Math 440-1

Syllabus

Notes:

Class notes

Homework:

Homework 1 (updated 3b!)

Homework 2 (updated problem 2!)

Question 2 solution

Homework 3

Homework 4 (updated problem 3!)

Solutions for the final exam

Materials from the previous year:

Homework:

Homework 1

Homework 1.3 solution

Homework 2

Homework 2 solutions

Homework 3

Homework 3 solutions

Homework 4

Homework 4 solutions

Homework 5

Homework 5 solutions

Solutions for the final exam

Notes:

Introduction, Vector fields and flows

Whitney embedding theorem

Vector fields as operators and Frobenius integrability

Sard’s theorem

Classification of 1-manifolds, mod-2 degree, and mod-2 intersection number

Orientations

Vector bundles, the de Rham complex, and integration of forms

Affine connections, geodesics, Riemannian metrics, and etc.