356
+
357
+ <section class="navigation">
358
+ <h2>Navigation</h2>
359
+ <div class="nav-links">
360
+ <a href="chemistry_index.html" class="nav-link">← Back to Chemistry Index</a>
361
+ <a href="chemistry_batch_02.html" class="nav-link">Next: Physical Chemistry →</a>
362
+ <a href="index.html" class="nav-link">Programming Framework Home</a>
363
+ </div>
364
+ </section>
365
+
366
+ <footer>
367
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
368
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
369
+ <div class="contact-info">
370
+ <p><strong>Gary Welz</strong></p>
371
+ <p>Retired Faculty Member</p>
372
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
373
+ <p>Borough of Manhattan Community College, CUNY</p>
374
+ <p>CUNY Graduate Center (New Media Lab)</p>
375
+ <p>Email: gwelz@jjay.cuny.edu</p>
376
+ </div>
377
+ </footer>
378
+ </div>
379
+ </body>
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+ </html>
chemistry_batch_02.html ADDED
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1
+ <!DOCTYPE html>
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+ <html lang="en">
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+ <head>
4
+ <meta charset="UTF-8" />
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+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Chemistry Batch 02 - Physical Chemistry - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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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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+ });
22
+ </script>
23
+ </head>
24
+ <body>
25
+ <div class="container">
26
+ <header>
27
+ <h1>⚛️ Chemistry Batch 02 - Physical Chemistry</h1>
28
+ <p class="subtitle">Thermodynamics, Kinetics, and Spectroscopy</p>
29
+ </header>
30
+
31
+ <section class="batch-info">
32
+ <h2>Physical Chemistry Processes</h2>
33
+ <p>This batch demonstrates the Programming Framework's application to fundamental physical chemistry operations. Each process shows the computational logic behind thermodynamic calculations, reaction kinetics, and spectroscopic analysis.</p>
34
+ </section>
35
+
36
+ <section class="process">
37
+ <h2>1. Thermodynamic Calculations Process</h2>
38
+ <div class="figure">
39
+ <div class="mermaid">
40
+ graph TD
41
+ A1[System Definition] --> B1[State Variables Analysis]
42
+ C1[Energy Conservation] --> D1[First Law Application]
43
+ E1[Entropy Analysis] --> F1[Second Law Application]
44
+
45
+ B1 --> G1[Temperature Pressure Volume]
46
+ D1 --> H1[Internal Energy Change]
47
+ F1 --> I1[Entropy Change Calculation]
48
+
49
+ G1 --> J1[State Function Determination]
50
+ H1 --> K1[Heat Work Calculation]
51
+ I1 --> L1[Reversible Process Analysis]
52
+
53
+ J1 --> M1[Enthalpy Calculation]
54
+ K1 --> L1
55
+ L1 --> N1[Gibbs Free Energy]
56
+
57
+ M1 --> O1[Helmholtz Free Energy]
58
+ N1 --> P1[Chemical Potential]
59
+ O1 --> Q1[Thermodynamic Equilibrium]
60
+
61
+ P1 --> R1[Phase Equilibrium]
62
+ Q1 --> S1[Reaction Equilibrium]
63
+ R1 --> T1[Thermodynamic Result]
64
+
65
+ S1 --> U1[Equilibrium Constant]
66
+ T1 --> V1[Thermodynamic Validation]
67
+ U1 --> W1[Thermodynamic Output]
68
+
69
+ V1 --> X1[Thermodynamic Analysis]
70
+ W1 --> Y1[Thermodynamic Final Result]
71
+ X1 --> Z1[Thermodynamic Analysis Complete]
72
+
73
+ style A1 fill:#ff6b6b,color:#fff
74
+ style C1 fill:#ff6b6b,color:#fff
75
+ style E1 fill:#ff6b6b,color:#fff
76
+
77
+ style B1 fill:#ffd43b,color:#000
78
+ style D1 fill:#ffd43b,color:#000
79
+ style F1 fill:#ffd43b,color:#000
80
+ style G1 fill:#ffd43b,color:#000
81
+ style H1 fill:#ffd43b,color:#000
82
+ style I1 fill:#ffd43b,color:#000
83
+ style J1 fill:#ffd43b,color:#000
84
+ style K1 fill:#ffd43b,color:#000
85
+ style L1 fill:#ffd43b,color:#000
86
+ style M1 fill:#ffd43b,color:#000
87
+ style N1 fill:#ffd43b,color:#000
88
+ style O1 fill:#ffd43b,color:#000
89
+ style P1 fill:#ffd43b,color:#000
90
+ style Q1 fill:#ffd43b,color:#000
91
+ style R1 fill:#ffd43b,color:#000
92
+ style S1 fill:#ffd43b,color:#000
93
+ style T1 fill:#ffd43b,color:#000
94
+ style U1 fill:#ffd43b,color:#000
95
+ style V1 fill:#ffd43b,color:#000
96
+ style W1 fill:#ffd43b,color:#000
97
+ style X1 fill:#ffd43b,color:#000
98
+ style Y1 fill:#ffd43b,color:#000
99
+ style Z1 fill:#ffd43b,color:#000
100
+
101
+ style M1 fill:#51cf66,color:#fff
102
+ style N1 fill:#51cf66,color:#fff
103
+ style O1 fill:#51cf66,color:#fff
104
+ style P1 fill:#51cf66,color:#fff
105
+ style Q1 fill:#51cf66,color:#fff
106
+ style R1 fill:#51cf66,color:#fff
107
+ style S1 fill:#51cf66,color:#fff
108
+ style T1 fill:#51cf66,color:#fff
109
+ style U1 fill:#51cf66,color:#fff
110
+ style V1 fill:#51cf66,color:#fff
111
+ style W1 fill:#51cf66,color:#fff
112
+ style X1 fill:#51cf66,color:#fff
113
+ style Y1 fill:#51cf66,color:#fff
114
+ style Z1 fill:#51cf66,color:#fff
115
+
116
+ style Z1 fill:#b197fc,color:#fff
117
+ </div>
118
+
119
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
120
+ <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;">
121
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
122
+ </div>
123
+ <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;">
124
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Thermodynamic Methods
125
+ </div>
126
+ <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;">
127
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Thermodynamic Operations
128
+ </div>
129
+ <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;">
130
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
131
+ </div>
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:#b197fc;"></span>Products
134
+ </div>
135
+ </div>
136
+
137
+ <div class="figure-caption">
138
+ <strong>Figure 1.</strong> Thermodynamic Calculations Process. This physical chemistry process visualization demonstrates thermodynamic state functions and equilibrium calculations. The flowchart shows system inputs and energy conservation, thermodynamic methods and laws, thermodynamic operations and calculations, intermediate results, and final thermodynamic analysis outputs.
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="process">
144
+ <h2>2. Chemical Kinetics Process</h2>
145
+ <div class="figure">
146
+ <div class="mermaid">
147
+ graph TD
148
+ A2[Reaction System] --> B2[Rate Law Determination]
149
+ C2[Concentration Analysis] --> D2[Reaction Order]
150
+ E2[Temperature Effects] --> F2[Activation Energy]
151
+
152
+ B2 --> G2[Rate Constant k]
153
+ D2 --> H2[Zero Order Reaction]
154
+ F2 --> I2[Arrhenius Equation]
155
+
156
+ G2 --> J2[First Order Reaction]
157
+ H2 --> K2[Second Order Reaction]
158
+ I2 --> L2[Activation Energy Calculation]
159
+
160
+ J2 --> M2[Rate Expression]
161
+ K2 --> L2
162
+ L2 --> N2[Collision Theory]
163
+
164
+ M2 --> O2[Transition State Theory]
165
+ N2 --> P2[Reaction Mechanism]
166
+ O2 --> Q2[Kinetic Analysis]
167
+
168
+ P2 --> R2[Elementary Steps]
169
+ Q2 --> S2[Rate Determining Step]
170
+ R2 --> T2[Chemical Kinetics Result]
171
+
172
+ S2 --> U2[Kinetic Validation]
173
+ T2 --> V2[Kinetic Parameters]
174
+ U2 --> W2[Chemical Kinetics Output]
175
+
176
+ V2 --> X2[Chemical Kinetics Analysis]
177
+ W2 --> Y2[Chemical Kinetics Final Result]
178
+ X2 --> Z2[Chemical Kinetics Analysis Complete]
179
+
180
+ style A2 fill:#ff6b6b,color:#fff
181
+ style C2 fill:#ff6b6b,color:#fff
182
+ style E2 fill:#ff6b6b,color:#fff
183
+
184
+ style B2 fill:#ffd43b,color:#000
185
+ style D2 fill:#ffd43b,color:#000
186
+ style F2 fill:#ffd43b,color:#000
187
+ style G2 fill:#ffd43b,color:#000
188
+ style H2 fill:#ffd43b,color:#000
189
+ style I2 fill:#ffd43b,color:#000
190
+ style J2 fill:#ffd43b,color:#000
191
+ style K2 fill:#ffd43b,color:#000
192
+ style L2 fill:#ffd43b,color:#000
193
+ style M2 fill:#ffd43b,color:#000
194
+ style N2 fill:#ffd43b,color:#000
195
+ style O2 fill:#ffd43b,color:#000
196
+ style P2 fill:#ffd43b,color:#000
197
+ style Q2 fill:#ffd43b,color:#000
198
+ style R2 fill:#ffd43b,color:#000
199
+ style S2 fill:#ffd43b,color:#000
200
+ style T2 fill:#ffd43b,color:#000
201
+ style U2 fill:#ffd43b,color:#000
202
+ style V2 fill:#ffd43b,color:#000
203
+ style W2 fill:#ffd43b,color:#000
204
+ style X2 fill:#ffd43b,color:#000
205
+ style Y2 fill:#ffd43b,color:#000
206
+ style Z2 fill:#ffd43b,color:#000
207
+
208
+ style M2 fill:#51cf66,color:#fff
209
+ style N2 fill:#51cf66,color:#fff
210
+ style O2 fill:#51cf66,color:#fff
211
+ style P2 fill:#51cf66,color:#fff
212
+ style Q2 fill:#51cf66,color:#fff
213
+ style R2 fill:#51cf66,color:#fff
214
+ style S2 fill:#51cf66,color:#fff
215
+ style T2 fill:#51cf66,color:#fff
216
+ style U2 fill:#51cf66,color:#fff
217
+ style V2 fill:#51cf66,color:#fff
218
+ style W2 fill:#51cf66,color:#fff
219
+ style X2 fill:#51cf66,color:#fff
220
+ style Y2 fill:#51cf66,color:#fff
221
+ style Z2 fill:#51cf66,color:#fff
222
+
223
+ style Z2 fill:#b197fc,color:#fff
224
+ </div>
225
+
226
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
227
+ <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;">
228
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
229
+ </div>
230
+ <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;">
231
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Kinetic Methods
232
+ </div>
233
+ <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;">
234
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Kinetic Operations
235
+ </div>
236
+ <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;">
237
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
238
+ </div>
239
+ <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;">
240
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
241
+ </div>
242
+ </div>
243
+
244
+ <div class="figure-caption">
245
+ <strong>Figure 2.</strong> Chemical Kinetics Process. This physical chemistry process visualization demonstrates reaction rate analysis and mechanism determination. The flowchart shows reaction system inputs and concentration analysis, kinetic methods and rate laws, kinetic operations and calculations, intermediate results, and final chemical kinetics outputs.
246
+ </div>
247
+ </div>
248
+ </section>
249
+
250
+ <section class="process">
251
+ <h2>3. Spectroscopy Analysis Process</h2>
252
+ <div class="figure">
253
+ <div class="mermaid">
254
+ graph TD
255
+ A3[Sample Preparation] --> B3[Spectroscopic Method Selection]
256
+ C3[Energy Source] --> D3[Wavelength Selection]
257
+ E3[Detector Setup] --> F3[Signal Processing]
258
+
259
+ B3 --> G3[UV Visible Spectroscopy]
260
+ D3 --> H3[Infrared Spectroscopy]
261
+ F3 --> I3[Nuclear Magnetic Resonance]
262
+
263
+ G3 --> J3[Absorption Spectrum]
264
+ H3 --> K3[Vibrational Modes]
265
+ I3 --> L3[Chemical Shift Analysis]
266
+
267
+ J3 --> M3[Electronic Transitions]
268
+ K3 --> L3
269
+ L3 --> N3[Spin Spin Coupling]
270
+
271
+ M3 --> O3[Beer Lambert Law]
272
+ N3 --> P3[Peak Integration]
273
+ O3 --> Q3[Spectroscopic Analysis]
274
+
275
+ P3 --> R3[Peak Assignment]
276
+ Q3 --> S3[Concentration Determination]
277
+ R3 --> T3[Spectroscopy Result]
278
+
279
+ S3 --> U3[Spectroscopy Validation]
280
+ T3 --> V3[Spectroscopic Parameters]
281
+ U3 --> W3[Spectroscopy Output]
282
+
283
+ V3 --> X3[Spectroscopy Analysis]
284
+ W3 --> Y3[Spectroscopy Final Result]
285
+ X3 --> Z3[Spectroscopy Analysis Complete]
286
+
287
+ style A3 fill:#ff6b6b,color:#fff
288
+ style C3 fill:#ff6b6b,color:#fff
289
+ style E3 fill:#ff6b6b,color:#fff
290
+
291
+ style B3 fill:#ffd43b,color:#000
292
+ style D3 fill:#ffd43b,color:#000
293
+ style F3 fill:#ffd43b,color:#000
294
+ style G3 fill:#ffd43b,color:#000
295
+ style H3 fill:#ffd43b,color:#000
296
+ style I3 fill:#ffd43b,color:#000
297
+ style J3 fill:#ffd43b,color:#000
298
+ style K3 fill:#ffd43b,color:#000
299
+ style L3 fill:#ffd43b,color:#000
300
+ style M3 fill:#ffd43b,color:#000
301
+ style N3 fill:#ffd43b,color:#000
302
+ style O3 fill:#ffd43b,color:#000
303
+ style P3 fill:#ffd43b,color:#000
304
+ style Q3 fill:#ffd43b,color:#000
305
+ style R3 fill:#ffd43b,color:#000
306
+ style S3 fill:#ffd43b,color:#000
307
+ style T3 fill:#ffd43b,color:#000
308
+ style U3 fill:#ffd43b,color:#000
309
+ style V3 fill:#ffd43b,color:#000
310
+ style W3 fill:#ffd43b,color:#000
311
+ style X3 fill:#ffd43b,color:#000
312
+ style Y3 fill:#ffd43b,color:#000
313
+ style Z3 fill:#ffd43b,color:#000
314
+
315
+ style M3 fill:#51cf66,color:#fff
316
+ style N3 fill:#51cf66,color:#fff
317
+ style O3 fill:#51cf66,color:#fff
318
+ style P3 fill:#51cf66,color:#fff
319
+ style Q3 fill:#51cf66,color:#fff
320
+ style R3 fill:#51cf66,color:#fff
321
+ style S3 fill:#51cf66,color:#fff
322
+ style T3 fill:#51cf66,color:#fff
323
+ style U3 fill:#51cf66,color:#fff
324
+ style V3 fill:#51cf66,color:#fff
325
+ style W3 fill:#51cf66,color:#fff
326
+ style X3 fill:#51cf66,color:#fff
327
+ style Y3 fill:#51cf66,color:#fff
328
+ style Z3 fill:#51cf66,color:#fff
329
+
330
+ style Z3 fill:#b197fc,color:#fff
331
+ </div>
332
+
333
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
334
+ <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;">
335
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
336
+ </div>
337
+ <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;">
338
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Spectroscopic Methods
339
+ </div>
340
+ <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;">
341
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Spectroscopic Operations
342
+ </div>
343
+ <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;">
344
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
345
+ </div>
346
+ <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;">
347
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
348
+ </div>
349
+ </div>
350
+
351
+ <div class="figure-caption">
352
+ <strong>Figure 3.</strong> Spectroscopy Analysis Process. This physical chemistry process visualization demonstrates spectroscopic techniques and molecular analysis. The flowchart shows sample inputs and energy sources, spectroscopic methods and techniques, spectroscopic operations and analysis, intermediate results, and final spectroscopy analysis outputs.
