---
description: math runway, jephian, nsysu, 林晉宏
tags: learning-together, math-runway
---

# Math Runway :airplane_departure: --- taking off to the math sky!

- [111 Academic year](https://hackmd.io/@jephianlin/math-runway-2022)
- [112 Academic year](https://hackmd.io/@jephianlin/math-runway-2023)

## arXiv of activities

[Guidelines](https://hackmd.io/@jephianlin/SJQmolam6)

Introduction of Mathematics

- [Dimension of the Cantor set](https://hackmd.io/@jephianlin/SJxqiqUcT)
- hat guessing game
- Understanding bijection and cardinality

General

- Studying aboard

Calculus

- Gradient descent
- Computing the volume physically
- Area of $\frac{\sin x}{x}$

Analysis

Differential Equations

- JPEG image compression algorithm

Linear Algebra

- Triangle in a space
- [Matrix-tree-theorem](https://www.math.nsysu.edu.tw/~chlin/math-runway/matrix-tree-theorem.pdf)
- Vector as a sequence of item
- Matrix as a machine
- Perceptron learning algorithm
- Linear regression
- Denoise an image or a voice
- Area of a parallelogram
- Polynomial bases (standard, Lagrange, Stirling, Taylor expansions at different points)
- Image compression by singular value decomposition
- Recommendation system
- Spectral embedding

Algebra

- Symmetric group as actions
- Knot theory
- Representation theory (Chemistry?)

Discrete Mathematics

- Markov chain & PageRank
- Tiling a chessboard with dominos
- Matrix tree theory
- Seven-bridge problem
- $K_{3,3}$ on a mug
- Hamiltonian cycle
- Sperner's lemma

Probability

- [Buffon’s needle problem](https://hackmd.io/@jephianlin/rk5kPt5ca)
- [Covariance estimation](https://hackmd.io/@jephianlin/BybuzQo96)
- Monty Hall
- Geometric distribution
- Galton board

Statistics

- Principal component analysis
- Estimation of the variance

Programming

- [Swapping two variables](https://hackmd.io/@jephianlin/r17eZViqa)

Numerical Analysis

- Power method

In-class activities

- Yes-No jigsaw
- Run the definition
- Keyword partner
- Collaboration in calculation: permutation expansion