MathLearningNotes

Repository for mathematics learning notes, covering topics like trigonometry, precalculus, calculus, and discrete math.

Table of Contents

• Overview
• Installation
• Jupyter Notebooks
  • Root Directory Notebooks
  • Algebra
  • Calculus
  • Discrete Mathematics
    • Combinatorics
    • Logic
    • Series and Sequences
      • Arithmetic Sum
      • Sum of Cubes
      • Sum of Squares
      • Symmetric Sums
    • Number Theory
  • Fractals
  • Trigonometry
  • Translated Notebooks (中文翻译笔记本)
    • Discrete Mathematics (离散数学)
      • Combinatorics (组合学)
      • Series and Sequences (数列与级数)
• Usage
• Contributing
• License

Overview

This repository contains a collection of Jupyter notebooks documenting various mathematical concepts, proofs, and explorations. The notebooks are organized by mathematical discipline and include both theoretical explanations and practical examples. Additionally, this repository includes Chinese translations of many notebooks to make the content accessible to Chinese-speaking learners.

Installation

To use these notebooks, you'll need to have Jupyter installed. You can set up the environment using either the provided environment.yml file (for conda) or requirements.txt (for pip).

Using Conda

conda env create -f environment.yml
conda activate math-learning

Using Pip

pip install -r requirements.txt

Jupyter Notebooks

Root Directory Notebooks

Notebook	Description
Math-Lessons.ipynb	Main notebook with comprehensive math lessons compiled from previous Google Docs
Template_Notebook.ipynb	Template for creating new detailed notes
Template_QUICKNOTE.ipynb	Template for creating quick notes

Algebra

Notebook	Description
general-properties.ipynb	General properties of algebraic operations

Calculus

The calculus section contains a series of advancement reports documenting progress in learning calculus concepts, as well as specific topic notebooks.

Notebook	Description
derivative-proofs.ipynb	Proofs related to derivatives
advancements-report-14th-march-2025.ipynb	Progress report from March 14, 2025
advancements-report-15th-march-2025.ipynb	Progress report from March 15, 2025
advancements-report-16th-april-2025.ipynb	Progress report from April 16, 2025
advancements-report-16th-march-2025.ipynb	Progress report from March 16, 2025
advancements-report-17th-march-2025.ipynb	Progress report from March 17, 2025
advancements-report-18th-march-2025.ipynb	Progress report from March 18, 2025
advancements-report-19th-march-2025.ipynb	Progress report from March 19, 2025
advancements-report-20th-march-2025.ipynb	Progress report from March 20, 2025
advancements-report-21st-march-2025.ipynb	Progress report from March 21, 2025
advancements-report-23rd-march-2025.ipynb	Progress report from March 23, 2025
advancements-report-25th-march-2025.ipynb	Progress report from March 25, 2025
advancements-report-27th-march-2025.ipynb	Progress report from March 27, 2025

Discrete Mathematics

Combinatorics

Notebook	Description
binomial-expansion.ipynb	Binomial expansion formulas and applications
pascals-triangle.ipynb	Pascal's triangle properties and applications
permutation-and-combination.ipynb	Permutation and combination concepts

Logic

Notebook	Description
if-p-then-q-explained.ipynb	Explanation of conditional statements in logic
learnings-1st-april.ipynb	Logic concepts learned on April 1st, 2025

Series and Sequences

Arithmetic Sum

Notebook	Description
arithmetic-sum-generalisation.ipynb	Generalizations of arithmetic sum formulas
arithmetic-sum.ipynb	Basic arithmetic sum concepts and formulas
sum-of-consecutive-multiples.ipynb	Sums of consecutive multiples

Sum of Cubes

Notebook	Description
cubes-as-sum-of-consecutive-odd-numbers.ipynb	Representing cubes as sums of consecutive odd numbers
[sum-of-cubes-with-arithmetic-sum (compressed).ipynb](discrete-mathematics/series-and-sequences/sum-of-cubes/sum-of-cubes-with-arithmetic-sum (compressed).ipynb)	Compressed version of sum of cubes using arithmetic sums
sum-of-cubes-with-arithmetic-sum.ipynb	Sum of cubes using arithmetic sum formulas
sum-of-cubes-with-sum-of-squares.ipynb	Relationship between sum of cubes and sum of squares

Sum of Squares

Notebook	Description
sum-of-squares-with-arithmetic-sum.ipynb	Sum of squares using arithmetic sum formulas
sum-of-squares-with-symmetric-sum.ipynb	Sum of squares using symmetric sum approach

Symmetric Sums

Notebook	Description
sum-of-cubes-with-symmetric-sums.ipynb	Sum of cubes using symmetric sum approach
symmetric-sum-of-even-numbers.ipynb	Symmetric approach to summing even numbers
symmetric-sum-of-odd-numbers.ipynb	Symmetric approach to summing odd numbers
sum-of-fourth-powers-symmetric.ipynb	Derivation of sum of fourth powers using symmetric approach