353
+ </div>
354
+ </div>
355
+ </section>
356
+
357
+ <section class="navigation">
358
+ <h2>Navigation</h2>
359
+ <div class="nav-links">
360
+ <a href="chemistry_index.html" class="nav-link">← Back to Chemistry Index</a>
361
+ <a href="chemistry_batch_01.html" class="nav-link">← Previous: Organic Chemistry</a>
362
+ <a href="chemistry_batch_03.html" class="nav-link">Next: Analytical Chemistry →</a>
363
+ <a href="index.html" class="nav-link">Programming Framework Home</a>
364
+ </div>
365
+ </section>
366
+
367
+ <footer>
368
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
369
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
370
+ <div class="contact-info">
371
+ <p><strong>Gary Welz</strong></p>
372
+ <p>Retired Faculty Member</p>
373
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
374
+ <p>Borough of Manhattan Community College, CUNY</p>
375
+ <p>CUNY Graduate Center (New Media Lab)</p>
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+ <p>Email: gwelz@jjay.cuny.edu</p>
377
+ </div>
378
+ </footer>
379
+ </div>
380
+ </body>
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+ </html>
chemistry_index.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Chemistry - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
13
+ flowchart: {
14
+ useMaxWidth: false,
15
+ htmlLabels: true,
16
+ curve: 'linear',
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>⚗️ Chemistry - Programming Framework Analysis</h1>
28
+ <p class="subtitle">Systematic visualization of chemical processes and reaction mechanisms</p>
29
+ </header>
30
+
31
+ <section class="overview">
32
+ <h2>Chemistry Overview</h2>
33
+ <p>This collection demonstrates the Programming Framework's application to chemical processes across all major branches of chemistry. Each batch contains detailed flowcharts representing the computational logic and reaction mechanisms inherent in chemical operations.</p>
34
+
35
+ <div class="color-legend">
36
+ <h3>Universal Color Coding System</h3>
37
+ <div class="color-grid">
38
+ <div class="color-item">
39
+ <span class="color-box" style="background: #ff6b6b;"></span>
40
+ <span class="color-label">Red - Triggers & Inputs</span>
41
+ </div>
42
+ <div class="color-item">
43
+ <span class="color-box" style="background: #ffd43b;"></span>
44
+ <span class="color-label">Yellow - Structures & Objects</span>
45
+ </div>
46
+ <div class="color-item">
47
+ <span class="color-box" style="background: #51cf66;"></span>
48
+ <span class="color-label">Green - Processing & Operations</span>
49
+ </div>
50
+ <div class="color-item">
51
+ <span class="color-box" style="background: #74c0fc;"></span>
52
+ <span class="color-label">Blue - Intermediates & States</span>
53
+ </div>
54
+ <div class="color-item">
55
+ <span class="color-box" style="background: #b197fc;"></span>
56
+ <span class="color-label">Violet - Products & Outputs</span>
57
+ </div>
58
+ </div>
59
+ </div>
60
+ </section>
61
+
62
+ <section class="batch-navigation">
63
+ <h2>Chemistry Process Batches</h2>
64
+
65
+ <div class="batch-category">
66
+ <h3>🧪 Organic Chemistry</h3>
67
+ <div class="batch-links">
68
+ <a href="chemistry_batch_01.html" class="batch-link">
69
+ <span class="batch-number">Batch 01</span>
70
+ <span class="batch-title">Reaction Mechanisms & Synthesis</span>
71
+ <span class="batch-count">3 processes</span>
72
+ </a>
73
+ </div>
74
+ </div>
75
+
76
+ <div class="batch-category">
77
+ <h3>⚛️ Physical Chemistry</h3>
78
+ <div class="batch-links">
79
+ <a href="chemistry_batch_02.html" class="batch-link">
80
+ <span class="batch-number">Batch 02</span>
81
+ <span class="batch-title">Thermodynamics & Kinetics</span>
82
+ <span class="batch-count">3 processes</span>
83
+ </a>
84
+ </div>
85
+ </div>
86
+
87
+ <div class="batch-category">
88
+ <h3>🔬 Analytical Chemistry</h3>
89
+ <div class="batch-links">
90
+ <a href="chemistry_batch_03.html" class="batch-link">
91
+ <span class="batch-number">Batch 03</span>
92
+ <span class="batch-title">Spectroscopy & Chromatography</span>
93
+ <span class="batch-count">3 processes</span>
94
+ </a>
95
+ </div>
96
+ </div>
97
+
98
+ <div class="batch-category">
99
+ <h3>⚡ Inorganic Chemistry</h3>
100
+ <div class="batch-links">
101
+ <a href="chemistry_batch_04.html" class="batch-link">
102
+ <span class="batch-number">Batch 04</span>
103
+ <span class="batch-title">Coordination Chemistry & Catalysis</span>
104
+ <span class="batch-count">3 processes</span>
105
+ </a>
106
+ </div>
107
+ </div>
108
+
109
+ <div class="batch-category">
110
+ <h3>🧬 Biochemistry</h3>
111
+ <div class="batch-links">
112
+ <a href="chemistry_batch_05.html" class="batch-link">
113
+ <span class="batch-number">Batch 05</span>
114
+ <span class="batch-title">Enzyme Kinetics & Metabolism</span>
115
+ <span class="batch-count">3 processes</span>
116
+ </a>
117
+ </div>
118
+ </div>
119
+
120
+ <div class="batch-category">
121
+ <h3>🔋 Materials Chemistry</h3>
122
+ <div class="batch-links">
123
+ <a href="chemistry_batch_06.html" class="batch-link">
124
+ <span class="batch-number">Batch 06</span>
125
+ <span class="batch-title">Polymer Chemistry & Nanomaterials</span>
126
+ <span class="batch-count">3 processes</span>
127
+ </a>
128
+ </div>
129
+ </div>
130
+
131
+ <div class="batch-category">
132
+ <h3>🌍 Environmental Chemistry</h3>
133
+ <div class="batch-links">
134
+ <a href="chemistry_batch_07.html" class="batch-link">
135
+ <span class="batch-number">Batch 07</span>
136
+ <span class="batch-title">Atmospheric Chemistry & Green Chemistry</span>
137
+ <span class="batch-count">3 processes</span>
138
+ </a>
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="navigation">
144
+ <h2>Navigation</h2>
145
+ <div class="nav-links">
146
+ <a href="index.html" class="nav-link">← Back to Programming Framework</a>
147
+ <a href="mathematics_index.html" class="nav-link">Mathematics Processes</a>
148
+ <a href="computer_science_index.html" class="nav-link">Computer Science Processes</a>
149
+ <a href="physics_index.html" class="nav-link">Physics Processes</a>
150
+ <a href="https://huggingface.co/spaces/garywelz/glmp" class="nav-link" target="_blank">Biology Processes (GLMP)</a>
151
+ </div>
152
+ </section>
153
+
154
+ <footer>
155
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
156
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
157
+ <div class="contact-info">
158
+ <p><strong>Gary Welz</strong></p>
159
+ <p>Retired Faculty Member</p>
160
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
161
+ <p>Borough of Manhattan Community College, CUNY</p>
162
+ <p>CUNY Graduate Center (New Media Lab)</p>
163
+ <p>Email: gwelz@jjay.cuny.edu</p>
164
+ </div>
165
+ </footer>
166
+ </div>
167
+ </body>
168
+ </html>
computer_science_batch_01.html ADDED
@@ -0,0 +1,380 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Computer Science Batch 01 - Algorithms & Data Structures - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
13
+ flowchart: {
14
+ useMaxWidth: false,
15
+ htmlLabels: true,
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+ curve: 'linear',
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+ nodeSpacing: 30,
18
+ rankSpacing: 30,
19
+ padding: 10
20
+ }
21
+ });
22
+ </script>
23
+ </head>
24
+ <body>
25
+ <div class="container">
26
+ <header>
27
+ <h1>🔧 Computer Science Batch 01 - Algorithms & Data Structures</h1>
28
+ <p class="subtitle">Sorting Algorithms, Graph Algorithms, and Dynamic Programming</p>
29
+ </header>
30
+
31
+ <section class="batch-info">
32
+ <h2>Algorithms & Data Structures Processes</h2>
33
+ <p>This batch demonstrates the Programming Framework's application to fundamental algorithmic operations. Each process shows the computational logic behind sorting algorithms, graph traversal, and dynamic programming solutions.</p>
34
+ </section>
35
+
36
+ <section class="process">
37
+ <h2>1. Sorting Algorithms Process</h2>
38
+ <div class="figure">
39
+ <div class="mermaid">
40
+ graph TD
41
+ A1[Input Array] --> B1[Algorithm Selection]
42
+ C1[Array Analysis] --> D1[Complexity Analysis]
43
+ E1[Memory Constraints] --> F1[Optimization Strategy]
44
+
45
+ B1 --> G1[Comparison Based Sorting]
46
+ D1 --> H1[Time Complexity O n squared]
47
+ F1 --> I1[Space Complexity Analysis]
48
+
49
+ G1 --> J1[Bubble Sort Algorithm]
50
+ H1 --> K1[Quick Sort Algorithm]
51
+ I1 --> L1[Merge Sort Algorithm]
52
+
53
+ J1 --> M1[Adjacent Element Comparison]
54
+ K1 --> L1
55
+ L1 --> N1[Divide and Conquer]
56
+
57
+ M1 --> O1[Element Swapping]
58
+ N1 --> P1[Pivot Selection]
59
+ O1 --> Q1[Sorting Process]
60
+
61
+ P1 --> R1[Partitioning Strategy]
62
+ Q1 --> S1[Recursive Sorting]
63
+ R1 --> T1[Sorting Algorithm Result]
64
+
65
+ S1 --> U1[Algorithm Validation]
66
+ T1 --> V1[Sorted Array Output]
67
+ U1 --> W1[Sorting Algorithm Output]
68
+
69
+ V1 --> X1[Sorting Algorithm Analysis]
70
+ W1 --> Y1[Sorting Algorithm Final Result]
71
+ X1 --> Z1[Sorting Algorithm Analysis Complete]
72
+
73
+ style A1 fill:#ff6b6b,color:#fff
74
+ style C1 fill:#ff6b6b,color:#fff
75
+ style E1 fill:#ff6b6b,color:#fff
76
+
77
+ style B1 fill:#ffd43b,color:#000
78
+ style D1 fill:#ffd43b,color:#000
79
+ style F1 fill:#ffd43b,color:#000
80
+ style G1 fill:#ffd43b,color:#000
81
+ style H1 fill:#ffd43b,color:#000
82
+ style I1 fill:#ffd43b,color:#000
83
+ style J1 fill:#ffd43b,color:#000
84
+ style K1 fill:#ffd43b,color:#000
85
+ style L1 fill:#ffd43b,color:#000
86
+ style M1 fill:#ffd43b,color:#000
87
+ style N1 fill:#ffd43b,color:#000
88
+ style O1 fill:#ffd43b,color:#000
89
+ style P1 fill:#ffd43b,color:#000
90
+ style Q1 fill:#ffd43b,color:#000
91
+ style R1 fill:#ffd43b,color:#000
92
+ style S1 fill:#ffd43b,color:#000
93
+ style T1 fill:#ffd43b,color:#000
94
+ style U1 fill:#ffd43b,color:#000
95
+ style V1 fill:#ffd43b,color:#000
96
+ style W1 fill:#ffd43b,color:#000
97
+ style X1 fill:#ffd43b,color:#000
98
+ style Y1 fill:#ffd43b,color:#000
99
+ style Z1 fill:#ffd43b,color:#000
100
+
101
+ style M1 fill:#51cf66,color:#fff
102
+ style N1 fill:#51cf66,color:#fff
103
+ style O1 fill:#51cf66,color:#fff
104
+ style P1 fill:#51cf66,color:#fff
105
+ style Q1 fill:#51cf66,color:#fff
106
+ style R1 fill:#51cf66,color:#fff
107
+ style S1 fill:#51cf66,color:#fff
108
+ style T1 fill:#51cf66,color:#fff
109
+ style U1 fill:#51cf66,color:#fff
110
+ style V1 fill:#51cf66,color:#fff
111
+ style W1 fill:#51cf66,color:#fff
112
+ style X1 fill:#51cf66,color:#fff
113
+ style Y1 fill:#51cf66,color:#fff
114
+ style Z1 fill:#51cf66,color:#fff
115
+
116
+ style Z1 fill:#b197fc,color:#fff
117
+ </div>
118
+
119
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
120
+ <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;">
121
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
122
+ </div>
123
+ <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;">
124
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Algorithm Methods
125
+ </div>
126
+ <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;">
127
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Sorting Operations
128
+ </div>
129
+ <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;">
130
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
131
+ </div>
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:#b197fc;"></span>Products
134
+ </div>
135
+ </div>
136
+
137
+ <div class="figure-caption">
138
+ <strong>Figure 1.</strong> Sorting Algorithms Process. This computer science process visualization demonstrates comparison-based sorting algorithms. The flowchart shows input array and complexity analysis, algorithm methods and selection, sorting operations and comparisons, intermediate results, and final sorted array outputs.
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="process">
144
+ <h2>2. Graph Algorithms Process</h2>
145
+ <div class="figure">
146
+ <div class="mermaid">
147
+ graph TD
148
+ A2[Graph Representation] --> B2[Graph Type Analysis]
149
+ C2[Vertex Edge Analysis] --> D2[Traversal Strategy]
150
+ E2[Path Finding] --> F2[Algorithm Selection]
151
+
152
+ B2 --> G2[Directed Graph]
153
+ D2 --> H2[Undirected Graph]
154
+ F2 --> I2[Weighted Graph]
155
+
156
+ G2 --> J2[Depth First Search]
157
+ H2 --> K2[Breadth First Search]
158
+ I2 --> L2[Dijkstra Algorithm]
159
+
160
+ J2 --> M2[Stack Based Traversal]
161
+ K2 --> L2
162
+ L2 --> N2[Queue Based Traversal]
163
+
164
+ M2 --> O2[Priority Queue]
165
+ N2 --> P2[Shortest Path]
166
+ O2 --> Q2[Graph Algorithm Process]
167
+
168
+ P2 --> R2[Minimum Spanning Tree]
169
+ Q2 --> S2[Topological Sorting]
170
+ R2 --> T2[Graph Algorithm Result]
171
+
172
+ S2 --> U2[Algorithm Validation]
173
+ T2 --> V2[Graph Analysis Output]
174
+ U2 --> W2[Graph Algorithm Output]
175
+
176
+ V2 --> X2[Graph Algorithm Analysis]
177
+ W2 --> Y2[Graph Algorithm Final Result]
178
+ X2 --> Z2[Graph Algorithm Analysis Complete]
179
+
180
+ style A2 fill:#ff6b6b,color:#fff
181
+ style C2 fill:#ff6b6b,color:#fff
182
+ style E2 fill:#ff6b6b,color:#fff
183
+
184
+ style B2 fill:#ffd43b,color:#000
185
+ style D2 fill:#ffd43b,color:#000
186
+ style F2 fill:#ffd43b,color:#000
187
+ style G2 fill:#ffd43b,color:#000
188
+ style H2 fill:#ffd43b,color:#000
189
+ style I2 fill:#ffd43b,color:#000
190
+ style J2 fill:#ffd43b,color:#000
191
+ style K2 fill:#ffd43b,color:#000
192
+ style L2 fill:#ffd43b,color:#000
193
+ style M2 fill:#ffd43b,color:#000
194
+ style N2 fill:#ffd43b,color:#000
195
+ style O2 fill:#ffd43b,color:#000
196
+ style P2 fill:#ffd43b,color:#000
197
+ style Q2 fill:#ffd43b,color:#000
198
+ style R2 fill:#ffd43b,color:#000
199
+ style S2 fill:#ffd43b,color:#000
200
+ style T2 fill:#ffd43b,color:#000
201
+ style U2 fill:#ffd43b,color:#000
202
+ style V2 fill:#ffd43b,color:#000
203
+ style W2 fill:#ffd43b,color:#000
204
+ style X2 fill:#ffd43b,color:#000
205
+ style Y2 fill:#ffd43b,color:#000
206
+ style Z2 fill:#ffd43b,color:#000
207
+
208
+ style M2 fill:#51cf66,color:#fff
209
+ style N2 fill:#51cf66,color:#fff
210
+ style O2 fill:#51cf66,color:#fff
211
+ style P2 fill:#51cf66,color:#fff
212
+ style Q2 fill:#51cf66,color:#fff
213
+ style R2 fill:#51cf66,color:#fff
214
+ style S2 fill:#51cf66,color:#fff
215
+ style T2 fill:#51cf66,color:#fff
216
+ style U2 fill:#51cf66,color:#fff
217
+ style V2 fill:#51cf66,color:#fff
218
+ style W2 fill:#51cf66,color:#fff
219
+ style X2 fill:#51cf66,color:#fff
220
+ style Y2 fill:#51cf66,color:#fff
221
+ style Z2 fill:#51cf66,color:#fff
222
+
223
+ style Z2 fill:#b197fc,color:#fff
224
+ </div>
225
+
226
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
227
+ <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;">
228
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
229
+ </div>
230
+ <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;">
231
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Graph Methods
232
+ </div>
233
+ <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;">
234
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Traversal Operations
235
+ </div>
236
+ <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;">
237
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
238
+ </div>
239
+ <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;">
240
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
241
+ </div>
242
+ </div>
243
+
244
+ <div class="figure-caption">
245
+ <strong>Figure 2.</strong> Graph Algorithms Process. This computer science process visualization demonstrates graph traversal and path finding algorithms. The flowchart shows graph representation and vertex analysis, graph methods and traversal strategies, traversal operations and path finding, intermediate results, and final graph algorithm outputs.
246
+ </div>
247
+ </div>
248
+ </section>
249
+
250
+ <section class="process">
251
+ <h2>3. Dynamic Programming Process</h2>
252
+ <div class="figure">
253
+ <div class="mermaid">
254
+ graph TD
255
+ A3[Problem Analysis] --> B3[Optimal Substructure]
256
+ C3[Overlapping Subproblems] --> D3[Recursive Formulation]
257
+ E3[Memoization Strategy] --> F3[Tabulation Method]
258
+
259
+ B3 --> G3[Subproblem Identification]
260
+ D3 --> H3[Recursive Solution]
261
+ F3 --> I3[Bottom Up Approach]
262
+
263
+ G3 --> J3[State Definition]
264
+ H3 --> K3[Top Down Approach]
265
+ I3 --> L3[Table Construction]
266
+
267
+ J3 --> M3[Transition Function]
268
+ K3 --> L3
269
+ L3 --> N3[Space Optimization]
270
+
271
+ M3 --> O3[Base Case Definition]
272
+ N3 --> P3[Time Complexity]
273
+ O3 --> Q3[Dynamic Programming Process]
274
+
275
+ P3 --> R3[Space Complexity]
276
+ Q3 --> S3[Solution Reconstruction]
277
+ R3 --> T3[Dynamic Programming Result]
278
+
279
+ S3 --> U3[Algorithm Validation]
280
+ T3 --> V3[Optimal Solution]
281
+ U3 --> W3[Dynamic Programming Output]
282
+
283
+ V3 --> X3[Dynamic Programming Analysis]
284
+ W3 --> Y3[Dynamic Programming Final Result]
285
+ X3 --> Z3[Dynamic Programming Analysis Complete]
286
+
287
+ style A3 fill:#ff6b6b,color:#fff
288
+ style C3 fill:#ff6b6b,color:#fff
289
+ style E3 fill:#ff6b6b,color:#fff
290
+
291
+ style B3 fill:#ffd43b,color:#000
292
+ style D3 fill:#ffd43b,color:#000
293
+ style F3 fill:#ffd43b,color:#000
294
+ style G3 fill:#ffd43b,color:#000
295
+ style H3 fill:#ffd43b,color:#000
296
+ style I3 fill:#ffd43b,color:#000
297
+ style J3 fill:#ffd43b,color:#000
298
+ style K3 fill:#ffd43b,color:#000
299
+ style L3 fill:#ffd43b,color:#000
300
+ style M3 fill:#ffd43b,color:#000
301
+ style N3 fill:#ffd43b,color:#000
302
+ style O3 fill:#ffd43b,color:#000
303
+ style P3 fill:#ffd43b,color:#000
304
+ style Q3 fill:#ffd43b,color:#000
305
+ style R3 fill:#ffd43b,color:#000
306
+ style S3 fill:#ffd43b,color:#000
307
+ style T3 fill:#ffd43b,color:#000
308
+ style U3 fill:#ffd43b,color:#000
309
+ style V3 fill:#ffd43b,color:#000
310
+ style W3 fill:#ffd43b,color:#000
311
+ style X3 fill:#ffd43b,color:#000
312
+ style Y3 fill:#ffd43b,color:#000
313
+ style Z3 fill:#ffd43b,color:#000
314
+
315
+ style M3 fill:#51cf66,color:#fff
316
+ style N3 fill:#51cf66,color:#fff
317
+ style O3 fill:#51cf66,color:#fff
318
+ style P3 fill:#51cf66,color:#fff
319
+ style Q3 fill:#51cf66,color:#fff
320
+ style R3 fill:#51cf66,color:#fff
321
+ style S3 fill:#51cf66,color:#fff
322
+ style T3 fill:#51cf66,color:#fff
323
+ style U3 fill:#51cf66,color:#fff
324
+ style V3 fill:#51cf66,color:#fff
325
+ style W3 fill:#51cf66,color:#fff
326
+ style X3 fill:#51cf66,color:#fff
327
+ style Y3 fill:#51cf66,color:#fff
328
+ style Z3 fill:#51cf66,color:#fff
329
+
330
+ style Z3 fill:#b197fc,color:#fff
331
+ </div>
332
+
333
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
334
+ <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;">
335
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
336
+ </div>
337
+ <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;">
338
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Dynamic Programming Methods
339
+ </div>
340
+ <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;">
341
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Optimization Operations
342
+ </div>
343
+ <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;">
344
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
345
+ </div>
346
+ <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;">
347
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
348
+ </div>
349
+ </div>
350
+
351
+ <div class="figure-caption">
352
+ <strong>Figure 3.</strong> Dynamic Programming Process. This computer science process visualization demonstrates optimal substructure and overlapping subproblems. The flowchart shows problem analysis and subproblem identification, dynamic programming methods and strategies, optimization operations and solution construction, intermediate results, and final dynamic programming outputs.
