로그인 바로가기
하위 메뉴 바로가기
본문 바로가기
검색
로그인 / 회원가입
새로운 사고를 가져다 줄 수학질문 12가지
UNIST 김윤호 교수 외
공유하기
URL복사
밴드
페이스북
트위터
새로운 사고를 가져다 줄 수학질문 12가지
새로운 사고를 가져다 줄 수학질문 12가지
http://unist.edwith.org/mth-2020/lecture/60273
좋아요
5
수강생
202
전체 메뉴 열기
하위 메뉴
강의목록
강좌 전체목록보기
1. How did mathematicians find the epsilon-delta definition of continuity? : Introduction to basic
1) Why should we use the mysterious epsilon-delta definition of coninuity?
2) Basic introduction to logic
3) Basic introduction to quantifiers
4) Deducing the epsilon-delta definition of continuity
Quiz(week 1)
2. Why should we study abstract mathematics? : Construction of real numbers.
1) Why should we study abstract mathematics? : Construction of real numbers.
Quiz(week 2)
3. Why should we study abstract mathematics? : Finding totally new numbers.
1) Why should we study abstract mathematics? : Finding totally new numbers.
Quiz(week 3)
Week 04: Why are the polynomials of degree five not solvable? : Introduction to modern abstract ...
4-1 Finding roots of polynomials : story of Abel and Galois
4-2 Groups of permutations of the roots
4-3 Solvable groups and solvability of cubic and quartic equations.
4-4 Modern formulation of Galois theory and insolvability of the quintic equations.
Quiz(week 4)
Week 05: Solvability of ordinary differential equations.
5-1 Existence and uniqueness for ordinary differential equations
5-2 Global existence vs finite time blow-up
Quiz(week 5)
Week 06: Isoperimetric problem
6-1 Geometric approach to isoperimetric problem
6-2 Euler-Lagrange equations for isoperimetric problem
Quiz(week 6)
Week 07: what is infinite dimensional space, and where is it?
7-1 vector spaces with inner product
7-2 Convergence of Fourier series
Quiz(week 7)
Week 08: Why does Jacobian appear in the change of variables for multiple integrals?
8-1 Jacobian of a linear transformation as volume change
8-2 Jacobian of a nonlinear transformation as local volume change
8-3 Jacobian and multiple integrals on differentiable manifolds I
8-4 Jacobian and multiple integrals on differentiable manifolds II
Quiz(week 8)
Week 09: I have trouble with eigenvaluse and eigenvectors. Why should I care?
9-1 Eigenvalues and Eigenvectors
9-2 Singular values and singular vectors
9-3 Application I : Differential Equation
9-4 Application II : Statistics - PCA
Quiz(week 9)
Week 10: Should I study math to become a fund manager? (Lagrange multiplier method)
10-1 Idea of Modern Portfolio Theory
10-2 Formulation of portfolio selection problem
10-3 Lagrange Multiplier Method
10-4 Solution of Mean-Variance Portfolio Optimization Problem
Quiz(week 10)
Week 11: Should I study math to become a quant? (Black-Scholes equation)
11-1 Concept of Derivative Pricing
11-2 Black-Scholes Model
11-3 Black-Scholes equation
11-4 Solution of Black-Scholes Equation
Quiz(week 11)
Week 12: Should I study math to become an economist? (Brouwer’s fixed point theorem)
12-1 Concept of Game and Nash Equilibrium
12-2 Existence of Nash equilibrium
12-3 Sperner’s Lemma
12-4 Proof of Brouwer’s Fixed Point Theorem
Quiz(week 12)
Week 13: MATLAB Examples for Chapters 8 and 9
13-1 Singular Value Decompositions (SVD)
13-2 Dimensionality Reduction via SVD
13-3 Principal Component Analysis (PCA)
13-4 Numerical Comparison Between the Heat flow and the BV flow
Week 14: A taste for optimization
14-1 Basic Optimization Theory Part I (Method of Least Squares)
14-2 Basic Optimization Theory Part II (Method of Least Squares)
14-3 Applications to Image Processing : Noise and Blur removal
Quiz(week 14)
공지게시판
12-4 Proof of Brouwer’s Fixed Point Theorem
공유하기
URL복사
밴드
페이스북
트위터
12-4 Proof of Brouwer’s Fixed Point Theorem - Jason Lee
12-4 Proof of Brouwer’s Fixed Point Theorem - Jason Lee
좋아요 0
수강완료
수강이 완료되었습니다.
닫기
수강이 완료되었습니다.
이제
다음 강의
를 확인하세요.
닫기
닫기
12-3 Sperner’s Lemma
Quiz(week 12)