Other Series and Sequences

Notebook	Description
geometric-sum.ipynb	Geometric series concepts and formulas
sharing-and-splitting.ipynb	Problems involving sharing and splitting sequences
sum-of-even-numbers.ipynb	Formulas for sum of even numbers
sum-of-odd-numbers-is-square.ipynb	Proof that sum of odd numbers equals perfect squares
sum-of-positive-integers-to-odd-or-even-integer.ipynb	Sum formulas for positive integers up to odd or even numbers
sum-of-reciprocal-consecutive-multiples.ipynb	Sums of reciprocals of consecutive multiples
triangular-numbers-and-their-sum.ipynb	Triangular numbers and their sum formulas

Number Theory

Notebook	Description
divisibility-by-1.ipynb	Rules and properties of divisibility by 1
divisibility-by-2.ipynb	Rules and properties of divisibility by 2
divisibility-by-3.ipynb	Rules and properties of divisibility by 3
divisibility-by-4.ipynb	Rules and properties of divisibility by 4
divisibility-by-5.ipynb	Rules and properties of divisibility by 5
divisibility-by-6.ipynb	Rules and properties of divisibility by 6
divisibility-by-8.ipynb	Rules and properties of divisibility by 8
divisibility-by-9.ipynb	Rules and properties of divisibility by 9
divisibility-by-10.ipynb	Rules and properties of divisibility by 10
divisibility-nomenclature.ipynb	Terminology and definitions related to divisibility
factoring-and-divisibility.ipynb	Relationship between factoring and divisibility
digit-sum-and-divisibility.ipynb	How digit sums relate to divisibility rules
prime-numbers-and-divisibility.ipynb	Prime numbers and their role in divisibility

Fractals

Notebook	Description
mandelbrot.ipynb	Mandelbrot fractal exploration and visualization

Trigonometry

Notebook	Description
fun-simulations.ipynb	Trigonometric function simulations
getting-definitions-right.ipynb	Precise definitions of trigonometric concepts
r-formula.ipynb	R-formula in trigonometry
the-way-is-to-simplify-case-study.ipynb	Case study on simplification techniques
advancements-report-4th-march-2025.ipynb	Progress report from March 4, 2025
advancements-report-8th-march-2025.ipynb	Progress report from March 8, 2025
advancements-report-10th-march-2025.ipynb	Progress report from March 10, 2025

Translated Notebooks (中文翻译笔记本)

The translated-notebooks directory contains Chinese translations of various notebooks, making the mathematical content accessible to Chinese-speaking learners. These translations are generated and maintained using the translate_notebooks.py script.

Discrete Mathematics (离散数学)

Combinatorics (组合学)

Notebook	Description
二项展开式.ipynb	二项展开式公式与应用 (Binomial expansion formulas and applications)
排列与组合.ipynb	排列与组合概念 (Permutation and combination concepts)
杨辉三角.ipynb	杨辉三角的性质与应用 (Pascal's triangle properties and applications)

Series and Sequences (数列与级数)

Notebook	Description
三角形数与之求和.ipynb	三角形数及其求和公式 (Triangular numbers and their sum formulas)
几何级数.ipynb	几何级数概念与公式 (Geometric series concepts and formulas)
奇数之和为平方数.ipynb	奇数之和等于平方数的证明 (Proof that sum of odd numbers equals perfect squares)
偶数之和.ipynb	偶数之和公式 (Formulas for sum of even numbers)
正整数之和为奇数或偶数.ipynb	正整数之和为奇数或偶数的公式 (Sum formulas for positive integers up to odd or even numbers)
连续倍数之和.ipynb	连续倍数之和 (Sums of consecutive multiples)
连续倍数倒数之和.ipynb	连续倍数倒数之和 (Sums of reciprocals of consecutive multiples)
算术级数.ipynb	算术级数概念与公式 (Basic arithmetic sum concepts and formulas)
算术级数推广.ipynb	算术级数推广 (Generalizations of arithmetic sum formulas)
立方数之和与算术级数 (压缩版).ipynb	立方数之和与算术级数 (压缩版) (Compressed version of sum of cubes using arithmetic sums)
立方数之和与算术级数.ipynb	立方数之和与算术级数 (Sum of cubes using arithmetic sum formulas)
立方数之和与平方数之和.ipynb	立方数之和与平方数之和的关系 (Relationship between sum of cubes and sum of squares)
立方数之和与对称和.ipynb	立方数之和与对称和 (Sum of cubes using symmetric sum approach)
平方数之和与算术级数.ipynb	平方数之和与算术级数 (Sum of squares using arithmetic sum formulas)
平方数之和与对称和.ipynb	平方数之和与对称和 (Sum of squares using symmetric sum approach)
偶数对称和.ipynb	偶数对称和 (Symmetric approach to summing even numbers)
奇数对称和.ipynb	奇数对称和 (Symmetric approach to summing odd numbers)
平方和的对称和之推导.ipynb	平方和的对称和之推导 (Derivation of sum of squares using symmetric sum)

Usage

To use these notebooks:

1. Clone the repository:

   git clone https://github.com/B67687/MathLearningNotes.git

2. Set up the environment as described in the Installation section.

3. Launch Jupyter Notebook or Jupyter Lab:

   jupyter notebook
   # or
   jupyter lab

4. Navigate to the notebook of interest and open it.

Contributing

Contributions are welcome! If you'd like to contribute:

1. Fork the repository
2. Create a new branch for your feature
3. Add your changes
4. Submit a pull request

License

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