MathLearningNotes

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

Table of Contents

• Overview
• Installation
• Markdown Notes
  • Root Directory Notes
  • Algebra
  • Calculus
  • Discrete Mathematics
    • Combinatorics
    • Logic
    • Series and Sequences
      • Arithmetic Sum
      • Sum of Cubes
      • Sum of Squares
      • Symmetric Sums
    • Number Theory
  • Fractals
  • Trigonometry
  • Translated Notes (中文翻译笔记)
    • 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 Markdown notes documenting various mathematical concepts, proofs, and explorations. The notes are organized by mathematical discipline and include both theoretical explanations and practical examples. Additionally, this repository includes Chinese translations of many notes to make the content accessible to Chinese-speaking learners.

Installation

To work with the archived 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

Markdown Notes

Root Directory Notes

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

Algebra

Note	Description
general-properties.md	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 notes.

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

Discrete Mathematics

Combinatorics

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

Logic

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

Series and Sequences

Arithmetic Sum

Note	Description
arithmetic-sum-generalisation.md	Generalizations of arithmetic sum formulas
arithmetic-sum.md	Basic arithmetic sum concepts and formulas
sum-of-consecutive-multiples.md	Sums of consecutive multiples

Sum of Cubes

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

Sum of Squares

Note	Description
sum-of-squares-with-arithmetic-sum.md	Sum of squares using arithmetic sum formulas
sum-of-squares-with-symmetric-sum.md	Sum of squares using symmetric sum approach

Symmetric Sums

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

Other Series and Sequences

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

Number Theory

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

Fractals

Note	Description
mandelbrot.md	Mandelbrot fractal exploration and visualization

Trigonometry

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

Translated Notes (中文翻译笔记)

The translated-notebooks directory contains Chinese translations of various notes, making the mathematical content accessible to Chinese-speaking learners. Older translations are preserved from the notebook workflow; future canonical work should prefer Markdown.

Discrete Mathematics (离散数学)

Combinatorics (组合学)

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

Series and Sequences (数列与级数)

Note	Description
三角形数与之求和.md	三角形数及其求和公式 (Triangular numbers and their sum formulas)
几何级数.md	几何级数概念与公式 (Geometric series concepts and formulas)
奇数之和为平方数.md	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.md	偶数之和公式 (Formulas for sum of even numbers)
正整数之和为奇数或偶数.md	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.md	连续倍数之和 (Sums of consecutive multiples)
连续倍数倒数之和.md	连续倍数倒数之和 (Sums of reciprocals of consecutive multiples)
算术级数.md	算术级数概念与公式 (Basic arithmetic sum concepts and formulas)
算术级数推广.md	算术级数推广 (Generalizations of arithmetic sum formulas)
立方数之和与算术级数 (压缩版).md	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.md	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.md	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.md	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.md	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.md	平方数之和与对称和 (Sum of squares using symmetric sum approach)
偶数对称和.md	偶数对称和 (Symmetric approach to summing even numbers)
奇数对称和.md	奇数对称和 (Symmetric approach to summing odd numbers)
平方和的对称和之推导.md	平方和的对称和之推导 (Derivation of sum of squares using symmetric sum)

Usage

To work with the archived 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.