https://github.com/kimtth/science-companion-mindmap

🧪References and notes for science mindmap — College-level science overview
https://github.com/kimtth/science-companion-mindmap

biology chemistry college mermaid-diagrams physics science

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🧪References and notes for science mindmap — College-level science overview

• Host: GitHub
• URL: https://github.com/kimtth/science-companion-mindmap
• Owner: kimtth
• Created: 2025-11-01T18:01:36.000Z (8 months ago)
• Default Branch: main
• Last Pushed: 2025-11-21T11:16:27.000Z (7 months ago)
• Last Synced: 2025-11-21T11:24:09.026Z (7 months ago)
• Topics: biology, chemistry, college, mermaid-diagrams, physics, science
• Homepage:
• Size: 719 KB
• Stars: 1
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# 🧪🔬🧬 Science Companion Mindmaps

> **Comprehensive visual learning guides for college-level science courses**

[![Mermaid](https://img.shields.io/badge/Made%20with-Mermaid-ff69b4)](https://mermaid.js.org/)

[![College Level](https://img.shields.io/badge/Level-College-blue)](https://github.com)

This repository is inspired by [Grokipedia](https://grokipedia.com/), which demonstrates how LLMs can understand world knowledge.

## 📖 Overview

This repository contains **interactive flowchart mindmaps** for four core science and mathematics disciplines, designed to help students visualize and understand the hierarchical relationships between concepts in:

- ⚛️ **General Physics** - From mechanics to quantum physics

- 🧬 **General Biology** - From cells to ecosystems  

- 🧪 **General Chemistry** - From atoms to organic molecules

- 🔢 **College Mathematics** - From calculus to mathematical foundations

Each mindmap is created using **Mermaid diagrams** with color-coded categories, concise descriptions, and practical context for every concept.

**✅ Comprehensive Coverage:** All diagrams provide complete coverage of standard college-level introductory courses, aligned with leading textbooks (Campbell Biology, Zumdahl Chemistry, Halliday/Resnick Physics).

## 🎯 Features

✨ **Comprehensive Coverage** - 2,600+ concepts across 27 detailed diagrams covering all major topics in introductory college-level science and mathematics courses  

🎨 **Color-Coded** - Physics (blue), Biology (green), Chemistry (orange), Mathematics (purple) with 3-4 tier visual hierarchy  

📊 **Hierarchical Structure** - 3-4 levels of depth showing concept relationships from foundational principles to specific applications  

💡 **Contextual Learning** - Each node includes 2-3 line descriptions: concept name, definition, and practical significance  

📱 **Interactive** - Renders in any Mermaid-compatible viewer and natively on GitHub  

📚 **Textbook-Aligned** - Based on standard college textbooks with equations, formulas, and key principles included  

🎓 **Exam-Ready** - Perfect for MCAT, DAT, AP courses, and undergraduate science requirements  

✅ **Verified Structure** - All diagrams verified with proper node connections and consistent color coding

## 📂 Repository Structure

```

science-companion-mindmap/

│

├── 📘 **Navigation Hub Files** (Root Level)

│   ├── biology.md          # 🧭 Biology navigation hub → biology/*.md

│   ├── chemistry.md        # 🧭 Chemistry navigation hub → chemistry/*.md

│   ├── math.md             # 🧭 Mathematics navigation hub → math/*.md

│   └── physhics.md         # 🧭 Physics navigation hub → physics/*.md (note: filename typo preserved for compatibility)

│

├── 📗 **biology/** - Biology Topic Diagrams (Green Theme)

│   ├── biology-cell.md                 # Cell structure, metabolism, division

│   ├── biology-genetics.md             # DNA, inheritance, gene expression

│   ├── biology-evolution.md            # Natural selection, speciation

│   ├── biology-ecology.md              # Populations, ecosystems, conservation

│   ├── biology-organisms.md            # Plant & animal systems

│   └── biology-diversity.md            # Taxonomy, phylogeny, biodiversity

│

├── 📙 **chemistry/** - Chemistry Topic Diagrams (Orange Theme)

│   ├── chemistry-atomic.md             # Atomic structure, periodic table

│   ├── chemistry-bonding.md            # Ionic, covalent, molecular geometry

│   ├── chemistry-stoichiometry.md      # Moles, reactions, states of matter

│   ├── chemistry-thermochem-kinetics.md # Energy, reaction rates

│   ├── chemistry-equilibrium.md        # Equilibrium, Le Châtelier

│   ├── chemistry-acids-bases.md        # pH, buffers, titration

│   ├── chemistry-redox.md              # Oxidation-reduction, electrochemistry

│   ├── chemistry-organic.md            # Hydrocarbons, functional groups

│   └── chemistry-transition-nuclear.md # Transition metals, radioactivity

│

├── 🟣 **math/** - Mathematics Topic Diagrams (Purple Theme)

│   ├── math-calculus.md                # Limits, derivatives, integrals, series, multivariable

│   ├── math-linear-algebra.md          # Vectors, matrices, eigenvalues, vector spaces

│   ├── math-differential-equations.md  # ODEs, PDEs, Laplace transforms, applications

│   ├── math-probability-statistics.md  # Probability, distributions, inference, regression

│   ├── math-discrete.md                # Logic, set theory, combinatorics, graph theory

│   └── math-logic-foundations.md       # Set theory, number theory, formal systems

│

├── 📗 **physics/** - Physics Topic Diagrams (Blue Theme)

│   ├── physics-mechanics.md            # Mechanics, kinematics, dynamics

│   ├── physics-waves.md                # Waves, SHM, sound

│   ├── physics-thermodynamics.md       # Heat, entropy, engines

│   ├── physics-electromagnetism.md     # Fields, circuits, EM waves

│   ├── physics-optics.md               # Geometric & wave optics

│   └── physics-modern.md               # Relativity, quantum, nuclear

│

├── 📘 **note/** - Study Guides & Formulas

│   ├── physhics-note.md                # Physics formulas & concepts

│   ├── biology-note.md                 # Biology formulas & concepts

│   ├── chemistry-note.md               # Chemistry formulas & concepts

│   └── math-note.md                    # Mathematics formulas & concepts

│

└── 📋 README.md                        