353
+ </div>
354
+ </div>
355
+ </section>
356
+
357
+ <section class="navigation">
358
+ <h2>Navigation</h2>
359
+ <div class="nav-links">
360
+ <a href="computer_science_index.html" class="nav-link">← Back to Computer Science Index</a>
361
+ <a href="computer_science_batch_02.html" class="nav-link">Next: Software Engineering →</a>
362
+ <a href="index.html" class="nav-link">Programming Framework Home</a>
363
+ </div>
364
+ </section>
365
+
366
+ <footer>
367
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
368
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
369
+ <div class="contact-info">
370
+ <p><strong>Gary Welz</strong></p>
371
+ <p>Retired Faculty Member</p>
372
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
373
+ <p>Borough of Manhattan Community College, CUNY</p>
374
+ <p>CUNY Graduate Center (New Media Lab)</p>
375
+ <p>Email: gwelz@jjay.cuny.edu</p>
376
+ </div>
377
+ </footer>
378
+ </div>
379
+ </body>
380
+ </html>
computer_science_index.html ADDED
@@ -0,0 +1,168 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Computer Science - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
13
+ flowchart: {
14
+ useMaxWidth: false,
15
+ htmlLabels: true,
16
+ curve: 'linear',
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>💻 Computer Science - Programming Framework Analysis</h1>
28
+ <p class="subtitle">Systematic visualization of algorithms and computational processes</p>
29
+ </header>
30
+
31
+ <section class="overview">
32
+ <h2>Computer Science Overview</h2>
33
+ <p>This collection demonstrates the Programming Framework's application to computational processes across all major branches of computer science. Each batch contains detailed flowcharts representing the computational logic and algorithmic patterns inherent in software systems.</p>
34
+
35
+ <div class="color-legend">
36
+ <h3>Universal Color Coding System</h3>
37
+ <div class="color-grid">
38
+ <div class="color-item">
39
+ <span class="color-box" style="background: #ff6b6b;"></span>
40
+ <span class="color-label">Red - Triggers & Inputs</span>
41
+ </div>
42
+ <div class="color-item">
43
+ <span class="color-box" style="background: #ffd43b;"></span>
44
+ <span class="color-label">Yellow - Structures & Objects</span>
45
+ </div>
46
+ <div class="color-item">
47
+ <span class="color-box" style="background: #51cf66;"></span>
48
+ <span class="color-label">Green - Processing & Operations</span>
49
+ </div>
50
+ <div class="color-item">
51
+ <span class="color-box" style="background: #74c0fc;"></span>
52
+ <span class="color-label">Blue - Intermediates & States</span>
53
+ </div>
54
+ <div class="color-item">
55
+ <span class="color-box" style="background: #b197fc;"></span>
56
+ <span class="color-label">Violet - Products & Outputs</span>
57
+ </div>
58
+ </div>
59
+ </div>
60
+ </section>
61
+
62
+ <section class="batch-navigation">
63
+ <h2>Computer Science Process Batches</h2>
64
+
65
+ <div class="batch-category">
66
+ <h3>🔧 Algorithms & Data Structures</h3>
67
+ <div class="batch-links">
68
+ <a href="computer_science_batch_01.html" class="batch-link">
69
+ <span class="batch-number">Batch 01</span>
70
+ <span class="batch-title">Sorting Algorithms & Graph Algorithms</span>
71
+ <span class="batch-count">3 processes</span>
72
+ </a>
73
+ </div>
74
+ </div>
75
+
76
+ <div class="batch-category">
77
+ <h3>🏗️ Software Engineering</h3>
78
+ <div class="batch-links">
79
+ <a href="computer_science_batch_02.html" class="batch-link">
80
+ <span class="batch-number">Batch 02</span>
81
+ <span class="batch-title">Design Patterns & Architecture</span>
82
+ <span class="batch-count">3 processes</span>
83
+ </a>
84
+ </div>
85
+ </div>
86
+
87
+ <div class="batch-category">
88
+ <h3>🤖 Artificial Intelligence</h3>
89
+ <div class="batch-links">
90
+ <a href="computer_science_batch_03.html" class="batch-link">
91
+ <span class="batch-number">Batch 03</span>
92
+ <span class="batch-title">Machine Learning & Neural Networks</span>
93
+ <span class="batch-count">3 processes</span>
94
+ </a>
95
+ </div>
96
+ </div>
97
+
98
+ <div class="batch-category">
99
+ <h3>🔐 Computer Security</h3>
100
+ <div class="batch-links">
101
+ <a href="computer_science_batch_04.html" class="batch-link">
102
+ <span class="batch-number">Batch 04</span>
103
+ <span class="batch-title">Cryptography & Network Security</span>
104
+ <span class="batch-count">3 processes</span>
105
+ </a>
106
+ </div>
107
+ </div>
108
+
109
+ <div class="batch-category">
110
+ <h3>🌐 Computer Networks</h3>
111
+ <div class="batch-links">
112
+ <a href="computer_science_batch_05.html" class="batch-link">
113
+ <span class="batch-number">Batch 05</span>
114
+ <span class="batch-title">Protocols & Distributed Systems</span>
115
+ <span class="batch-count">3 processes</span>
116
+ </a>
117
+ </div>
118
+ </div>
119
+
120
+ <div class="batch-category">
121
+ <h3>💾 Database Systems</h3>
122
+ <div class="batch-links">
123
+ <a href="computer_science_batch_06.html" class="batch-link">
124
+ <span class="batch-number">Batch 06</span>
125
+ <span class="batch-title">Query Processing & Transaction Management</span>
126
+ <span class="batch-count">3 processes</span>
127
+ </a>
128
+ </div>
129
+ </div>
130
+
131
+ <div class="batch-category">
132
+ <h3>🎮 Computer Graphics</h3>
133
+ <div class="batch-links">
134
+ <a href="computer_science_batch_07.html" class="batch-link">
135
+ <span class="batch-number">Batch 07</span>
136
+ <span class="batch-title">Rendering & Game Development</span>
137
+ <span class="batch-count">3 processes</span>
138
+ </a>
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="navigation">
144
+ <h2>Navigation</h2>
145
+ <div class="nav-links">
146
+ <a href="index.html" class="nav-link">← Back to Programming Framework</a>
147
+ <a href="mathematics_index.html" class="nav-link">Mathematics Processes</a>
148
+ <a href="chemistry_index.html" class="nav-link">Chemistry Processes</a>
149
+ <a href="physics_index.html" class="nav-link">Physics Processes</a>
150
+ <a href="https://huggingface.co/spaces/garywelz/glmp" class="nav-link" target="_blank">Biology Processes (GLMP)</a>
151
+ </div>
152
+ </section>
153
+
154
+ <footer>
155
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
156
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
157
+ <div class="contact-info">
158
+ <p><strong>Gary Welz</strong></p>
159
+ <p>Retired Faculty Member</p>
160
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
161
+ <p>Borough of Manhattan Community College, CUNY</p>
162
+ <p>CUNY Graduate Center (New Media Lab)</p>
163
+ <p>Email: gwelz@jjay.cuny.edu</p>
164
+ </div>
165
+ </footer>
166
+ </div>
167
+ </body>
168
+ </html>
index.html CHANGED
@@ -306,6 +306,46 @@
306
  </div>
307
  </div>
308
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
309
  <div class="resources">
310
  <h2>Key Resources & Documentation</h2>
311
  <div class="resource-grid">
@@ -318,31 +358,31 @@
318
  <div class="resource-card">
319
  <h3>🧬 Biology</h3>
320
  <p>Biological system analysis with GLMP integration</p>
321
- <a href="biology_processes.html">Explore Biology</a>
322
  </div>
323
 
324
  <div class="resource-card">
325
  <h3>⚗️ Chemistry</h3>
326
  <p>Chemical reaction mechanisms and visualizations</p>
327
- <a href="chemistry_processes.html">Explore Chemistry</a>
328
  </div>
329
 
330
  <div class="resource-card">
331
  <h3>💻 Computer Science</h3>
332
  <p>Algorithm and computational analysis</p>
333
- <a href="computer_science_processes.html">Explore CS</a>
334
  </div>
335
 
336
  <div class="resource-card">
337
  <h3>⚛️ Physics</h3>
338
  <p>Physical system dynamics and quantum processes</p>
339
- <a href="physics_processes.html">Explore Physics</a>
340
  </div>
341
 
342
  <div class="resource-card">
343
  <h3>📐 Mathematics</h3>
344
  <p>Mathematical proof and calculation processes</p>
345
- <a href="mathematics_processes.html">Explore Math</a>
346
  </div>
347
 
348
  <div class="resource-card">
 
306
  </div>
307
  </div>
308
 
309
+ <div class="batch-status">
310
+ <h2>📊 Batch Architecture Status</h2>
311
+ <div class="status-grid">
312
+ <div class="status-card complete">
313
+ <h3>📐 Mathematics</h3>
314
+ <p><strong>Status:</strong> Complete ✅</p>
315
+ <p><strong>Batches:</strong> 7/7 (21 processes)</p>
316
+ <p>Number Theory, Analysis & Calculus, Abstract Algebra, Geometry & Topology, Applied Mathematics, Discrete Mathematics, Historical & Educational</p>
317
+ </div>
318
+
319
+ <div class="status-card in-progress">
320
+ <h3>⚗️ Chemistry</h3>
321
+ <p><strong>Status:</strong> In Progress 🔄</p>
322
+ <p><strong>Batches:</strong> 2/7 (6 processes)</p>
323
+ <p>Organic Chemistry, Physical Chemistry, Analytical Chemistry, Inorganic Chemistry, Biochemistry, Materials Chemistry, Environmental Chemistry</p>
324
+ </div>
325
+
326
+ <div class="status-card in-progress">
327
+ <h3>💻 Computer Science</h3>
328
+ <p><strong>Status:</strong> In Progress 🔄</p>
329
+ <p><strong>Batches:</strong> 1/7 (3 processes)</p>
330
+ <p>Algorithms & Data Structures, Software Engineering, Artificial Intelligence, Computer Security, Computer Networks, Database Systems, Computer Graphics</p>
331
+ </div>
332
+
333
+ <div class="status-card in-progress">
334
+ <h3>⚛️ Physics</h3>
335
+ <p><strong>Status:</strong> In Progress 🔄</p>
336
+ <p><strong>Batches:</strong> 1/7 (3 processes)</p>
337
+ <p>Classical Mechanics, Electromagnetism, Thermodynamics, Quantum Mechanics, Relativity, Astrophysics, Particle Physics</p>
338
+ </div>
339
+
340
+ <div class="status-card external">
341
+ <h3>🧬 Biology</h3>
342
+ <p><strong>Status:</strong> External GLMP ✅</p>
343
+ <p><strong>Location:</strong> Hugging Face Space</p>
344
+ <p>Comprehensive biological systems analysis with genome logic modeling and metabolic pathway visualization</p>
345
+ </div>
346
+ </div>
347
+ </div>
348
+
349
  <div class="resources">
350
  <h2>Key Resources & Documentation</h2>
351
  <div class="resource-grid">
 
358
  <div class="resource-card">
359
  <h3>🧬 Biology</h3>
360
  <p>Biological system analysis with GLMP integration</p>
361
+ <a href="https://huggingface.co/spaces/garywelz/glmp" target="_blank">Explore Biology (GLMP)</a>
362
  </div>
363
 
364
  <div class="resource-card">
365
  <h3>⚗️ Chemistry</h3>
366
  <p>Chemical reaction mechanisms and visualizations</p>
367
+ <a href="chemistry_index.html">Explore Chemistry</a>
368
  </div>
369
 
370
  <div class="resource-card">
371
  <h3>💻 Computer Science</h3>
372
  <p>Algorithm and computational analysis</p>
373
+ <a href="computer_science_index.html">Explore CS</a>
374
  </div>
375
 
376
  <div class="resource-card">
377
  <h3>⚛️ Physics</h3>
378
  <p>Physical system dynamics and quantum processes</p>
379
+ <a href="physics_index.html">Explore Physics</a>
380
  </div>
381
 
382
  <div class="resource-card">
383
  <h3>📐 Mathematics</h3>
384
  <p>Mathematical proof and calculation processes</p>
385
+ <a href="mathematics_index.html">Explore Math</a>
386
  </div>
387
 
388
  <div class="resource-card">
mathematics_batch_01.html ADDED
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+ <!DOCTYPE html>
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+ <html lang="en">
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+ <head>
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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>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
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+ <script>
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+ mermaid.initialize({
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+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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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>
23
+ </head>
24
+ <body>
25
+ <div class="container">
26
+ <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]
47
+ F1 --> I1[Factorization Method Selection]
48
+
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
82
+ style C1 fill:#ff6b6b,color:#fff
83
+ style E1 fill:#ff6b6b,color:#fff
84
+
85
+ style B1 fill:#ffd43b,color:#000
86
+ style D1 fill:#ffd43b,color:#000
87
+ style F1 fill:#ffd43b,color:#000
88
+ style G1 fill:#ffd43b,color:#000
89
+ style H1 fill:#ffd43b,color:#000
90
+ style I1 fill:#ffd43b,color:#000
91
+ style J1 fill:#ffd43b,color:#000
92
+ style K1 fill:#ffd43b,color:#000
93
+ style L1 fill:#ffd43b,color:#000
94
+ style M1 fill:#ffd43b,color:#000
95
+ style N1 fill:#ffd43b,color:#000
96
+ style O1 fill:#ffd43b,color:#000
97
+ style P1 fill:#ffd43b,color:#000
98
+ style Q1 fill:#ffd43b,color:#000
99
+ style R1 fill:#ffd43b,color:#000
100
+ style S1 fill:#ffd43b,color:#000
101
+ style T1 fill:#ffd43b,color:#000
102
+ style U1 fill:#ffd43b,color:#000
103
+ style V1 fill:#ffd43b,color:#000
104
+ style W1 fill:#ffd43b,color:#000
105
+ style X1 fill:#ffd43b,color:#000
106
+ style Y1 fill:#ffd43b,color:#000
107
+ style Z1 fill:#ffd43b,color:#000
108
+ style AA1 fill:#ffd43b,color:#000
109
+ style BB1 fill:#ffd43b,color:#000
110
+ style CC1 fill:#ffd43b,color:#000
111
+ style DD1 fill:#ffd43b,color:#000
112
+ style EE1 fill:#ffd43b,color:#000
113
+ style FF1 fill:#ffd43b,color:#000
114
+ style GG1 fill:#ffd43b,color:#000
115
+
116
+ style M1 fill:#51cf66,color:#fff
117
+ style N1 fill:#51cf66,color:#fff
118
+ style O1 fill:#51cf66,color:#fff
119
+ style P1 fill:#51cf66,color:#fff
120
+ style Q1 fill:#51cf66,color:#fff
121
+ style R1 fill:#51cf66,color:#fff
122
+ style S1 fill:#51cf66,color:#fff
123
+ style T1 fill:#51cf66,color:#fff
124
+ style U1 fill:#51cf66,color:#fff
125
+ style V1 fill:#51cf66,color:#fff
126
+ style W1 fill:#51cf66,color:#fff
127
+ style X1 fill:#51cf66,color:#fff
128
+ style Y1 fill:#51cf66,color:#fff
129
+ style Z1 fill:#51cf66,color:#fff
130
+ style AA1 fill:#51cf66,color:#fff
131
+ style BB1 fill:#51cf66,color:#fff
132
+ style CC1 fill:#51cf66,color:#fff
133
+ style DD1 fill:#51cf66,color:#fff
134
+ style EE1 fill:#51cf66,color:#fff
135
+ style FF1 fill:#51cf66,color:#fff
136
+ style GG1 fill:#51cf66,color:#fff
137
+
138
+ style BB1 fill:#b197fc,color:#fff
139
+ style CC1 fill:#b197fc,color:#fff
140
+ style DD1 fill:#b197fc,color:#fff
141
+ style EE1 fill:#b197fc,color:#fff
142
+ style FF1 fill:#b197fc,color:#fff
143
+ style GG1 fill:#b197fc,color:#fff
144
+ </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
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:#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
216
+ style C2 fill:#ff6b6b,color:#fff
217
+ style E2 fill:#ff6b6b,color:#fff
218
+
219
+ style B2 fill:#ffd43b,color:#000
220
+ style D2 fill:#ffd43b,color:#000
221
+ style F2 fill:#ffd43b,color:#000
222
+ style G2 fill:#ffd43b,color:#000
223
+ style H2 fill:#ffd43b,color:#000
224
+ style I2 fill:#ffd43b,color:#000
225
+ style J2 fill:#ffd43b,color:#000
226
+ style K2 fill:#ffd43b,color:#000
227
+ style L2 fill:#ffd43b,color:#000
228
+ style M2 fill:#ffd43b,color:#000
229
+ style N2 fill:#ffd43b,color:#000
230
+ style O2 fill:#ffd43b,color:#000
231
+ style P2 fill:#ffd43b,color:#000
232
+ style Q2 fill:#ffd43b,color:#000
233
+ style R2 fill:#ffd43b,color:#000
234
+ style S2 fill:#ffd43b,color:#000
235
+ style T2 fill:#ffd43b,color:#000
236
+ style U2 fill:#ffd43b,color:#000
237
+ style V2 fill:#ffd43b,color:#000
238
+ style W2 fill:#ffd43b,color:#000
239
+ style X2 fill:#ffd43b,color:#000
240
+ style Y2 fill:#ffd43b,color:#000
241
+ style Z2 fill:#ffd43b,color:#000
242
+ style AA2 fill:#ffd43b,color:#000
243
+ style BB2 fill:#ffd43b,color:#000
244
+ style CC2 fill:#ffd43b,color:#000
245
+ style DD2 fill:#ffd43b,color:#000
246
+ style EE2 fill:#ffd43b,color:#000
247
+ style FF2 fill:#ffd43b,color:#000
248
+ style GG2 fill:#ffd43b,color:#000
249
+
250
+ style M2 fill:#51cf66,color:#fff
251
+ style N2 fill:#51cf66,color:#fff
252
+ style O2 fill:#51cf66,color:#fff
253
