Math Runway –- taking off to the math sky!

• 111 Academic year
• 112 Academic year
• 113 Academic year

arXiv of activities

Guidelines

Introduction of Mathematics

• Dimension of the Cantor set
• 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
• 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
• Covariance estimation
• Monty Hall
• Geometric distribution
• Galton board

Statistics

• Principal component analysis
• Estimation of the variance

Programming

• Swapping two variables

Numerical Analysis

• Power method

In-class activities

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

Computer skills

• Python-basic
• Python-NumPy
• Python-pandas
• Python-matplotlib
• Python-Scikit-Learn
• Python-NetworkX
• LaTeX
• Git
• Linux