```

**📌 Navigation:** Start with root-level hub files (`biology.md`, `chemistry.md`, `math.md`, `physhics.md`) which link to detailed topic diagrams in their respective folders.

## 🔬 Subject Guides

### ⚛️ Physics (Blue Theme) - 6 Detailed Diagrams

1. **physics-mechanics.md** (~220 nodes)  

   Kinematics • Dynamics (Newton's laws) • Energy & Work • Momentum • Rotation • Fluids

2. **physics-waves.md** (~180 nodes)  

   Simple Harmonic Motion • Wave Properties • Sound (Doppler, intensity)

3. **physics-thermodynamics.md** (~190 nodes)  

   Temperature & Heat • Gas Laws • First Law (ΔU = Q - W) • Second Law (entropy, Carnot)

4. **physics-electromagnetism.md** (~210 nodes)  

   Electric Fields (Coulomb, Gauss) • Electric Potential • Circuits (Ohm, Kirchhoff) • Magnetism • EM Induction (Faraday, Lenz)

5. **physics-optics.md** (~185 nodes)  

   Geometric Optics (mirrors, lenses, Snell's law) • Wave Optics (interference, diffraction, polarization)

6. **physics-modern.md** (~200 nodes)  

   Special Relativity (E=mc²) • Quantum Mechanics (uncertainty, Schrödinger) • Atomic Physics (Bohr model) • Nuclear Physics (fission/fusion)

### 🧬 Biology (Green Theme) - 6 Detailed Diagrams

1. **biology-cell.md** (~180 nodes)  

   Cell Theory • Prokaryotes vs Eukaryotes • Organelles • Membrane Transport • Cell Signaling • Cell Cycle (mitosis/meiosis)

2. **biology-genetics.md** (~175 nodes)  

   DNA Structure & Replication • Gene Expression (transcription/translation) • Gene Regulation • Inheritance (Mendel's laws) • CRISPR

3. **biology-evolution.md** (~165 nodes)  

   Natural Selection • Evidence (fossils, comparative anatomy) • Speciation • Population Genetics (Hardy-Weinberg) • Phylogeny

4. **biology-ecology.md** (~155 nodes)  

   Population Ecology (growth models) • Community Ecology (competition, succession) • Ecosystem Ecology (energy flow, nutrient cycles) • Conservation

5. **biology-organisms.md** (~170 nodes)  

   Plant Structure & Reproduction • Animal Organ Systems (circulatory, respiratory, digestive, nervous, endocrine, immune) • Homeostasis

6. **biology-diversity.md** (~165 nodes)  

   Viruses • Prokaryotes (bacteria, archaea) • Protists • Fungi • Plant Diversity • Animal Diversity (invertebrates/vertebrates) • Phylogeny

### 🧪 Chemistry (Orange Theme) - 9 Detailed Diagrams

1. **chemistry-atomic.md** (~155 nodes)  

   Subatomic Particles • Isotopes • Electron Configuration (quantum numbers, Aufbau, Pauli, Hund) • Periodic Table • Periodic Trends

2. **chemistry-bonding.md** (~180 nodes)  