+ style P2 fill:#51cf66,color:#fff
254
+ style Q2 fill:#51cf66,color:#fff
255
+ style R2 fill:#51cf66,color:#fff
256
+ style S2 fill:#51cf66,color:#fff
257
+ style T2 fill:#51cf66,color:#fff
258
+ style U2 fill:#51cf66,color:#fff
259
+ style V2 fill:#51cf66,color:#fff
260
+ style W2 fill:#51cf66,color:#fff
261
+ style X2 fill:#51cf66,color:#fff
262
+ style Y2 fill:#51cf66,color:#fff
263
+ style Z2 fill:#51cf66,color:#fff
264
+ style AA2 fill:#51cf66,color:#fff
265
+ style BB2 fill:#51cf66,color:#fff
266
+ style CC2 fill:#51cf66,color:#fff
267
+ style DD2 fill:#51cf66,color:#fff
268
+ style EE2 fill:#51cf66,color:#fff
269
+ style FF2 fill:#51cf66,color:#fff
270
+ style GG2 fill:#51cf66,color:#fff
271
+
272
+ style EE2 fill:#b197fc,color:#fff
273
+ style FF2 fill:#b197fc,color:#fff
274
+ style GG2 fill:#b197fc,color:#fff
275
+ </div>
276
+
277
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
278
+ <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;">
279
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
280
+ </div>
281
+ <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;">
282
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Modular Arithmetic Methods
283
+ </div>
284
+ <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;">
285
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Modular Operations
286
+ </div>
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:#74c0fc;"></span>Intermediates
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:#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]
340
+ AA3 --> CC3[Final Solution Display]
341
+
342
+ style A3 fill:#ff6b6b,color:#fff
343
+ style C3 fill:#ff6b6b,color:#fff
344
+ style E3 fill:#ff6b6b,color:#fff
345
+
346
+ style B3 fill:#ffd43b,color:#000
347
+ style D3 fill:#ffd43b,color:#000
348
+ style F3 fill:#ffd43b,color:#000
349
+ style G3 fill:#ffd43b,color:#000
350
+ style H3 fill:#ffd43b,color:#000
351
+ style I3 fill:#ffd43b,color:#000
352
+ style J3 fill:#ffd43b,color:#000
353
+ style K3 fill:#ffd43b,color:#000
354
+ style L3 fill:#ffd43b,color:#000
355
+ style M3 fill:#ffd43b,color:#000
356
+ style N3 fill:#ffd43b,color:#000
357
+ style O3 fill:#ffd43b,color:#000
358
+ style P3 fill:#ffd43b,color:#000
359
+ style Q3 fill:#ffd43b,color:#000
360
+ style R3 fill:#ffd43b,color:#000
361
+ style S3 fill:#ffd43b,color:#000
362
+ style T3 fill:#ffd43b,color:#000
363
+ style U3 fill:#ffd43b,color:#000
364
+ style V3 fill:#ffd43b,color:#000
365
+ style W3 fill:#ffd43b,color:#000
366
+ style X3 fill:#ffd43b,color:#000
367
+ style Y3 fill:#ffd43b,color:#000
368
+ style Z3 fill:#ffd43b,color:#000
369
+ style AA3 fill:#ffd43b,color:#000
370
+ style BB3 fill:#ffd43b,color:#000
371
+ style CC3 fill:#ffd43b,color:#000
372
+
373
+ style M3 fill:#51cf66,color:#fff
374
+ style N3 fill:#51cf66,color:#fff
375
+ style O3 fill:#51cf66,color:#fff
376
+ style P3 fill:#51cf66,color:#fff
377
+ style Q3 fill:#51cf66,color:#fff
378
+ style R3 fill:#51cf66,color:#fff
379
+ style S3 fill:#51cf66,color:#fff
380
+ style T3 fill:#51cf66,color:#fff
381
+ style U3 fill:#51cf66,color:#fff
382
+ style V3 fill:#51cf66,color:#fff
383
+ style W3 fill:#51cf66,color:#fff
384
+ style X3 fill:#51cf66,color:#fff
385
+ style Y3 fill:#51cf66,color:#fff
386
+ style Z3 fill:#51cf66,color:#fff
387
+ style AA3 fill:#51cf66,color:#fff
388
+ style BB3 fill:#51cf66,color:#fff
389
+ style CC3 fill:#51cf66,color:#fff
390
+
391
+ style AA3 fill:#b197fc,color:#fff
392
+ style BB3 fill:#b197fc,color:#fff
393
+ style CC3 fill:#b197fc,color:#fff
394
+ </div>
395
+
396
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
397
+ <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;">
398
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
399
+ </div>
400
+ <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;">
401
+ <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;">
404
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Solution Operations
405
+ </div>
406
+ <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;">
407
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
408
+ </div>
409
+ <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;">
410
+ <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">
433
+ <p><strong>Gary Welz</strong></p>
434
+ <p>Retired Faculty Member</p>
435
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
436
+ <p>Borough of Manhattan Community College, CUNY</p>
437
+ <p>CUNY Graduate Center (New Media Lab)</p>
438
+ <p>Email: gwelz@jjay.cuny.edu</p>
439
+ </div>
440
+ </footer>
441
+ </div>
442
+ </body>
443
+ </html>
mathematics_batch_02.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
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/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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+ nodeSpacing: 30,
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+ rankSpacing: 30,
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+ padding: 10
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+ }
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
87
+ style E1 fill:#ff6b6b,color:#fff
88
+
89
+ style B1 fill:#ffd43b,color:#000
90
+ style D1 fill:#ffd43b,color:#000
91
+ style F1 fill:#ffd43b,color:#000
92
+ style G1 fill:#ffd43b,color:#000
93
+ style H1 fill:#ffd43b,color:#000
94
+ style I1 fill:#ffd43b,color:#000
95
+ style J1 fill:#ffd43b,color:#000
96
+ style K1 fill:#ffd43b,color:#000
97
+ style L1 fill:#ffd43b,color:#000
98
+ style M1 fill:#ffd43b,color:#000
99
+ style N1 fill:#ffd43b,color:#000
100
+ style O1 fill:#ffd43b,color:#000
101
+ style P1 fill:#ffd43b,color:#000
102
+ style Q1 fill:#ffd43b,color:#000
103
+ style R1 fill:#ffd43b,color:#000
104
+ style S1 fill:#ffd43b,color:#000
105
+ style T1 fill:#ffd43b,color:#000
106
+ style U1 fill:#ffd43b,color:#000
107
+ style V1 fill:#ffd43b,color:#000
108
+ style W1 fill:#ffd43b,color:#000
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
124
+ style O1 fill:#51cf66,color:#fff
125
+ style P1 fill:#51cf66,color:#fff
126
+ style Q1 fill:#51cf66,color:#fff
127
+ style R1 fill:#51cf66,color:#fff
128
+ style S1 fill:#51cf66,color:#fff
129
+ style T1 fill:#51cf66,color:#fff
130
+ style U1 fill:#51cf66,color:#fff
131
+ style V1 fill:#51cf66,color:#fff
132
+ style W1 fill:#51cf66,color:#fff
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
224
+ style E2 fill:#ff6b6b,color:#fff
225
+
226
+ style B2 fill:#ffd43b,color:#000
227
+ style D2 fill:#ffd43b,color:#000
228
+ style F2 fill:#ffd43b,color:#000
229
+ style G2 fill:#ffd43b,color:#000
230
+ style H2 fill:#ffd43b,color:#000
231
+ style I2 fill:#ffd43b,color:#000
232
+ style J2 fill:#ffd43b,color:#000
233
+ style K2 fill:#ffd43b,color:#000
234
+ style L2 fill:#ffd43b,color:#000
235
+ style M2 fill:#ffd43b,color:#000
236
+ style N2 fill:#ffd43b,color:#000
237
+ style O2 fill:#ffd43b,color:#000
238
+ style P2 fill:#ffd43b,color:#000
239
+ style Q2 fill:#ffd43b,color:#000
240
+ style R2 fill:#ffd43b,color:#000
241
+ style S2 fill:#ffd43b,color:#000
242
+ style T2 fill:#ffd43b,color:#000
243
+ style U2 fill:#ffd43b,color:#000
244
+ style V2 fill:#ffd43b,color:#000
245
+ style W2 fill:#ffd43b,color:#000
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
261
+ style O2 fill:#51cf66,color:#fff
262
+ style P2 fill:#51cf66,color:#fff
263
+ style Q2 fill:#51cf66,color:#fff
264
+ style R2 fill:#51cf66,color:#fff
265
+ style S2 fill:#51cf66,color:#fff
266
+ style T2 fill:#51cf66,color:#fff
267
+ style U2 fill:#51cf66,color:#fff
268
+ style V2 fill:#51cf66,color:#fff
269
+ style W2 fill:#51cf66,color:#fff
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
361
+ style E3 fill:#ff6b6b,color:#fff
362
+
363
+ style B3 fill:#ffd43b,color:#000
364
+ style D3 fill:#ffd43b,color:#000
365
+ style F3 fill:#ffd43b,color:#000
366
+ style G3 fill:#ffd43b,color:#000
367
+ style H3 fill:#ffd43b,color:#000
368
+ style I3 fill:#ffd43b,color:#000
369
+ style J3 fill:#ffd43b,color:#000
370
+ style K3 fill:#ffd43b,color:#000
371
+ style L3 fill:#ffd43b,color:#000
372
+ style M3 fill:#ffd43b,color:#000
373
+ style N3 fill:#ffd43b,color:#000
374
+ style O3 fill:#ffd43b,color:#000
375
+ style P3 fill:#ffd43b,color:#000
376
+ style Q3 fill:#ffd43b,color:#000
377
+ style R3 fill:#ffd43b,color:#000
378
+ style S3 fill:#ffd43b,color:#000
379
+ style T3 fill:#ffd43b,color:#000
380
+ style U3 fill:#ffd43b,color:#000
381
+ style V3 fill:#ffd43b,color:#000
382
+ style W3 fill:#ffd43b,color:#000
383
+ style X3 fill:#ffd43b,color:#000
384
+ style Y3 fill:#ffd43b,color:#000
385
+ style Z3 fill:#ffd43b,color:#000
386
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396
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+ style V3 fill:#51cf66,color:#fff
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+ style W3 fill:#51cf66,color:#fff
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+ style Y3 fill:#51cf66,color:#fff
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+ style DD3 fill:#51cf66,color:#fff
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+ style EE3 fill:#51cf66,color:#fff
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+ style FF3 fill:#51cf66,color:#fff
416
+ style GG3 fill:#51cf66,color:#fff
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+ 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">
461
+ <p><strong>Gary Welz</strong></p>
462
+ <p>Retired Faculty Member</p>
463
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
464
+ <p>Borough of Manhattan Community College, CUNY</p>
465
+ <p>CUNY Graduate Center (New Media Lab)</p>
466
+ <p>Email: gwelz@jjay.cuny.edu</p>
467
+ </div>
468
+ </footer>
469
+ </div>
470
+ </body>
471
+ </html>
mathematics_batch_03.html ADDED
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+ <!DOCTYPE html>
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+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
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+ <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">
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+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
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+ <script>
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+ mermaid.initialize({
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+ rankSpacing: 30,
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+ }
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+ });
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+ </script>
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+ </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
87
+ style E1 fill:#ff6b6b,color:#fff
88
+
89
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90
+ style D1 fill:#ffd43b,color:#000
91
+ style F1 fill:#ffd43b,color:#000
92
+ style G1 fill:#ffd43b,color:#000
93
+ style H1 fill:#ffd43b,color:#000
94
+ style I1 fill:#ffd43b,color:#000
95
+ style J1 fill:#ffd43b,color:#000
96
+ style K1 fill:#ffd43b,color:#000
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+ style L1 fill:#ffd43b,color:#000
98
+ style M1 fill:#ffd43b,color:#000
99
+ style N1 fill:#ffd43b,color:#000
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+ style O1 fill:#ffd43b,color:#000
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+ style P1 fill:#ffd43b,color:#000
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+ style Q1 fill:#ffd43b,color:#000
103
+ style R1 fill:#ffd43b,color:#000
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+ style S1 fill:#ffd43b,color:#000
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+ style T1 fill:#ffd43b,color:#000
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+ style U1 fill:#ffd43b,color:#000
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+ style V1 fill:#ffd43b,color:#000
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+ style W1 fill:#ffd43b,color:#000
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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
118
+ style GG1 fill:#ffd43b,color:#000
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+ style HH1 fill:#ffd43b,color:#000
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+ style II1 fill:#ffd43b,color:#000
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+
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+ style M1 fill:#51cf66,color:#fff
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+ style N1 fill:#51cf66,color:#fff
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+ style O1 fill:#51cf66,color:#fff
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+ style P1 fill:#51cf66,color:#fff
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+ style Q1 fill:#51cf66,color:#fff
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+ style T1 fill:#51cf66,color:#fff
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+ style Y1 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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+ style HH1 fill:#51cf66,color:#fff
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+ style II1 fill:#51cf66,color:#fff
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+
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
224
+ style E2 fill:#ff6b6b,color:#fff
225
+
226
+ style B2 fill:#ffd43b,color:#000
227
+ style D2 fill:#ffd43b,color:#000
228
+ style F2 fill:#ffd43b,color:#000
229
+ style G2 fill:#ffd43b,color:#000
230
+ style H2 fill:#ffd43b,color:#000
231
+ style I2 fill:#ffd43b,color:#000
232
+ style J2 fill:#ffd43b,color:#000
233
+ style K2 fill:#ffd43b,color:#000
234
+ style L2 fill:#ffd43b,color:#000
235
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236
+ style N2 fill:#ffd43b,color:#000
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+ style T2 fill:#ffd43b,color:#000
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+ style U2 fill:#ffd43b,color:#000
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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
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+ style O2 fill:#51cf66,color:#fff
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+ style P2 fill:#51cf66,color:#fff
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+ style U2 fill:#51cf66,color:#fff
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+ style V2 fill:#51cf66,color:#fff
269
+ style W2 fill:#51cf66,color:#fff
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
357
+ style E3 fill:#ff6b6b,color:#fff
358
+
359
+ style B3 fill:#ffd43b,color:#000
360
+ style D3 fill:#ffd43b,color:#000
361
+ style F3 fill:#ffd43b,color:#000
362
+ style G3 fill:#ffd43b,color:#000
363
+ style H3 fill:#ffd43b,color:#000
364
+ style I3 fill:#ffd43b,color:#000
365
+ style J3 fill:#ffd43b,color:#000
366
+ style K3 fill:#ffd43b,color:#000
367
+ style L3 fill:#ffd43b,color:#000
368
+ style M3 fill:#ffd43b,color:#000
369
+ style N3 fill:#ffd43b,color:#000
370
+ style O3 fill:#ffd43b,color:#000
371
+ style P3 fill:#ffd43b,color:#000
372
+ style Q3 fill:#ffd43b,color:#000
373
+ style R3 fill:#ffd43b,color:#000
374
+ style S3 fill:#ffd43b,color:#000
375
+ style T3 fill:#ffd43b,color:#000
376
+ style U3 fill:#ffd43b,color:#000
377
+ style V3 fill:#ffd43b,color:#000
378
+ style W3 fill:#ffd43b,color:#000
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
391
+ style O3 fill:#51cf66,color:#fff
392
+ style P3 fill:#51cf66,color:#fff
393
+ style Q3 fill:#51cf66,color:#fff
394
+ style R3 fill:#51cf66,color:#fff
395
+ style S3 fill:#51cf66,color:#fff
396
+ style T3 fill:#51cf66,color:#fff
397
+ style U3 fill:#51cf66,color:#fff
398
+ style V3 fill:#51cf66,color:#fff
399
+ style W3 fill:#51cf66,color:#fff
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">
451
+ <p><strong>Gary Welz</strong></p>
452
+ <p>Retired Faculty Member</p>
453
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
454
+ <p>Borough of Manhattan Community College, CUNY</p>
455
