Comprehensive Mathematics Learning Roadmap

A structured approach to learning mathematics, from foundations to advanced topics.

Overview

This repository provides a comprehensive roadmap for learning mathematics, complete with:

• Detailed course outlines
• Python implementations
• Practice problems
• Assessment frameworks
• Learning resources

Learning Tracks

Foundation Track A: Calculus Sequence (9-12 months)

1. Single Variable Calculus (3-4 months)
2. Multivariable Calculus (3-4 months)
3. Differential Equations (3-4 months)

Foundation Track B: Linear Algebra and Discrete Mathematics (10-12 months)

1. Proofs and Mathematical Logic (2-3 months)
2. Discrete Mathematics (3-4 months)
3. Linear Algebra (3-4 months)
4. Computational Matrix Theory (2-3 months)

Intermediate Track A: Analysis and Geometry (14-17 months)

1. Real Analysis I & II (5-6 months)
2. Complex Analysis (3-4 months)
3. Differential Geometry (3-4 months)
4. Measure Theory (3-4 months)

Intermediate Track B: Algebra and Topology (12-14 months)

1. Number Theory (3-4 months)
2. Abstract Algebra (4-5 months)
3. Point-Set Topology (3 months)
4. Advanced Combinatorics (2-3 months)

Advanced Track A: Applied Analysis and Geometric Methods (10-12 months)

1. Functional Analysis (4-5 months)
2. Algebraic Topology (3-4 months)
3. Numerical Analysis (3-4 months)

Advanced Track B: Probability and Statistics (8-10 months)

1. Probability Theory (4-5 months)
2. Statistical Theory (4-5 months)

Repository Structure

mathematics-learning-roadmap/
├── docs/                  # Course documentation and guides
├── code/                  # Python implementations
│   ├── utils/            # Utility functions
│   ├── implementations/  # Core implementations
│   └── visualizations/   # Plotting tools
├── assessments/          # Practice problems and tests
├── projects/             # Hands-on projects
└── resources/            # Additional learning materials

Getting Started

Prerequisites

• Python 3.11+
• Basic programming knowledge
• High school mathematics

Installation

1. Clone the repository

git clone https://github.com/melmustafa/pure-math-roadmap

2. Install required packages

pip install -r requirements.txt

Learning Path Usage

1. Start with Foundation Track A or B based on your background
2. Complete practice problems and programming exercises
3. Build your portfolio through projects
4. Track your progress with assessments
5. Use provided resources for deeper understanding

Study Guide

Content Structure

🔵 Core Content (Essential foundations)
🟡 Recommended Optional (Enhances understanding)
🟢 Advanced Optional (Deeper exploration)
⭐ Special Interest (Specialized applications)

Study Tips

1. Follow the recommended time allocations
2. Complete all core content before moving on
3. Work through practice problems consistently
4. Implement concepts in code
5. Build on prerequisites before advancing

Resources

• Each course includes specific textbook recommendations
• Online course suggestions
• Video lectures and tutorials
• Interactive tools and visualizations
• Practice problem sets

Contributing

Improvements to the roadmap are welcome:

• Additional practice problems
• Better explanations
• Code optimizations
• Resource suggestions
• Error corrections

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• Mathematical concepts from standard university curricula
• Inspired by various open-source mathematical software
• Visual examples adapted from educational resources