   Ionic/Covalent/Metallic Bonding • Lewis Structures • VSEPR Theory (5 geometries) • Polarity • Intermolecular Forces • Hybridization

3. **chemistry-stoichiometry.md** (~220 nodes)  

   Mole Concept (Avogadro 6.022×10²³) • Balancing Equations • Limiting Reactant • Gas Laws (PV=nRT) • Phase Changes • Solutions • Colligative Properties

4. **chemistry-thermochem-kinetics.md** (~190 nodes)  

   Thermochemistry (enthalpy, ΔG=ΔH-TΔS, Hess's law) • Kinetics (rate laws, Arrhenius equation, activation energy, catalysis)

5. **chemistry-equilibrium.md** (~160 nodes)  

   Equilibrium Constant (K, Kp) • Reaction Quotient Q • Le Châtelier's Principle • ICE Tables • Solubility (Ksp)

6. **chemistry-acids-bases.md** (~175 nodes)  

   Acid-Base Theories (Arrhenius, Brønsted-Lowry, Lewis) • pH Scale • Henderson-Hasselbalch • Buffers • Titrations

7. **chemistry-redox.md** (~150 nodes)  

   Oxidation States • Balancing Redox • Electrochemistry (galvanic/electrolytic cells, Nernst equation) • Batteries

8. **chemistry-organic.md** (~185 nodes)  

   Hydrocarbons (alkanes/alkenes/alkynes/aromatic) • Functional Groups (7 major) • Isomers (structural/geometric/optical) • Polymers • Biological Molecules

9. **chemistry-transition-nuclear.md** (~170 nodes)  

   Transition Metals (coordination compounds, crystal field theory) • Nuclear Chemistry (radioactive decay, fission/fusion, half-life)

### 🔢 Mathematics (Purple Theme) - 6 Detailed Diagrams

1. **math-calculus.md** (~150 nodes)  

   Limits & Continuity • Derivatives (4 rules, optimization) • Integration (5 techniques, FTC) • Sequences & Series (convergence tests, Taylor series) • Multivariable (partial derivatives, Lagrange multipliers) • Vector Calculus (Green's, Stokes', Divergence theorems)

2. **math-linear-algebra.md** (~120 nodes)  

   Vectors (dot/cross products) • Matrices (operations, RREF, inverses) • Systems of Equations • Determinants • Eigenvalues/Eigenvectors • Vector Spaces • Linear Transformations • Inner Product Spaces (Gram-Schmidt)

3. **math-differential-equations.md** (~180 nodes)  

   First Order ODEs (separable, linear, exact) • Second Order ODEs (characteristic equation) • Systems • Laplace Transform • Series Solutions • PDEs (heat/wave/Laplace) • Numerical Methods (Euler, RK4)

4. **math-probability-statistics.md** (~200 nodes)  

   Probability Theory (Bayes' theorem, counting) • Random Variables (PMF, PDF, CDF) • Distributions (binomial, normal, CLT, chi-square, t) • Descriptive Statistics • Point/Interval Estimation (MLE, CI) • Hypothesis Testing (p-value, Type I/II errors) • Regression • ANOVA

5. **math-discrete.md** (~190 nodes)  

   Logic & Proofs (induction, contradiction) • Set Theory (relations, functions) • Combinatorics (P(n,r), C(n,r), binomial theorem) • Graph Theory (Euler/Hamiltonian, trees, MST, BFS/DFS/Dijkstra) • Algorithms (Big O, sorting, dynamic programming)

6. **math-logic-foundations.md** (~140 nodes)  

   Set Theory (ZFC axioms, cardinals ℵ₀, Cantor's theorem) • Number Theory (GCD, primes, modular arithmetic, RSA) • Mathematical Induction • Formal Systems (Gödel's incompleteness, computability, Turing machines)

## 🚀 How to Use

**View on GitHub** - All diagrams render natively in `.md` files  

**Mermaid Live Editor** - Copy/paste diagrams to [mermaid.live](https://mermaid.live/)  

**VS Code** - Install [Markdown Preview Mermaid Support](https://marketplace.visualstudio.com/items?itemName=bierner.markdown-mermaid), press Ctrl+Shift+V  

**Navigation** - Start with hub files (`biology.md`, `chemistry.md`, `math.md`, `physics.md`) → Navigate to topic diagrams in folders  

**Study Notes** - Formulas and equations in `note/` folder

## 📚 Based on Standard Textbooks

**Physics** - Halliday/Resnick *University Physics*  

**Chemistry** - Zumdahl *Chemistry*  

**Biology** - Campbell *Biology* 12th ed  

**Mathematics** - Stewart *Calculus*, Strang *Linear Algebra*, Boyce & DiPrima *Differential Equations*, Ross *Probability*, Rosen *Discrete Mathematics*