+ <p>CUNY Graduate Center (New Media Lab)</p>
456
+ <p>Email: gwelz@jjay.cuny.edu</p>
457
+ </div>
458
+ </footer>
459
+ </div>
460
+ </body>
461
+ </html>
mathematics_batch_04.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
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">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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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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+ });
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
79
+ style E1 fill:#ff6b6b,color:#fff
80
+
81
+ style B1 fill:#ffd43b,color:#000
82
+ style D1 fill:#ffd43b,color:#000
83
+ style F1 fill:#ffd43b,color:#000
84
+ style G1 fill:#ffd43b,color:#000
85
+ style H1 fill:#ffd43b,color:#000
86
+ style I1 fill:#ffd43b,color:#000
87
+ style J1 fill:#ffd43b,color:#000
88
+ style K1 fill:#ffd43b,color:#000
89
+ style L1 fill:#ffd43b,color:#000
90
+ style M1 fill:#ffd43b,color:#000
91
+ style N1 fill:#ffd43b,color:#000
92
+ style O1 fill:#ffd43b,color:#000
93
+ style P1 fill:#ffd43b,color:#000
94
+ style Q1 fill:#ffd43b,color:#000
95
+ style R1 fill:#ffd43b,color:#000
96
+ style S1 fill:#ffd43b,color:#000
97
+ style T1 fill:#ffd43b,color:#000
98
+ style U1 fill:#ffd43b,color:#000
99
+ style V1 fill:#ffd43b,color:#000
100
+ style W1 fill:#ffd43b,color:#000
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
111
+ style O1 fill:#51cf66,color:#fff
112
+ style P1 fill:#51cf66,color:#fff
113
+ style Q1 fill:#51cf66,color:#fff
114
+ style R1 fill:#51cf66,color:#fff
115
+ style S1 fill:#51cf66,color:#fff
116
+ style T1 fill:#51cf66,color:#fff
117
+ style U1 fill:#51cf66,color:#fff
118
+ style V1 fill:#51cf66,color:#fff
119
+ style W1 fill:#51cf66,color:#fff
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
198
+ style E2 fill:#ff6b6b,color:#fff
199
+
200
+ style B2 fill:#ffd43b,color:#000
201
+ style D2 fill:#ffd43b,color:#000
202
+ style F2 fill:#ffd43b,color:#000
203
+ style G2 fill:#ffd43b,color:#000
204
+ style H2 fill:#ffd43b,color:#000
205
+ style I2 fill:#ffd43b,color:#000
206
+ style J2 fill:#ffd43b,color:#000
207
+ style K2 fill:#ffd43b,color:#000
208
+ style L2 fill:#ffd43b,color:#000
209
+ style M2 fill:#ffd43b,color:#000
210
+ style N2 fill:#ffd43b,color:#000
211
+ style O2 fill:#ffd43b,color:#000
212
+ style P2 fill:#ffd43b,color:#000
213
+ style Q2 fill:#ffd43b,color:#000
214
+ style R2 fill:#ffd43b,color:#000
215
+ style S2 fill:#ffd43b,color:#000
216
+ style T2 fill:#ffd43b,color:#000
217
+ style U2 fill:#ffd43b,color:#000
218
+ style V2 fill:#ffd43b,color:#000
219
+ style W2 fill:#ffd43b,color:#000
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
230
+ style O2 fill:#51cf66,color:#fff
231
+ style P2 fill:#51cf66,color:#fff
232
+ style Q2 fill:#51cf66,color:#fff
233
+ style R2 fill:#51cf66,color:#fff
234
+ style S2 fill:#51cf66,color:#fff
235
+ style T2 fill:#51cf66,color:#fff
236
+ style U2 fill:#51cf66,color:#fff
237
+ style V2 fill:#51cf66,color:#fff
238
+ style W2 fill:#51cf66,color:#fff
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
317
+ style E3 fill:#ff6b6b,color:#fff
318
+
319
+ style B3 fill:#ffd43b,color:#000
320
+ style D3 fill:#ffd43b,color:#000
321
+ style F3 fill:#ffd43b,color:#000
322
+ style G3 fill:#ffd43b,color:#000
323
+ style H3 fill:#ffd43b,color:#000
324
+ style I3 fill:#ffd43b,color:#000
325
+ style J3 fill:#ffd43b,color:#000
326
+ style K3 fill:#ffd43b,color:#000
327
+ style L3 fill:#ffd43b,color:#000
328
+ style M3 fill:#ffd43b,color:#000
329
+ style N3 fill:#ffd43b,color:#000
330
+ style O3 fill:#ffd43b,color:#000
331
+ style P3 fill:#ffd43b,color:#000
332
+ style Q3 fill:#ffd43b,color:#000
333
+ style R3 fill:#ffd43b,color:#000
334
+ style S3 fill:#ffd43b,color:#000
335
+ style T3 fill:#ffd43b,color:#000
336
+ style U3 fill:#ffd43b,color:#000
337
+ style V3 fill:#ffd43b,color:#000
338
+ style W3 fill:#ffd43b,color:#000
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
348
+ style O3 fill:#51cf66,color:#fff
349
+ style P3 fill:#51cf66,color:#fff
350
+ style Q3 fill:#51cf66,color:#fff
351
+ style R3 fill:#51cf66,color:#fff
352
+ style S3 fill:#51cf66,color:#fff
353
+ style T3 fill:#51cf66,color:#fff
354
+ style U3 fill:#51cf66,color:#fff
355
+ style V3 fill:#51cf66,color:#fff
356
+ style W3 fill:#51cf66,color:#fff
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">
405
+ <p><strong>Gary Welz</strong></p>
406
+ <p>Retired Faculty Member</p>
407
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
408
+ <p>Borough of Manhattan Community College, CUNY</p>
409
+ <p>CUNY Graduate Center (New Media Lab)</p>
410
+ <p>Email: gwelz@jjay.cuny.edu</p>
411
+ </div>
412
+ </footer>
413
+ </div>
414
+ </body>
415
+ </html>
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
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
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
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+ <script>
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+ mermaid.initialize({
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+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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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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+ });
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
41
+ A1[Numerical Problem Input] --> B1[Method Selection]
42
+ C1[Error Analysis] --> D1[Convergence Study]
43
+ E1[Algorithm Design] --> F1[Implementation Strategy]
44
+
45
+ B1 --> G1[Root Finding Methods]
46
+ D1 --> H1[Convergence Criteria]
47
+ F1 --> I1[Numerical Algorithm]
48
+
49
+ G1 --> J1[Bisection Method]
50
+ H1 --> K1[Tolerance Setting]
51
+ I1 --> L1[Iterative Process]
52
+
53
+ J1 --> M1[Newton Raphson Method]
54
+ K1 --> N1[Error Estimation]
55
+ L1 --> O1[Convergence Check]
56
+
57
+ M1 --> P1[Secant Method]
58
+ N1 --> Q1[Stability Analysis]
59
+ O1 --> R1[Solution Refinement]
60
+
61
+ P1 --> S1[Fixed Point Iteration]
62
+ Q1 --> T1[Error Bounds]
63
+ R1 --> U1[Numerical Solution]
64
+
65
+ S1 --> V1[Integration Methods]
66
+ T1 --> W1[Accuracy Assessment]
67
+ U1 --> X1[Solution Validation]
68
+
69
+ V1 --> Y1[Trapezoidal Rule]
70
+ W1 --> Z1[Numerical Result]
71
+ X1 --> AA1[Numerical Output]
72
+
73
+ Y1 --> BB1[Simpson Rule]
74
+ Z1 --> CC1[Numerical Analysis]
75
+ AA1 --> DD1[Numerical Methods Output]
76
+
77
+ style A1 fill:#ff6b6b,color:#fff
78
+ style C1 fill:#ff6b6b,color:#fff
79
+ style E1 fill:#ff6b6b,color:#fff
80
+
81
+ style B1 fill:#ffd43b,color:#000
82
+ style D1 fill:#ffd43b,color:#000
83
+ style F1 fill:#ffd43b,color:#000
84
+ style G1 fill:#ffd43b,color:#000
85
+ style H1 fill:#ffd43b,color:#000
86
+ style I1 fill:#ffd43b,color:#000
87
+ style J1 fill:#ffd43b,color:#000
88
+ style K1 fill:#ffd43b,color:#000
89
+ style L1 fill:#ffd43b,color:#000
90
+ style M1 fill:#ffd43b,color:#000
91
+ style N1 fill:#ffd43b,color:#000
92
+ style O1 fill:#ffd43b,color:#000
93
+ style P1 fill:#ffd43b,color:#000
94
+ style Q1 fill:#ffd43b,color:#000
95
+ style R1 fill:#ffd43b,color:#000
96
+ style S1 fill:#ffd43b,color:#000
97
+ style T1 fill:#ffd43b,color:#000
98
+ style U1 fill:#ffd43b,color:#000
99
+ style V1 fill:#ffd43b,color:#000
100
+ style W1 fill:#ffd43b,color:#000
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
111
+ style O1 fill:#51cf66,color:#fff
112
+ style P1 fill:#51cf66,color:#fff
113
+ style Q1 fill:#51cf66,color:#fff
114
+ style R1 fill:#51cf66,color:#fff
115
+ style S1 fill:#51cf66,color:#fff
116
+ style T1 fill:#51cf66,color:#fff
117
+ style U1 fill:#51cf66,color:#fff
118
+ style V1 fill:#51cf66,color:#fff
119
+ style W1 fill:#51cf66,color:#fff
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>Numerical 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>Numerical 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> 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
160
+ A2[Data Set Input] --> B2[Statistical Method Selection]
161
+ C2[Hypothesis Testing] --> D2[Test Design]
162
+ E2[Regression Analysis] --> F2[Model Selection]
163
+
164
+ B2 --> G2[Descriptive Statistics]
165
+ D2 --> H2[Null Hypothesis H0]
166
+ F2 --> I2[Linear Regression]
167
+
168
+ G2 --> J2[Mean Median Mode]
169
+ H2 --> K2[Alternative Hypothesis H1]
170
+ I2 --> L2[Multiple Regression]
171
+
172
+ J2 --> M2[Variance Standard Deviation]
173
+ K2 --> N2[Significance Level Alpha]
174
+ L2 --> O2[Model Fitting]
175
+
176
+ M2 --> P2[Correlation Analysis]
177
+ N2 --> O2
178
+ O2 --> Q2[Parameter Estimation]
179
+
180
+ P2 --> R2[Inferential Statistics]
181
+ Q2 --> S2[Residual Analysis]
182
+ R2 --> T2[Confidence Intervals]
183
+
184
+ S2 --> U2[Model Validation]
185
+ T2 --> V2[Statistical Tests]
186
+ U2 --> W2[Statistical Result]
187
+
188
+ V2 --> X2[Statistical Analysis]
189
+ W2 --> Y2[Statistical Output]
190
+ X2 --> Z2[Statistical Analysis Output]
191
+
192
+ Y2 --> AA2[Statistical Analysis Final Result]
193
+ Z2 --> BB2[Statistical Analysis Complete]
194
+ AA2 --> CC2[Statistical Analysis Output]
195
+
196
+ style A2 fill:#ff6b6b,color:#fff
197
+ style C2 fill:#ff6b6b,color:#fff
198
+ style E2 fill:#ff6b6b,color:#fff
199
+
200
+ style B2 fill:#ffd43b,color:#000
201
+ style D2 fill:#ffd43b,color:#000
202
+ style F2 fill:#ffd43b,color:#000
203
+ style G2 fill:#ffd43b,color:#000
204
+ style H2 fill:#ffd43b,color:#000
205
+ style I2 fill:#ffd43b,color:#000
206
+ style J2 fill:#ffd43b,color:#000
207
+ style K2 fill:#ffd43b,color:#000
208
+ style L2 fill:#ffd43b,color:#000
209
+ style M2 fill:#ffd43b,color:#000
210
+ style N2 fill:#ffd43b,color:#000
211
+ style O2 fill:#ffd43b,color:#000
212
+ style P2 fill:#ffd43b,color:#000
213
+ style Q2 fill:#ffd43b,color:#000
214
+ style R2 fill:#ffd43b,color:#000
215
+ style S2 fill:#ffd43b,color:#000
216
+ style T2 fill:#ffd43b,color:#000
217
+ style U2 fill:#ffd43b,color:#000
218
+ style V2 fill:#ffd43b,color:#000
219
+ style W2 fill:#ffd43b,color:#000
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
+
227
+ style M2 fill:#51cf66,color:#fff
228
+ style N2 fill:#51cf66,color:#fff
229
+ style O2 fill:#51cf66,color:#fff
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+ style P2 fill:#51cf66,color:#fff
231
+ style Q2 fill:#51cf66,color:#fff
232
+ style R2 fill:#51cf66,color:#fff
233
+ style S2 fill:#51cf66,color:#fff
234
+ style T2 fill:#51cf66,color:#fff
235
+ style U2 fill:#51cf66,color:#fff
236
+ style V2 fill:#51cf66,color:#fff
237
+ style W2 fill:#51cf66,color:#fff
238
+ style X2 fill:#51cf66,color:#fff
239
+ style Y2 fill:#51cf66,color:#fff
240
+ style Z2 fill:#51cf66,color:#fff
241
+ style AA2 fill:#51cf66,color:#fff
242
+ style BB2 fill:#51cf66,color:#fff
243
+ style CC2 fill:#51cf66,color:#fff
244
+
245
+ style CC2 fill:#b197fc,color:#fff
246
+ </div>
247
+
248
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
249
+ <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;">
250
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
251
+ </div>
252
+ <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;">
253
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Statistical Methods
254
+ </div>
255
+ <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;">
256
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Statistical Operations
257
+ </div>
258
+ <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;">
259
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
260
+ </div>
261
+ <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;">
262
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
263
+ </div>
264
+ </div>
265
+
266
+ <div class="figure-caption">
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
277
+ A3[Plaintext Message] --> B3[Cryptographic Method Selection]
278
+ C3[Key Generation] --> D3[Key Management]
279
+ E3[Encryption Algorithm] --> F3[Algorithm Implementation]
280
+
281
+ B3 --> G3[RSA Algorithm]
282
+ D3 --> H3[Public Key Generation]
283
+ F3 --> I3[Encryption Process]
284
+
285
+ G3 --> J3[Prime Number Generation]
286
+ H3 --> K3[Private Key Generation]
287
+ I3 --> L3[Message Encoding]
288
+
289
+ J3 --> M3[Modular Exponentiation]
290
+ K3 --> L3
291
+ L3 --> N3[Ciphertext Generation]
292
+
293
+ M3 --> O3[Elliptic Curve Cryptography]
294
+ N3 --> P3[Decryption Process]
295
+ O3 --> Q3[Point Multiplication]
296
+
297
+ P3 --> R3[Hash Function Application]
298
+ Q3 --> S3[Digital Signature]
299
+ R3 --> T3[Message Authentication]
300
+
301
+ S3 --> U3[Cryptographic Hash]
302
+ T3 --> V3[Key Exchange Protocol]
303
+ U3 --> W3[Cryptographic Result]
304
+
305
+ V3 --> X3[Cryptographic Analysis]
306
+ W3 --> Y3[Cryptographic Output]
307
+ X3 --> Z3[Cryptographic Analysis Output]
308
+
309
+ Y3 --> AA3[Cryptographic Analysis Final Result]
310
+ Z3 --> BB3[Cryptographic Analysis Complete]
311
+ AA3 --> CC3[Cryptographic Analysis Output]
312
+
313
+ style A3 fill:#ff6b6b,color:#fff
314
+ style C3 fill:#ff6b6b,color:#fff
315
+ style E3 fill:#ff6b6b,color:#fff
316
+
317
+ style B3 fill:#ffd43b,color:#000
318
+ style D3 fill:#ffd43b,color:#000
319
+ style F3 fill:#ffd43b,color:#000
320
+ style G3 fill:#ffd43b,color:#000
321
+ style H3 fill:#ffd43b,color:#000
322
+ style I3 fill:#ffd43b,color:#000
323
+ style J3 fill:#ffd43b,color:#000
324
+ style K3 fill:#ffd43b,color:#000
325
+ style L3 fill:#ffd43b,color:#000
326
+ style M3 fill:#ffd43b,color:#000
327
+ style N3 fill:#ffd43b,color:#000
328
+ style O3 fill:#ffd43b,color:#000
329
+ style P3 fill:#ffd43b,color:#000
330
+ style Q3 fill:#ffd43b,color:#000
331
+ style R3 fill:#ffd43b,color:#000
332
+ style S3 fill:#ffd43b,color:#000
333
+ style T3 fill:#ffd43b,color:#000
334
+ style U3 fill:#ffd43b,color:#000
335
+ style V3 fill:#ffd43b,color:#000
336
+ style W3 fill:#ffd43b,color:#000
337
+ style X3 fill:#ffd43b,color:#000
338
+ style Y3 fill:#ffd43b,color:#000
339
+ style Z3 fill:#ffd43b,color:#000
340
+ style AA3 fill:#ffd43b,color:#000
341
+ style BB3 fill:#ffd43b,color:#000
342
+ style CC3 fill:#ffd43b,color:#000
343
+
344
+ style M3 fill:#51cf66,color:#fff
345
+ style N3 fill:#51cf66,color:#fff
346
+ style O3 fill:#51cf66,color:#fff
347
+ style P3 fill:#51cf66,color:#fff
348
+ style Q3 fill:#51cf66,color:#fff
349
+ style R3 fill:#51cf66,color:#fff
350
+ style S3 fill:#51cf66,color:#fff
351
+ style T3 fill:#51cf66,color:#fff
352
+ style U3 fill:#51cf66,color:#fff
353
+ style V3 fill:#51cf66,color:#fff
354
+ style W3 fill:#51cf66,color:#fff
355
+ style X3 fill:#51cf66,color:#fff
356
+ style Y3 fill:#51cf66,color:#fff
357
+ style Z3 fill:#51cf66,color:#fff
358
+ style AA3 fill:#51cf66,color:#fff
359
+ style BB3 fill:#51cf66,color:#fff
360
+ style CC3 fill:#51cf66,color:#fff
361
+
362
+ style CC3 fill:#b197fc,color:#fff
363
+ </div>
364
+
365
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
366
+ <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;">
367
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
368
+ </div>
369
+ <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;">
370
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Cryptographic Methods
371
+ </div>
372
+ <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;">
373
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Cryptographic Operations
374
+ </div>
375
+ <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;">
376
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
377
+ </div>
378
+ <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;">
379
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
380
+ </div>
381
+ </div>
382
+
383
+ <div class="figure-caption">
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">
403
+ <p><strong>Gary Welz</strong></p>
404
+ <p>Retired Faculty Member</p>
405
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
406
+ <p>Borough of Manhattan Community College, CUNY</p>
407
+ <p>CUNY Graduate Center (New Media Lab)</p>
408
+ <p>Email: gwelz@jjay.cuny.edu</p>
