MATH 250A, Fall 2019

Professor

Elham Izadi ; AP&M 6240 ; 858-534-2638 ; eizadi@math.ucsd.edu ; Office hours: 16:00-17:00 Mondays and 15:30-16:30 Fridays ;
Lectures: Tuesday, Thursday 9:30-10:50 AP&M 7321

Course description

This is the first quarter of the introductory sequence in Differential Geometry. We will cover some of Do Carmo's book, as time permits.

Prerequisites

Familiarity with Linear Algebra, Topology and advanced Calculus.

Text

Riemannian Geometry, By Manfredo P. Do Carmo.

Supplemental reference

Introduction to Smooth Manifolds, By John M. Lee

Presentations

This course will feature student presentations. It is well known that the best way to learn something is to explain it to others. When we present something to others, we have to think about it in many different ways and look at it from different angles. Giving presentations is very difficult, which is why, when you give presentations, I will not judge your performance, but will help you learn the material in the best way possible and also help you learn how to give presentations. This is a skill that will be very useful in many different contexts, regardless of what your career goals are. Any comments will not affect your grade, but will help you learn.

Some class notes:

09/26/2019 10/01/2019 10/03/2019 10/08/2019 Patrick's notes Yupei's notes Rongxuan's notes Zeyu's notes Gongping's notes Finn's notes Alex's notes Kevin's notes Gaojin's notes Shubham's notes Woonam's notes 11/26/2019 12/03/2019 Robi's notes 12/05/2019

Homework assignments:

Homework 1: due Tuesday October 22, in class
Chapter 0 of Do Carmo, #2, 3, 5, 6, 8, 9, 10, 12. If you would like more practice, you can also do the other exercises from this Chapter. They are all good. I have just picked the ones I like best. In general, it is a good idea to read all the exercises even if you don't do them: there are useful results in them.

Homework 2: due Tuesday November 19, in class
Chapter 1 of Do Carmo, #1, 2, 3 ; Chapter 2 of Do Carmo, #1, 2, 3, 4, 7

Homework 3: due Monday December 9
Chapter 3 of Do Carmo, #1, 2, 3, 4