## 📊 Coverage

**Total:** ~2,600+ nodes across 27 diagrams

- **Biology** (~1,010 nodes): Cell Biology • Genetics • Evolution • Ecology • Organisms • Diversity

- **Chemistry** (~1,385 nodes): Atomic Structure • Bonding • Stoichiometry • Thermochem/Kinetics • Equilibrium • Acids/Bases • Redox • Organic • Transition/Nuclear

- **Physics** (~1,185 nodes): Mechanics • Waves • Thermodynamics • Electromagnetism • Optics • Modern Physics

- **Mathematics** (~1,020 nodes): Calculus • Linear Algebra • Differential Equations • Probability/Statistics • Discrete Math • Logic/Foundations

**Ideal For:** Undergraduate STEM courses • AP courses (Biology, Chemistry, Physics, Calculus, Statistics) • Standardized tests (MCAT, DAT, GRE) • Pre-med, engineering, CS prerequisites

## 💡 Study Tips

🎓 Start with topic-specific diagrams matching your coursework  

🔍 Follow arrows to understand hierarchical relationships  

📝 Each node = flashcard (name/definition/context)  

🔄 Review regularly - visual memory aids retention  

🤝 Notice cross-disciplinary connections (e.g., thermodynamics in physics & chemistry)

## 🛠️ Technical Details

**Format:** Mermaid v9+ flowcharts in `.md` files  

**Colors:** 4-tier CSS hierarchy per subject  

**Math:** Unicode notation (H₂O, v², E=mc², ∆G, ∫, ∂)  

**Structure:** 4 hub files + 27 topic diagrams (Physics 6, Biology 6, Chemistry 9, Math 6)  

**Rendering:** GitHub native, Mermaid Live Editor, VS Code, Notion, Obsidian

## 🎨 Color Scheme

All nodes in the diagrams are consistently styled with a 4-tier color hierarchy:

| Subject | Primary | Secondary | Tertiary | Quaternary |

|---------|---------|-----------|----------|------------|

| ⚛️ **Physics** | Dark Blue (#1e40af) | Blue (#3b82f6) | Light Blue (#60a5fa) | Pale Blue (#93c5fd) |

| 🧬 **Biology** | Dark Green (#15803d) | Green (#22c55e) | Light Green (#4ade80) | Mint Green (#86efac) |

| 🧪 **Chemistry** | Dark Orange (#c2410c) | Orange (#ea580c) | Light Orange (#fb923c) | Peach (#fdba74) |

| 🔢 **Mathematics** | Dark Purple (#7c3aed) | Purple (#a78bfa) | Light Purple (#c4b5fd) | Pale Purple (#ddd6fe) |

**Color Application:**

- **Primary (:::blue/green/orange/purple)** - Root/Start nodes and major section headers

- **Secondary (:::lightblue/lightgreen/lightorange/lightpurple)** - Main topic categories

- **Tertiary (:::paleblue/palegreen/paleorange/palepurple)** - Subtopics and concepts

- **Quaternary (:::skyblue/mintgreen/peach/lavender)** - Detailed nodes and specific examples

## 🔧 Quality Assurance

All diagrams in this repository have been verified for:

✅ **Structural Integrity** - Every node is properly connected to the diagram tree (no orphaned nodes)  

✅ **Color Consistency** - All nodes have appropriate color class definitions matching the 4-tier hierarchy  

✅ **Unicode Math** - Mathematical notation uses Unicode characters (v², H₂O, ∆G, ∫, ∂) for universal compatibility  

✅ **Mermaid Compatibility** - Tested and validated across GitHub, Mermaid Live Editor, and VS Code  

✅ **Rendering Verification** - All 30 diagrams render correctly without errors

### Diagram Standards

**Node Connection:** All concept nodes trace back to the root `Start` node through parent-child relationships  

**Color Coding:** Consistent 4-tier visual hierarchy with proper CSS class definitions (:::blue, :::lightblue, :::paleblue, :::skyblue)  

**Mathematical Notation:** Unicode superscripts (⁰¹²³⁴⁵⁶⁷⁸⁹) and subscripts (₀₁₂₃₄₅₆₇₈₉) for formulas  

**Special Characters:** Greek letters (α, β, γ, θ, ω, λ, μ, π, ρ, σ, τ, φ, Ω), operators (±, ≥, ≤, ≠, ≈, ∞), set theory (∈, ∉, ⊂, ⊆, ∪, ∩), calculus (∂, ∫, ∑, ∏, √), arrows (→, ⇌)  

**Line Breaks:** HTML `
` tags for multi-line node descriptions

## 📜 License

This educational resource is provided as-is for learning purposes.