409
+ </div>
410
+ </footer>
411
+ </div>
412
+ </body>
413
+ </html>
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
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/mermaid@10.6.1/dist/mermaid.min.js"></script>
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+ <script>
10
+ mermaid.initialize({
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+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ curve: 'linear',
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+ nodeSpacing: 30,
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+ rankSpacing: 30,
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+ padding: 10
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+ }
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
41
+ A1[Graph G V E] --> B1[Graph Representation]
42
+ C1[Algorithm Selection] --> D1[Method Choice]
43
+ E1[Graph Properties] --> F1[Property Analysis]
44
+
45
+ B1 --> G1[Adjacency Matrix]
46
+ D1 --> H1[Shortest Path Algorithm]
47
+ F1 --> I1[Graph Connectivity]
48
+
49
+ G1 --> J1[Adjacency List]
50
+ H1 --> K1[Dijkstra Algorithm]
51
+ I1 --> L1[Graph Traversal]
52
+
53
+ J1 --> M1[Graph Structure]
54
+ K1 --> N1[Bellman Ford Algorithm]
55
+ L1 --> O1[Depth First Search]
56
+
57
+ M1 --> P1[Vertex Analysis]
58
+ N1 --> O1
59
+ O1 --> Q1[Breadth First Search]
60
+
61
+ P1 --> R1[Edge Analysis]
62
+ Q1 --> S1[Minimum Spanning Tree]
63
+ R1 --> T1[Graph Coloring]
64
+
65
+ S1 --> U1[Kruskal Algorithm]
66
+ T1 --> V1[Network Flow]
67
+ U1 --> W1[Graph Algorithm Result]
68
+
69
+ V1 --> X1[Ford Fulkerson Algorithm]
70
+ W1 --> Y1[Graph Analysis]
71
+ X1 --> Z1[Graph Theory Output]
72
+
73
+ Y1 --> AA1[Graph Theory Analysis]
74
+ Z1 --> BB1[Graph Theory Final Result]
75
+ AA1 --> CC1[Graph Theory Analysis Complete]
76
+
77
+ style A1 fill:#ff6b6b,color:#fff
78
+ style C1 fill:#ff6b6b,color:#fff
79
+ style E1 fill:#ff6b6b,color:#fff
80
+
81
+ style B1 fill:#ffd43b,color:#000
82
+ style D1 fill:#ffd43b,color:#000
83
+ style F1 fill:#ffd43b,color:#000
84
+ style G1 fill:#ffd43b,color:#000
85
+ style H1 fill:#ffd43b,color:#000
86
+ style I1 fill:#ffd43b,color:#000
87
+ style J1 fill:#ffd43b,color:#000
88
+ style K1 fill:#ffd43b,color:#000
89
+ style L1 fill:#ffd43b,color:#000
90
+ style M1 fill:#ffd43b,color:#000
91
+ style N1 fill:#ffd43b,color:#000
92
+ style O1 fill:#ffd43b,color:#000
93
+ style P1 fill:#ffd43b,color:#000
94
+ style Q1 fill:#ffd43b,color:#000
95
+ style R1 fill:#ffd43b,color:#000
96
+ style S1 fill:#ffd43b,color:#000
97
+ style T1 fill:#ffd43b,color:#000
98
+ style U1 fill:#ffd43b,color:#000
99
+ style V1 fill:#ffd43b,color:#000
100
+ style W1 fill:#ffd43b,color:#000
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
+
108
+ style M1 fill:#51cf66,color:#fff
109
+ style N1 fill:#51cf66,color:#fff
110
+ style O1 fill:#51cf66,color:#fff
111
+ style P1 fill:#51cf66,color:#fff
112
+ style Q1 fill:#51cf66,color:#fff
113
+ style R1 fill:#51cf66,color:#fff
114
+ style S1 fill:#51cf66,color:#fff
115
+ style T1 fill:#51cf66,color:#fff
116
+ style U1 fill:#51cf66,color:#fff
117
+ style V1 fill:#51cf66,color:#fff
118
+ style W1 fill:#51cf66,color:#fff
119
+ style X1 fill:#51cf66,color:#fff
120
+ style Y1 fill:#51cf66,color:#fff
121
+ style Z1 fill:#51cf66,color:#fff
122
+ style AA1 fill:#51cf66,color:#fff
123
+ style BB1 fill:#51cf66,color:#fff
124
+ style CC1 fill:#51cf66,color:#fff
125
+
126
+ style CC1 fill:#b197fc,color:#fff
127
+ </div>
128
+
129
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
130
+ <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;">
131
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
132
+ </div>
133
+ <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;">
134
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Graph Theory Methods
135
+ </div>
136
+ <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;">
137
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Graph Operations
138
+ </div>
139
+ <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;">
140
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
141
+ </div>
142
+ <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;">
143
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
144
+ </div>
145
+ </div>
146
+
147
+ <div class="figure-caption">
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
158
+ A2[Combinatorial Problem] --> B2[Counting Method Selection]
159
+ C2[Permutation Analysis] --> D2[Combination Analysis]
160
+ E2[Counting Principles] --> F2[Principle Application]
161
+
162
+ B2 --> G2[Multiplication Principle]
163
+ D2 --> H2[Combination Formula]
164
+ F2 --> I2[Addition Principle]
165
+
166
+ G2 --> J2[Permutation Formula]
167
+ H2 --> K2[Binomial Coefficient]
168
+ I2 --> L2[Inclusion Exclusion]
169
+
170
+ J2 --> M2[Factorial Calculation]
171
+ K2 --> N2[Pascal Triangle]
172
+ L2 --> O2[Set Cardinality]
173
+
174
+ M2 --> P2[Arrangement Counting]
175
+ N2 --> O2
176
+ O2 --> Q2[Partition Counting]
177
+
178
+ P2 --> R2[Selection Counting]
179
+ Q2 --> S2[Generating Functions]
180
+ R2 --> T2[Combinatorial Identity]
181
+
182
+ S2 --> U2[Recurrence Relations]
183
+ T2 --> V2[Combinatorial Proof]
184
+ U2 --> W2[Combinatorial Result]
185
+
186
+ V2 --> X2[Combinatorial Analysis]
187
+ W2 --> Y2[Combinatorial Output]
188
+ X2 --> Z2[Combinatorial Analysis Output]
189
+
190
+ Y2 --> AA2[Combinatorial Analysis Final Result]
191
+ Z2 --> BB2[Combinatorial Analysis Complete]
192
+ AA2 --> CC2[Combinatorial Analysis Output]
193
+
194
+ style A2 fill:#ff6b6b,color:#fff
195
+ style C2 fill:#ff6b6b,color:#fff
196
+ style E2 fill:#ff6b6b,color:#fff
197
+
198
+ style B2 fill:#ffd43b,color:#000
199
+ style D2 fill:#ffd43b,color:#000
200
+ style F2 fill:#ffd43b,color:#000
201
+ style G2 fill:#ffd43b,color:#000
202
+ style H2 fill:#ffd43b,color:#000
203
+ style I2 fill:#ffd43b,color:#000
204
+ style J2 fill:#ffd43b,color:#000
205
+ style K2 fill:#ffd43b,color:#000
206
+ style L2 fill:#ffd43b,color:#000
207
+ style M2 fill:#ffd43b,color:#000
208
+ style N2 fill:#ffd43b,color:#000
209
+ style O2 fill:#ffd43b,color:#000
210
+ style P2 fill:#ffd43b,color:#000
211
+ style Q2 fill:#ffd43b,color:#000
212
+ style R2 fill:#ffd43b,color:#000
213
+ style S2 fill:#ffd43b,color:#000
214
+ style T2 fill:#ffd43b,color:#000
215
+ style U2 fill:#ffd43b,color:#000
216
+ style V2 fill:#ffd43b,color:#000
217
+ style W2 fill:#ffd43b,color:#000
218
+ style X2 fill:#ffd43b,color:#000
219
+ style Y2 fill:#ffd43b,color:#000
220
+ style Z2 fill:#ffd43b,color:#000
221
+ style AA2 fill:#ffd43b,color:#000
222
+ style BB2 fill:#ffd43b,color:#000
223
+ style CC2 fill:#ffd43b,color:#000
224
+
225
+ style M2 fill:#51cf66,color:#fff
226
+ style N2 fill:#51cf66,color:#fff
227
+ style O2 fill:#51cf66,color:#fff
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+ style P2 fill:#51cf66,color:#fff
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+ style Q2 fill:#51cf66,color:#fff
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+ style R2 fill:#51cf66,color:#fff
231
+ style S2 fill:#51cf66,color:#fff
232
+ style T2 fill:#51cf66,color:#fff
233
+ style U2 fill:#51cf66,color:#fff
234
+ style V2 fill:#51cf66,color:#fff
235
+ style W2 fill:#51cf66,color:#fff
236
+ style X2 fill:#51cf66,color:#fff
237
+ style Y2 fill:#51cf66,color:#fff
238
+ style Z2 fill:#51cf66,color:#fff
239
+ style AA2 fill:#51cf66,color:#fff
240
+ style BB2 fill:#51cf66,color:#fff
241
+ style CC2 fill:#51cf66,color:#fff
242
+
243
+ style CC2 fill:#b197fc,color:#fff
244
+ </div>
245
+
246
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
247
+ <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;">
248
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
249
+ </div>
250
+ <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;">
251
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Combinatorial Methods
252
+ </div>
253
+ <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;">
254
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Counting Operations
255
+ </div>
256
+ <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;">
257
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
258
+ </div>
259
+ <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;">
260
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
261
+ </div>
262
+ </div>
263
+
264
+ <div class="figure-caption">
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
275
+ A3[Logical Statement Input] --> B3[Logical Analysis]
276
+ C3[Set Operations] --> D3[Set Theory Application]
277
+ E3[Proof Techniques] --> F3[Proof Strategy]
278
+
279
+ B3 --> G3[Boolean Algebra]
280
+ D3 --> H3[Set Union Intersection]
281
+ F3 --> I3[Direct Proof]
282
+
283
+ G3 --> J3[Logical Connectives]
284
+ H3 --> K3[Set Complement]
285
+ I3 --> L3[Contradiction Proof]
286
+
287
+ J3 --> M3[Truth Tables]
288
+ K3 --> L3
289
+ L3 --> N3[Induction Proof]
290
+
291
+ M3 --> O3[Logical Equivalence]
292
+ N3 --> P3[Proof by Cases]
293
+ O3 --> Q3[Set Cardinality]
294
+
295
+ P3 --> R3[Proof Validation]
296
+ Q3 --> S3[Set Operations Result]
297
+ R3 --> T3[Logical Result]
298
+
299
+ S3 --> U3[Set Theory Analysis]
300
+ T3 --> V3[Logical Analysis]
301
+ U3 --> W3[Logic Set Theory Result]
302
+
303
+ V3 --> X3[Logic Set Theory Analysis]
304
+ W3 --> Y3[Logic Set Theory Output]
305
+ X3 --> Z3[Logic Set Theory Analysis Output]
306
+
307
+ Y3 --> AA3[Logic Set Theory Analysis Final Result]
308
+ Z3 --> BB3[Logic Set Theory Analysis Complete]
309
+ AA3 --> CC3[Logic Set Theory Analysis Output]
310
+
311
+ style A3 fill:#ff6b6b,color:#fff
312
+ style C3 fill:#ff6b6b,color:#fff
313
+ style E3 fill:#ff6b6b,color:#fff
314
+
315
+ style B3 fill:#ffd43b,color:#000
316
+ style D3 fill:#ffd43b,color:#000
317
+ style F3 fill:#ffd43b,color:#000
318
+ style G3 fill:#ffd43b,color:#000
319
+ style H3 fill:#ffd43b,color:#000
320
+ style I3 fill:#ffd43b,color:#000
321
+ style J3 fill:#ffd43b,color:#000
322
+ style K3 fill:#ffd43b,color:#000
323
+ style L3 fill:#ffd43b,color:#000
324
+ style M3 fill:#ffd43b,color:#000
325
+ style N3 fill:#ffd43b,color:#000
326
+ style O3 fill:#ffd43b,color:#000
327
+ style P3 fill:#ffd43b,color:#000
328
+ style Q3 fill:#ffd43b,color:#000
329
+ style R3 fill:#ffd43b,color:#000
330
+ style S3 fill:#ffd43b,color:#000
331
+ style T3 fill:#ffd43b,color:#000
332
+ style U3 fill:#ffd43b,color:#000
333
+ style V3 fill:#ffd43b,color:#000
334
+ style W3 fill:#ffd43b,color:#000
335
+ style X3 fill:#ffd43b,color:#000
336
+ style Y3 fill:#ffd43b,color:#000
337
+ style Z3 fill:#ffd43b,color:#000
338
+ style AA3 fill:#ffd43b,color:#000
339
+ style BB3 fill:#ffd43b,color:#000
340
+ style CC3 fill:#ffd43b,color:#000
341
+
342
+ style M3 fill:#51cf66,color:#fff
343
+ style N3 fill:#51cf66,color:#fff
344
+ style O3 fill:#51cf66,color:#fff
345
+ style P3 fill:#51cf66,color:#fff
346
+ style Q3 fill:#51cf66,color:#fff
347
+ style R3 fill:#51cf66,color:#fff
348
+ style S3 fill:#51cf66,color:#fff
349
+ style T3 fill:#51cf66,color:#fff
350
+ style U3 fill:#51cf66,color:#fff
351
+ style V3 fill:#51cf66,color:#fff
352
+ style W3 fill:#51cf66,color:#fff
353
+ style X3 fill:#51cf66,color:#fff
354
+ style Y3 fill:#51cf66,color:#fff
355
+ style Z3 fill:#51cf66,color:#fff
356
+ style AA3 fill:#51cf66,color:#fff
357
+ style BB3 fill:#51cf66,color:#fff
358
+ style CC3 fill:#51cf66,color:#fff
359
+
360
+ style CC3 fill:#b197fc,color:#fff
361
+ </div>
362
+
363
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
364
+ <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;">
365
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
366
+ </div>
367
+ <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;">
368
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Logic Set Methods
369
+ </div>
370
+ <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;">
371
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Proof Operations
372
+ </div>
373
+ <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;">
374
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
375
+ </div>
376
+ <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;">
377
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
378
+ </div>
379
+ </div>
380
+
381
+ <div class="figure-caption">
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">
401
+ <p><strong>Gary Welz</strong></p>
402
+ <p>Retired Faculty Member</p>
403
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
404
+ <p>Borough of Manhattan Community College, CUNY</p>
405
+ <p>CUNY Graduate Center (New Media Lab)</p>
406
+ <p>Email: gwelz@jjay.cuny.edu</p>
407
+ </div>
408
+ </footer>
409
+ </div>
410
+ </body>
411
+ </html>
mathematics_batch_07.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
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
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
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+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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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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+ });
22
+ </script>
23
+ </head>
24
+ <body>
25
+ <div class="container">
26
+ <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
41
+ A1[Geometric Problem] --> B1[Euclidean Axioms]
42
+ C1[Postulates] --> D1[Common Notions]
43
+ E1[Geometric Construction] --> F1[Proof Method]
44
+
45
+ B1 --> G1[Point Line Plane]
46
+ D1 --> H1[Equality Axioms]
47
+ F1 --> I1[Logical Deduction]
48
+
49
+ G1 --> J1[Postulate One]
50
+ H1 --> K1[Transitive Property]
51
+ I1 --> L1[Theorem Statement]
52
+
53
+ J1 --> M1[Postulate Two]
54
+ K1 --> N1[Reflexive Property]
55
+ L1 --> O1[Hypothesis Analysis]
56
+
57
+ M1 --> P1[Postulate Three]
58
+ N1 --> O1
59
+ O1 --> Q1[Conclusion Deduction]
60
+
61
+ P1 --> R1[Postulate Four]
62
+ Q1 --> S1[Proof Construction]
63
+ R1 --> T1[Postulate Five]
64
+
65
+ S1 --> U1[Geometric Proof]
66
+ T1 --> V1[Parallel Postulate]
67
+ U1 --> W1[Euclidean Result]
68
+
69
+ V1 --> X1[Euclidean Geometry]
70
+ W1 --> Y1[Geometric Analysis]
71
+ X1 --> Z1[Euclidean Geometry Output]
72
+
73
+ Y1 --> AA1[Euclidean Geometry Analysis]
74
+ Z1 --> BB1[Euclidean Geometry Final Result]
75
+ AA1 --> CC1[Euclidean Geometry Analysis Complete]
76
+
77
+ style A1 fill:#ff6b6b,color:#fff
78
+ style C1 fill:#ff6b6b,color:#fff
79
+ style E1 fill:#ff6b6b,color:#fff
80
+
81
+ style B1 fill:#ffd43b,color:#000
82
+ style D1 fill:#ffd43b,color:#000
83
+ style F1 fill:#ffd43b,color:#000
84
+ style G1 fill:#ffd43b,color:#000
85
+ style H1 fill:#ffd43b,color:#000
86
+ style I1 fill:#ffd43b,color:#000
87
+ style J1 fill:#ffd43b,color:#000
88
+ style K1 fill:#ffd43b,color:#000
89
+ style L1 fill:#ffd43b,color:#000
90
+ style M1 fill:#ffd43b,color:#000
91
+ style N1 fill:#ffd43b,color:#000
92
+ style O1 fill:#ffd43b,color:#000
93
+ style P1 fill:#ffd43b,color:#000
94
+ style Q1 fill:#ffd43b,color:#000
95
+ style R1 fill:#ffd43b,color:#000
96
+ style S1 fill:#ffd43b,color:#000
97
+ style T1 fill:#ffd43b,color:#000
98
+ style U1 fill:#ffd43b,color:#000
99
+ style V1 fill:#ffd43b,color:#000
100
+ style W1 fill:#ffd43b,color:#000
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
+
108
+ style M1 fill:#51cf66,color:#fff
109
+ style N1 fill:#51cf66,color:#fff
110
+ style O1 fill:#51cf66,color:#fff
111
+ style P1 fill:#51cf66,color:#fff
112
+ style Q1 fill:#51cf66,color:#fff
113
+ style R1 fill:#51cf66,color:#fff
114
+ style S1 fill:#51cf66,color:#fff
115
+ style T1 fill:#51cf66,color:#fff
116
+ style U1 fill:#51cf66,color:#fff
117
+ style V1 fill:#51cf66,color:#fff
118
+ style W1 fill:#51cf66,color:#fff
119
+ style X1 fill:#51cf66,color:#fff
120
+ style Y1 fill:#51cf66,color:#fff
121
+ style Z1 fill:#51cf66,color:#fff
122
+ style AA1 fill:#51cf66,color:#fff
123
+ style BB1 fill:#51cf66,color:#fff
124
+ style CC1 fill:#51cf66,color:#fff
125
+
126
+ style CC1 fill:#b197fc,color:#fff
