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  • Type MOOC course
  • Period 2019.08.30 ~ 2019.12.31
    17 weeks 5 days
  • hr Study freely
  • Course approval method Automatic approval

Instructor Introduction

Lecture plan

강의목록
  1. 1. How did mathematicians find the epsilon-delta definition of continuity? : Introduction to basic
    1. 1) Why should we use the mysterious epsilon-delta definition of coninuity?
    1. 2) Basic introduction to logic
    1. 3) Basic introduction to quantifiers
    1. 4) Deducing the epsilon-delta definition of continuity
    1. Quiz(week 1)
  2. 2. Why should we study abstract mathematics? : Construction of real numbers.
    1. 1) Why should we study abstract mathematics? : Construction of real numbers.
    1. Quiz(week 2)
  3. 3. Why should we study abstract mathematics? : Finding totally new numbers.
    1. 1) Why should we study abstract mathematics? : Finding totally new numbers.
    1. Quiz(week 3)
  4. Week 04: Why are the polynomials of degree five not solvable? : Introduction to modern abstract ...
    1. 4-1 Finding roots of polynomials : story of Abel and Galois
    1. 4-2 Groups of permutations of the roots
    1. 4-3 Solvable groups and solvability of cubic and quartic equations.
    1. 4-4 Modern formulation of Galois theory and insolvability of the quintic equations.
    1. Quiz(week 4)
  5. Week 05: Solvability of ordinary differential equations.
    1. 5-1 Existence and uniqueness for ordinary differential equations
    1. 5-2 Global existence vs finite time blow-up
    1. Quiz(week 5)
  6. Week 06: Isoperimetric problem
    1. 6-1 Geometric approach to isoperimetric problem
    1. 6-2 Euler-Lagrange equations for isoperimetric problem
    1. Quiz(week 6)
  7. Week 07: what is infinite dimensional space, and where is it?
    1. 7-1 vector spaces with inner product
    1. 7-2 Convergence of Fourier series
    1. Quiz(week 7)
  8. Week 08: Why does Jacobian appear in the change of variables for multiple integrals?
    1. 8-1 Jacobian of a linear transformation as volume change
    1. 8-2 Jacobian of a nonlinear transformation as local volume change
    1. 8-3 Jacobian and multiple integrals on differentiable manifolds I
    1. 8-4 Jacobian and multiple integrals on differentiable manifolds II
    1. Quiz(week 8)
  9. Week 09: I have trouble with eigenvaluse and eigenvectors. Why should I care?
    1. 9-1 Eigenvalues and Eigenvectors
    1. 9-2 Singular values and singular vectors
    1. 9-3 Application I : Differential Equation
    1. 9-4 Application II : Statistics - PCA
    1. Quiz(week 9)
  10. Week 10: Should I study math to become a fund manager? (Lagrange multiplier method)
    1. 10-1 Idea of Modern Portfolio Theory
    1. 10-2 Formulation of portfolio selection problem
    1. 10-3 Lagrange Multiplier Method
    1. 10-4 Solution of Mean-Variance Portfolio Optimization Problem
    1. Quiz(week 10)
  11. Week 11: Should I study math to become a quant? (Black-Scholes equation)
    1. 11-1 Concept of Derivative Pricing
    1. 11-2 Black-Scholes Model
    1. 11-3 Black-Scholes equation
    1. 11-4 Solution of Black-Scholes Equation
    1. Quiz(week 11)
  12. Week 12: Should I study math to become an economist? (Brouwer’s fixed point theorem)
    1. 12-1 Concept of Game and Nash Equilibrium
    1. 12-2 Existence of Nash equilibrium
    1. 12-3 Sperner’s Lemma
    1. 12-4 Proof of Brouwer’s Fixed Point Theorem
    1. Quiz(week 12)
  13. Week 13: MATLAB Examples for Chapters 8 and 9
    1. 13-1 Singular Value Decompositions (SVD)
    1. 13-2 Dimensionality Reduction via SVD
    1. 13-3 Principal Component Analysis (PCA)
    1. 13-4 Numerical Comparison Between the Heat flow and the BV flow
  14. Week 14: A taste for optimization
    1. 14-1 Basic Optimization Theory Part I (Method of Least Squares)
    1. 14-2 Basic Optimization Theory Part II (Method of Least Squares)
    1. 14-3 Applications to Image Processing : Noise and Blur removal
    1. Quiz(week 14)