127
+ </div>
128
+
129
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
130
+ <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;">
131
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
132
+ </div>
133
+ <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;">
134
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Euclidean Methods
135
+ </div>
136
+ <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;">
137
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Geometric Operations
138
+ </div>
139
+ <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;">
140
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
141
+ </div>
142
+ <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;">
143
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
144
+ </div>
145
+ </div>
146
+
147
+ <div class="figure-caption">
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
158
+ A2[Logical Premises] --> B2[Syllogistic Form]
159
+ C2[Major Premise] --> D2[Minor Premise]
160
+ E2[Conclusion] --> F2[Logical Validity]
161
+
162
+ B2 --> G2[Major Term]
163
+ D2 --> H2[Middle Term]
164
+ F2 --> I2[Minor Term]
165
+
166
+ G2 --> J2[Universal Affirmative]
167
+ H2 --> K2[Universal Negative]
168
+ I2 --> L2[Particular Affirmative]
169
+
170
+ J2 --> M2[Particular Negative]
171
+ K2 --> N2[Barbara Syllogism]
172
+ L2 --> O2[Celarent Syllogism]
173
+
174
+ M2 --> P2[Darii Syllogism]
175
+ N2 --> O2
176
+ O2 --> Q2[Ferio Syllogism]
177
+
178
+ P2 --> R2[Syllogistic Figure]
179
+ Q2 --> S2[Logical Form Analysis]
180
+ R2 --> T2[Validity Check]
181
+
182
+ S2 --> U2[Syllogistic Result]
183
+ T2 --> V2[Logical Conclusion]
184
+ U2 --> W2[Aristotelian Logic]
185
+
186
+ V2 --> X2[Syllogistic Analysis]
187
+ W2 --> Y2[Logical Analysis]
188
+ X2 --> Z2[Aristotelian Logic Output]
189
+
190
+ Y2 --> AA2[Aristotelian Logic Analysis]
191
+ Z2 --> BB2[Aristotelian Logic Final Result]
192
+ AA2 --> CC2[Aristotelian Logic Analysis Complete]
193
+
194
+ style A2 fill:#ff6b6b,color:#fff
195
+ style C2 fill:#ff6b6b,color:#fff
196
+ style E2 fill:#ff6b6b,color:#fff
197
+
198
+ style B2 fill:#ffd43b,color:#000
199
+ style D2 fill:#ffd43b,color:#000
200
+ style F2 fill:#ffd43b,color:#000
201
+ style G2 fill:#ffd43b,color:#000
202
+ style H2 fill:#ffd43b,color:#000
203
+ style I2 fill:#ffd43b,color:#000
204
+ style J2 fill:#ffd43b,color:#000
205
+ style K2 fill:#ffd43b,color:#000
206
+ style L2 fill:#ffd43b,color:#000
207
+ style M2 fill:#ffd43b,color:#000
208
+ style N2 fill:#ffd43b,color:#000
209
+ style O2 fill:#ffd43b,color:#000
210
+ style P2 fill:#ffd43b,color:#000
211
+ style Q2 fill:#ffd43b,color:#000
212
+ style R2 fill:#ffd43b,color:#000
213
+ style S2 fill:#ffd43b,color:#000
214
+ style T2 fill:#ffd43b,color:#000
215
+ style U2 fill:#ffd43b,color:#000
216
+ style V2 fill:#ffd43b,color:#000
217
+ style W2 fill:#ffd43b,color:#000
218
+ style X2 fill:#ffd43b,color:#000
219
+ style Y2 fill:#ffd43b,color:#000
220
+ style Z2 fill:#ffd43b,color:#000
221
+ style AA2 fill:#ffd43b,color:#000
222
+ style BB2 fill:#ffd43b,color:#000
223
+ style CC2 fill:#ffd43b,color:#000
224
+
225
+ style M2 fill:#51cf66,color:#fff
226
+ style N2 fill:#51cf66,color:#fff
227
+ style O2 fill:#51cf66,color:#fff
228
+ style P2 fill:#51cf66,color:#fff
229
+ style Q2 fill:#51cf66,color:#fff
230
+ style R2 fill:#51cf66,color:#fff
231
+ style S2 fill:#51cf66,color:#fff
232
+ style T2 fill:#51cf66,color:#fff
233
+ style U2 fill:#51cf66,color:#fff
234
+ style V2 fill:#51cf66,color:#fff
235
+ style W2 fill:#51cf66,color:#fff
236
+ style X2 fill:#51cf66,color:#fff
237
+ style Y2 fill:#51cf66,color:#fff
238
+ style Z2 fill:#51cf66,color:#fff
239
+ style AA2 fill:#51cf66,color:#fff
240
+ style BB2 fill:#51cf66,color:#fff
241
+ style CC2 fill:#51cf66,color:#fff
242
+
243
+ style CC2 fill:#b197fc,color:#fff
244
+ </div>
245
+
246
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
247
+ <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;">
248
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
249
+ </div>
250
+ <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;">
251
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Syllogistic Methods
252
+ </div>
253
+ <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;">
254
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Logical Operations
255
+ </div>
256
+ <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;">
257
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
258
+ </div>
259
+ <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;">
260
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
261
+ </div>
262
+ </div>
263
+
264
+ <div class="figure-caption">
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">
283
+ <p><strong>Gary Welz</strong></p>
284
+ <p>Retired Faculty Member</p>
285
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
286
+ <p>Borough of Manhattan Community College, CUNY</p>
287
+ <p>CUNY Graduate Center (New Media Lab)</p>
288
+ <p>Email: gwelz@jjay.cuny.edu</p>
289
+ </div>
290
+ </footer>
291
+ </div>
292
+ </body>
293
+ </html>
mathematics_index.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Mathematics - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
13
+ flowchart: {
14
+ useMaxWidth: false,
15
+ htmlLabels: true,
16
+ curve: 'linear',
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 - Programming Framework Analysis</h1>
28
+ <p class="subtitle">Systematic visualization of mathematical processes and computational logic</p>
29
+ </header>
30
+
31
+ <section class="overview">
32
+ <h2>Mathematics Overview</h2>
33
+ <p>This collection demonstrates the Programming Framework's application to mathematical processes across all major branches of mathematics. Each batch contains detailed flowcharts representing the computational logic and reasoning patterns inherent in mathematical operations.</p>
34
+
35
+ <div class="color-legend">
36
+ <h3>Universal Color Coding System</h3>
37
+ <div class="color-grid">
38
+ <div class="color-item">
39
+ <span class="color-box" style="background: #ff6b6b;"></span>
40
+ <span class="color-label">Red - Triggers & Inputs</span>
41
+ </div>
42
+ <div class="color-item">
43
+ <span class="color-box" style="background: #ffd43b;"></span>
44
+ <span class="color-label">Yellow - Structures & Objects</span>
45
+ </div>
46
+ <div class="color-item">
47
+ <span class="color-box" style="background: #51cf66;"></span>
48
+ <span class="color-label">Green - Processing & Operations</span>
49
+ </div>
50
+ <div class="color-item">
51
+ <span class="color-box" style="background: #74c0fc;"></span>
52
+ <span class="color-label">Blue - Intermediates & States</span>
53
+ </div>
54
+ <div class="color-item">
55
+ <span class="color-box" style="background: #b197fc;"></span>
56
+ <span class="color-label">Violet - Products & Outputs</span>
57
+ </div>
58
+ </div>
59
+ </div>
60
+ </section>
61
+
62
+ <section class="batch-navigation">
63
+ <h2>Mathematics Process Batches</h2>
64
+
65
+ <div class="batch-category">
66
+ <h3>🔢 Number Theory</h3>
67
+ <div class="batch-links">
68
+ <a href="mathematics_batch_01.html" class="batch-link">
69
+ <span class="batch-number">Batch 01</span>
70
+ <span class="batch-title">Prime Factorization & Modular Arithmetic</span>
71
+ <span class="batch-count">3 processes</span>
72
+ </a>
73
+ </div>
74
+ </div>
75
+
76
+ <div class="batch-category">
77
+ <h3>📊 Analysis & Calculus</h3>
78
+ <div class="batch-links">
79
+ <a href="mathematics_batch_02.html" class="batch-link">
80
+ <span class="batch-number">Batch 02</span>
81
+ <span class="batch-title">Series Expansion & Differential Equations</span>
82
+ <span class="batch-count">3 processes</span>
83
+ </a>
84
+ </div>
85
+ </div>
86
+
87
+ <div class="batch-category">
88
+ <h3>🔗 Abstract Algebra</h3>
89
+ <div class="batch-links">
90
+ <a href="mathematics_batch_03.html" class="batch-link">
91
+ <span class="batch-number">Batch 03</span>
92
+ <span class="batch-title">Group Theory & Ring Theory</span>
93
+ <span class="batch-count">3 processes</span>
94
+ </a>
95
+ </div>
96
+ </div>
97
+
98
+ <div class="batch-category">
99
+ <h3>📐 Geometry & Topology</h3>
100
+ <div class="batch-links">
101
+ <a href="mathematics_batch_04.html" class="batch-link">
102
+ <span class="batch-number">Batch 04</span>
103
+ <span class="batch-title">Geometric Constructions & Topological Transformations</span>
104
+ <span class="batch-count">3 processes</span>
105
+ </a>
106
+ </div>
107
+ </div>
108
+
109
+ <div class="batch-category">
110
+ <h3>⚙️ Applied Mathematics</h3>
111
+ <div class="batch-links">
112
+ <a href="mathematics_batch_05.html" class="batch-link">
113
+ <span class="batch-number">Batch 05</span>
114
+ <span class="batch-title">Numerical Methods & Statistical Analysis</span>
115
+ <span class="batch-count">3 processes</span>
116
+ </a>
117
+ </div>
118
+ </div>
119
+
120
+ <div class="batch-category">
121
+ <h3>🕸️ Discrete Mathematics</h3>
122
+ <div class="batch-links">
123
+ <a href="mathematics_batch_06.html" class="batch-link">
124
+ <span class="batch-number">Batch 06</span>
125
+ <span class="batch-title">Graph Theory & Combinatorics</span>
126
+ <span class="batch-count">3 processes</span>
127
+ </a>
128
+ </div>
129
+ </div>
130
+
131
+ <div class="batch-category">
132
+ <h3>🏛️ Historical & Educational</h3>
133
+ <div class="batch-links">
134
+ <a href="mathematics_batch_07.html" class="batch-link">
135
+ <span class="batch-number">Batch 07</span>
136
+ <span class="batch-title">Euclid's Geometry & Aristotle's Syllogism</span>
137
+ <span class="batch-count">2 processes</span>
138
+ </a>
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="navigation">
144
+ <h2>Navigation</h2>
145
+ <div class="nav-links">
146
+ <a href="index.html" class="nav-link">← Back to Programming Framework</a>
147
+ <a href="biology_processes.html" class="nav-link">Biology Processes</a>
148
+ <a href="chemistry_processes.html" class="nav-link">Chemistry Processes</a>
149
+ <a href="computer_science_processes.html" class="nav-link">Computer Science Processes</a>
150
+ <a href="physics_processes.html" class="nav-link">Physics Processes</a>
151
+ </div>
152
+ </section>
153
+
154
+ <footer>
155
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
156
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
157
+ <div class="contact-info">
158
+ <p><strong>Gary Welz</strong></p>
159
+ <p>Retired Faculty Member</p>
160
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
161
+ <p>Borough of Manhattan Community College, CUNY</p>
162
+ <p>CUNY Graduate Center (New Media Lab)</p>
163
+ <p>Email: gwelz@jjay.cuny.edu</p>
164
+ </div>
165
+ </footer>
166
+ </div>
167
+ </body>
168
+ </html>
physics_batch_01.html ADDED
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1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Physics Batch 01 - Classical Mechanics - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
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+ flowchart: {
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+ useMaxWidth: false,
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+ htmlLabels: true,
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+ curve: 'linear',
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+ nodeSpacing: 30,
18
+ rankSpacing: 30,
19
+ padding: 10
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+ }
21
+ });
22
+ </script>
23
+ </head>
24
+ <body>
25
+ <div class="container">
26
+ <header>
27
+ <h1>🔬 Physics Batch 01 - Classical Mechanics</h1>
28
+ <p class="subtitle">Newtonian Dynamics, Lagrangian Mechanics, and Hamiltonian Mechanics</p>
29
+ </header>
30
+
31
+ <section class="batch-info">
32
+ <h2>Classical Mechanics Processes</h2>
33
+ <p>This batch demonstrates the Programming Framework's application to fundamental classical mechanics operations. Each process shows the computational logic behind Newtonian dynamics, Lagrangian formulations, and Hamiltonian mechanics.</p>
34
+ </section>
35
+
36
+ <section class="process">
37
+ <h2>1. Newtonian Dynamics Process</h2>
38
+ <div class="figure">
39
+ <div class="mermaid">
40
+ graph TD
41
+ A1[System Definition] --> B1[Force Analysis]
42
+ C1[Mass Distribution] --> D1[Inertia Calculation]
43
+ E1[Initial Conditions] --> F1[Boundary Conditions]
44
+
45
+ B1 --> G1[Newton First Law]
46
+ D1 --> H1[Newton Second Law]
47
+ F1 --> I1[Newton Third Law]
48
+
49
+ G1 --> J1[Inertial Reference Frame]
50
+ H1 --> K1[Force Equals Mass Times Acceleration]
51
+ I1 --> L1[Action Reaction Pairs]
52
+
53
+ J1 --> M1[Equilibrium Analysis]
54
+ K1 --> L1
55
+ L1 --> N1[Momentum Conservation]
56
+
57
+ M1 --> O1[Static Equilibrium]
58
+ N1 --> P1[Angular Momentum]
59
+ O1 --> Q1[Newtonian Dynamics Process]
60
+
61
+ P1 --> R1[Torque Analysis]
62
+ Q1 --> S1[Energy Conservation]
63
+ R1 --> T1[Newtonian Dynamics Result]
64
+
65
+ S1 --> U1[Kinetic Energy]
66
+ T1 --> V1[Potential Energy]
67
+ U1 --> W1[Newtonian Dynamics Output]
68
+
69
+ V1 --> X1[Newtonian Dynamics Analysis]
70
+ W1 --> Y1[Newtonian Dynamics Final Result]
71
+ X1 --> Z1[Newtonian Dynamics Analysis Complete]
72
+
73
+ style A1 fill:#ff6b6b,color:#fff
74
+ style C1 fill:#ff6b6b,color:#fff
75
+ style E1 fill:#ff6b6b,color:#fff
76
+
77
+ style B1 fill:#ffd43b,color:#000
78
+ style D1 fill:#ffd43b,color:#000
79
+ style F1 fill:#ffd43b,color:#000
80
+ style G1 fill:#ffd43b,color:#000
81
+ style H1 fill:#ffd43b,color:#000
82
+ style I1 fill:#ffd43b,color:#000
83
+ style J1 fill:#ffd43b,color:#000
84
+ style K1 fill:#ffd43b,color:#000
85
+ style L1 fill:#ffd43b,color:#000
86
+ style M1 fill:#ffd43b,color:#000
87
+ style N1 fill:#ffd43b,color:#000
88
+ style O1 fill:#ffd43b,color:#000
89
+ style P1 fill:#ffd43b,color:#000
90
+ style Q1 fill:#ffd43b,color:#000
91
+ style R1 fill:#ffd43b,color:#000
92
+ style S1 fill:#ffd43b,color:#000
93
+ style T1 fill:#ffd43b,color:#000
94
+ style U1 fill:#ffd43b,color:#000
95
+ style V1 fill:#ffd43b,color:#000
96
+ style W1 fill:#ffd43b,color:#000
97
+ style X1 fill:#ffd43b,color:#000
98
+ style Y1 fill:#ffd43b,color:#000
99
+ style Z1 fill:#ffd43b,color:#000
100
+
101
+ style M1 fill:#51cf66,color:#fff
102
+ style N1 fill:#51cf66,color:#fff
103
+ style O1 fill:#51cf66,color:#fff
104
+ style P1 fill:#51cf66,color:#fff
105
+ style Q1 fill:#51cf66,color:#fff
106
+ style R1 fill:#51cf66,color:#fff
107
+ style S1 fill:#51cf66,color:#fff
108
+ style T1 fill:#51cf66,color:#fff
109
+ style U1 fill:#51cf66,color:#fff
110
+ style V1 fill:#51cf66,color:#fff
111
+ style W1 fill:#51cf66,color:#fff
112
+ style X1 fill:#51cf66,color:#fff
113
+ style Y1 fill:#51cf66,color:#fff
114
+ style Z1 fill:#51cf66,color:#fff
115
+
116
+ style Z1 fill:#b197fc,color:#fff
117
+ </div>
118
+
119
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
120
+ <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;">
121
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
122
+ </div>
123
+ <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;">
124
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Newtonian Methods
125
+ </div>
126
+ <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;">
127
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Dynamics Operations
128
+ </div>
129
+ <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;">
130
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
131
+ </div>
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:#b197fc;"></span>Products
134
+ </div>
135
+ </div>
136
+
137
+ <div class="figure-caption">
138
+ <strong>Figure 1.</strong> Newtonian Dynamics Process. This classical mechanics process visualization demonstrates Newton's laws of motion and force analysis. The flowchart shows system definition and initial conditions, Newtonian methods and laws, dynamics operations and energy analysis, intermediate results, and final Newtonian dynamics outputs.
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="process">
144
+ <h2>2. Lagrangian Mechanics Process</h2>
145
+ <div class="figure">
146
+ <div class="mermaid">
147
+ graph TD
148
+ A2[Generalized Coordinates] --> B2[Configuration Space]
149
+ C2[Constraint Analysis] --> D2[Virtual Displacement]
150
+ E2[Kinetic Energy] --> F2[Potential Energy]
151
+
152
+ B2 --> G2[Lagrangian Function]
153
+ D2 --> H2[Generalized Forces]
154
+ F2 --> I2[Conservative Forces]
155
+
156
+ G2 --> J2[L equals T minus V]
157
+ H2 --> K2[Non Conservative Forces]
158
+ I2 --> L2[Euler Lagrange Equations]
159
+
160
+ J2 --> M2[Action Integral]
161
+ K2 --> L2
162
+ L2 --> N2[Variational Principle]
163
+
164
+ M2 --> O2[Principle of Least Action]
165
+ N2 --> P2[Generalized Momentum]
166
+ O2 --> Q2[Lagrangian Mechanics Process]
167
+
168
+ P2 --> R2[Canonical Coordinates]
169
+ Q2 --> S2[Symmetry Analysis]
170
+ R2 --> T2[Lagrangian Mechanics Result]
171
+
172
+ S2 --> U2[Noether Theorem]
173
+ T2 --> V2[Conservation Laws]
174
+ U2 --> W2[Lagrangian Mechanics Output]
175
+
176
+ V2 --> X2[Lagrangian Mechanics Analysis]
177
+ W2 --> Y2[Lagrangian Mechanics Final Result]
178
+ X2 --> Z2[Lagrangian Mechanics Analysis Complete]
179
+
180
+ style A2 fill:#ff6b6b,color:#fff
181
+ style C2 fill:#ff6b6b,color:#fff
182
+ style E2 fill:#ff6b6b,color:#fff
183
+
184
+ style B2 fill:#ffd43b,color:#000
185
+ style D2 fill:#ffd43b,color:#000
186
+ style F2 fill:#ffd43b,color:#000
187
+ style G2 fill:#ffd43b,color:#000
188
+ style H2 fill:#ffd43b,color:#000
189
+ style I2 fill:#ffd43b,color:#000
190
+ style J2 fill:#ffd43b,color:#000
191
+ style K2 fill:#ffd43b,color:#000
192
+ style L2 fill:#ffd43b,color:#000
193
+ style M2 fill:#ffd43b,color:#000
194
+ style N2 fill:#ffd43b,color:#000
195
+ style O2 fill:#ffd43b,color:#000
196
+ style P2 fill:#ffd43b,color:#000
197
+ style Q2 fill:#ffd43b,color:#000
198
+ style R2 fill:#ffd43b,color:#000
199
+ style S2 fill:#ffd43b,color:#000
200
+ style T2 fill:#ffd43b,color:#000
201
+ style U2 fill:#ffd43b,color:#000
202
+ style V2 fill:#ffd43b,color:#000
203
+ style W2 fill:#ffd43b,color:#000
204
+ style X2 fill:#ffd43b,color:#000
205
+ style Y2 fill:#ffd43b,color:#000
206
+ style Z2 fill:#ffd43b,color:#000
207
+
208
+ style M2 fill:#51cf66,color:#fff
209
+ style N2 fill:#51cf66,color:#fff
210
+ style O2 fill:#51cf66,color:#fff
211
+ style P2 fill:#51cf66,color:#fff
212
+ style Q2 fill:#51cf66,color:#fff
213
+ style R2 fill:#51cf66,color:#fff
214
+ style S2 fill:#51cf66,color:#fff
215
+ style T2 fill:#51cf66,color:#fff
216
+ style U2 fill:#51cf66,color:#fff
217
+ style V2 fill:#51cf66,color:#fff
218
+ style W2 fill:#51cf66,color:#fff
219
+ style X2 fill:#51cf66,color:#fff
220
+ style Y2 fill:#51cf66,color:#fff
221
+ style Z2 fill:#51cf66,color:#fff
222
+
223
+ style Z2 fill:#b197fc,color:#fff
224
+ </div>
225
+
226
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
227
+ <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;">
228
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
229
+ </div>
230
+ <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;">
231
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Lagrangian Methods
232
+ </div>
233
+ <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;">
234
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Variational Operations
235
+ </div>
236
+ <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;">
237
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
238
+ </div>
239
+ <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;">
240
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
241
+ </div>
242
+ </div>
243
+
244
+ <div class="figure-caption">
245
+ <strong>Figure 2.</strong> Lagrangian Mechanics Process. This classical mechanics process visualization demonstrates variational principles and generalized coordinates. The flowchart shows generalized coordinates and constraint analysis, Lagrangian methods and variational principles, variational operations and symmetry analysis, intermediate results, and final Lagrangian mechanics outputs.
246
+ </div>
247
+ </div>
248
+ </section>
249
+
250
+ <section class="process">
251
+ <h2>3. Hamiltonian Mechanics Process</h2>
252
+ <div class="figure">
253
+ <div class="mermaid">
254
+ graph TD
255
+ A3[Phase Space] --> B3[Canonical Variables]
256
+ C3[Legendre Transform] --> D3[Hamiltonian Function]
257
+ E3[Poisson Brackets] --> F3[Canonical Equations]
258
+
259
+ B3 --> G3[Position Momentum Pairs]
260
+ D3 --> H3[H equals T plus V]
261
+ F3 --> I3[Hamilton Equations]
262
+
263
+ G3 --> J3[Canonical Transformations]
264
+ H3 --> K3[Energy Conservation]
265
+ I3 --> L3[Phase Space Evolution]
266
+
267
+ J3 --> M3[Action Angle Variables]
268
+ K3 --> L3
269
+ L3 --> N3[Liouville Theorem]
270
+
271
+ M3 --> O3[Integrable Systems]
272
+ N3 --> P3[Phase Space Volume]
273
+ O3 --> Q3[Hamiltonian Mechanics Process]
274
+
275
+ P3 --> R3[Chaotic Dynamics]
276
+ Q3 --> S3[Canonical Perturbation Theory]
277
+ R3 --> T3[Hamiltonian Mechanics Result]
278
+
279
+ S3 --> U3[Adiabatic Invariants]
280
+ T3 --> V3[Canonical Quantization]
281
+ U3 --> W3[Hamiltonian Mechanics Output]
282
+
283
+ V3 --> X3[Hamiltonian Mechanics Analysis]
284
+ W3 --> Y3[Hamiltonian Mechanics Final Result]
285
+ X3 --> Z3[Hamiltonian Mechanics Analysis Complete]
286
+
287
+ style A3 fill:#ff6b6b,color:#fff
288
+ style C3 fill:#ff6b6b,color:#fff
289
+ style E3 fill:#ff6b6b,color:#fff
290
+
291
+ style B3 fill:#ffd43b,color:#000
292
+ style D3 fill:#ffd43b,color:#000
293
+ style F3 fill:#ffd43b,color:#000
294
+ style G3 fill:#ffd43b,color:#000
295
+ style H3 fill:#ffd43b,color:#000
296
+ style I3 fill:#ffd43b,color:#000
297
+ style J3 fill:#ffd43b,color:#000
298
+ style K3 fill:#ffd43b,color:#000
299
+ style L3 fill:#ffd43b,color:#000
300
+ style M3 fill:#ffd43b,color:#000
301
+ style N3 fill:#ffd43b,color:#000
302
+ style O3 fill:#ffd43b,color:#000
303
+ style P3 fill:#ffd43b,color:#000
304
+ style Q3 fill:#ffd43b,color:#000
305
+ style R3 fill:#ffd43b,color:#000
306
+ style S3 fill:#ffd43b,color:#000
307
+ style T3 fill:#ffd43b,color:#000
308
+ style U3 fill:#ffd43b,color:#000
309
+ style V3 fill:#ffd43b,color:#000
310
+ style W3 fill:#ffd43b,color:#000
311
+ style X3 fill:#ffd43b,color:#000
312
+ style Y3 fill:#ffd43b,color:#000
313
+ style Z3 fill:#ffd43b,color:#000
314
+
315
+ style M3 fill:#51cf66,color:#fff
316
+ style N3 fill:#51cf66,color:#fff
317
+ style O3 fill:#51cf66,color:#fff
318
+ style P3 fill:#51cf66,color:#fff
319
+ style Q3 fill:#51cf66,color:#fff
320
+ style R3 fill:#51cf66,color:#fff
321
+ style S3 fill:#51cf66,color:#fff
322
+ style T3 fill:#51cf66,color:#fff
323
+ style U3 fill:#51cf66,color:#fff
324
+ style V3 fill:#51cf66,color:#fff
325
+ style W3 fill:#51cf66,color:#fff
326
+ style X3 fill:#51cf66,color:#fff
327
+ style Y3 fill:#51cf66,color:#fff
328
+ style Z3 fill:#51cf66,color:#fff
329
+
330
+ style Z3 fill:#b197fc,color:#fff
331
+ </div>
332
+
333
+ <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
334
+ <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;">
335
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
336
+ </div>
337
+ <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;">
338
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Hamiltonian Methods
339
+ </div>
340
+ <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;">
341
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Canonical Operations
342
+ </div>
343
+ <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;">
344
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
345
+ </div>
346
+ <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;">
347
+ <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
348
+ </div>
349
+ </div>
350
+
351
+ <div class="figure-caption">
352
+ <strong>Figure 3.</strong> Hamiltonian Mechanics Process. This classical mechanics process visualization demonstrates phase space dynamics and canonical transformations. The flowchart shows phase space and canonical variables, Hamiltonian methods and transformations, canonical operations and perturbation theory, intermediate results, and final Hamiltonian mechanics outputs.
353
+ </div>
354
+ </div>
355
+ </section>
356
+
357
+ <section class="navigation">
358
+ <h2>Navigation</h2>
359
+ <div class="nav-links">
360
+ <a href="physics_index.html" class="nav-link">← Back to Physics Index</a>
361
+ <a href="physics_batch_02.html" class="nav-link">Next: Electromagnetism →</a>
362
+ <a href="index.html" class="nav-link">Programming Framework Home</a>
363
+ </div>
364
+ </section>
365
+
366
+ <footer>
367
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
368
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
369
+ <div class="contact-info">
370
+ <p><strong>Gary Welz</strong></p>
371
+ <p>Retired Faculty Member</p>
372
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
373
+ <p>Borough of Manhattan Community College, CUNY</p>
374
+ <p>CUNY Graduate Center (New Media Lab)</p>
375
+ <p>Email: gwelz@jjay.cuny.edu</p>
376
+ </div>
377
+ </footer>
378
+ </div>
379
+ </body>
380
+ </html>
physics_index.html ADDED
@@ -0,0 +1,168 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ <!DOCTYPE html>
2
+ <html lang="en">
3
+ <head>
4
+ <meta charset="UTF-8" />
5
+ <meta name="viewport" content="width=device-width, initial-scale=1" />
6
+ <title>Physics - Programming Framework Analysis</title>
7
+ <link rel="stylesheet" href="style.css">
8
+ <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
9
+ <script>
10
+ mermaid.initialize({
11
+ startOnLoad: true,
12
+ theme: 'default',
13
+ flowchart: {
14
+ useMaxWidth: false,
15
+ htmlLabels: true,
16
+ curve: 'linear',
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>⚛️ Physics - Programming Framework Analysis</h1>
28
+ <p class="subtitle">Systematic visualization of physical processes and quantum phenomena</p>
29
+ </header>
30
+
31
+ <section class="overview">
32
+ <h2>Physics Overview</h2>
33
+ <p>This collection demonstrates the Programming Framework's application to physical processes across all major branches of physics. Each batch contains detailed flowcharts representing the computational logic and physical principles inherent in natural phenomena.</p>
34
+
35
+ <div class="color-legend">
36
+ <h3>Universal Color Coding System</h3>
37
+ <div class="color-grid">
38
+ <div class="color-item">
39
+ <span class="color-box" style="background: #ff6b6b;"></span>
40
+ <span class="color-label">Red - Triggers & Inputs</span>
41
+ </div>
42
+ <div class="color-item">
43
+ <span class="color-box" style="background: #ffd43b;"></span>
44
+ <span class="color-label">Yellow - Structures & Objects</span>
45
+ </div>
46
+ <div class="color-item">
47
+ <span class="color-box" style="background: #51cf66;"></span>
48
+ <span class="color-label">Green - Processing & Operations</span>
49
+ </div>
50
+ <div class="color-item">
51
+ <span class="color-box" style="background: #74c0fc;"></span>
52
+ <span class="color-label">Blue - Intermediates & States</span>
53
+ </div>
54
+ <div class="color-item">
55
+ <span class="color-box" style="background: #b197fc;"></span>
56
+ <span class="color-label">Violet - Products & Outputs</span>
57
+ </div>
58
+ </div>
59
+ </div>
60
+ </section>
61
+
62
+ <section class="batch-navigation">
63
+ <h2>Physics Process Batches</h2>
64
+
65
+ <div class="batch-category">
66
+ <h3>🔬 Classical Mechanics</h3>
67
+ <div class="batch-links">
68
+ <a href="physics_batch_01.html" class="batch-link">
69
+ <span class="batch-number">Batch 01</span>
70
+ <span class="batch-title">Newtonian Dynamics & Lagrangian Mechanics</span>
71
+ <span class="batch-count">3 processes</span>
72
+ </a>
73
+ </div>
74
+ </div>
75
+
76
+ <div class="batch-category">
77
+ <h3>⚡ Electromagnetism</h3>
78
+ <div class="batch-links">
79
+ <a href="physics_batch_02.html" class="batch-link">
80
+ <span class="batch-number">Batch 02</span>
81
+ <span class="batch-title">Maxwell Equations & Electromagnetic Waves</span>
82
+ <span class="batch-count">3 processes</span>
83
+ </a>
84
+ </div>
85
+ </div>
86
+
87
+ <div class="batch-category">
88
+ <h3>🌡️ Thermodynamics</h3>
89
+ <div class="batch-links">
90
+ <a href="physics_batch_03.html" class="batch-link">
91
+ <span class="batch-number">Batch 03</span>
92
+ <span class="batch-title">Statistical Mechanics & Entropy</span>
93
+ <span class="batch-count">3 processes</span>
94
+ </a>
95
+ </div>
96
+ </div>
97
+
98
+ <div class="batch-category">
99
+ <h3>⚛️ Quantum Mechanics</h3>
100
+ <div class="batch-links">
101
+ <a href="physics_batch_04.html" class="batch-link">
102
+ <span class="batch-number">Batch 04</span>
103
+ <span class="batch-title">Wave Functions & Quantum States</span>
104
+ <span class="batch-count">3 processes</span>
105
+ </a>
106
+ </div>
107
+ </div>
108
+
109
+ <div class="batch-category">
110
+ <h3>🌌 Relativity</h3>
111
+ <div class="batch-links">
112
+ <a href="physics_batch_05.html" class="batch-link">
113
+ <span class="batch-number">Batch 05</span>
114
+ <span class="batch-title">Special & General Relativity</span>
115
+ <span class="batch-count">3 processes</span>
116
+ </a>
117
+ </div>
118
+ </div>
119
+
120
+ <div class="batch-category">
121
+ <h3>🔭 Astrophysics</h3>
122
+ <div class="batch-links">
123
+ <a href="physics_batch_06.html" class="batch-link">
124
+ <span class="batch-number">Batch 06</span>
125
+ <span class="batch-title">Stellar Evolution & Cosmology</span>
126
+ <span class="batch-count">3 processes</span>
127
+ </a>
128
+ </div>
129
+ </div>
130
+
131
+ <div class="batch-category">
132
+ <h3>🔬 Particle Physics</h3>
133
+ <div class="batch-links">
134
+ <a href="physics_batch_07.html" class="batch-link">
135
+ <span class="batch-number">Batch 07</span>
136
+ <span class="batch-title">Standard Model & Particle Interactions</span>
137
+ <span class="batch-count">3 processes</span>
138
+ </a>
139
+ </div>
140
+ </div>
141
+ </section>
142
+
143
+ <section class="navigation">
144
+ <h2>Navigation</h2>
145
+ <div class="nav-links">
146
+ <a href="index.html" class="nav-link">← Back to Programming Framework</a>
147
+ <a href="mathematics_index.html" class="nav-link">Mathematics Processes</a>
148
+ <a href="chemistry_index.html" class="nav-link">Chemistry Processes</a>
149
+ <a href="computer_science_index.html" class="nav-link">Computer Science Processes</a>
150
+ <a href="https://huggingface.co/spaces/garywelz/glmp" class="nav-link" target="_blank">Biology Processes (GLMP)</a>
151
+ </div>
152
+ </section>
153
+
154
+ <footer>
155
+ <p><strong>Generated using the Programming Framework methodology</strong></p>
156
+ <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
157
+ <div class="contact-info">
158
+ <p><strong>Gary Welz</strong></p>
159
+ <p>Retired Faculty Member</p>
160
+ <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
161
+ <p>Borough of Manhattan Community College, CUNY</p>
162
+ <p>CUNY Graduate Center (New Media Lab)</p>
163
+ <p>Email: gwelz@jjay.cuny.edu</p>
164
+ </div>
165
+ </footer>
166
+ </div>
167
+ </body>
168
+ </html>
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230
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234
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235
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230
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+ /* Batch Status Section */
234
+ .batch-status {
235
+ margin: 3rem 0;
236
+ }
237
+
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+ .status-grid {
239
+ display: grid;
240
+ grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
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+ gap: 1.5rem;
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+ margin-top: 1.5rem;
243
+ }
244
+
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+ .status-card {
246
+ background: white;
247
+ border-radius: 12px;
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+ padding: 1.5rem;
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+ border: 2px solid #e9ecef;
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+ transition: all 0.3s ease;
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+ }
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+
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+ .status-card.complete {
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+ border-color: #51cf66;
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+ background: linear-gradient(135deg, #f8fff9 0%, #e8f5e8 100%);
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+
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+ .status-card.in-progress {
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+ .status-card.external {
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+ border-color: #74c0fc;
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+ }
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+ .status-card h3 {
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+ margin: 0 0 1rem 0;
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+ }
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+
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+ .status-card p {
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276
+ color: #666;
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+ line-height: 1.5;
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+
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+ .status-card p strong {
281
+ color: #333;
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285
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