Place: Room 10 Evans

Professor: Ian Agol

Office Hours: Monday 11-12 am, Wednesday 2:30-3:30 pm

including 12/7 & 12/9

Office: 921 Evans

Exams:

There will be two midterms in class

Thursday, October 1

Thursday, November 5

There will be a review on Thursday, December 10.

The review will be at the regular class time and classroom, 2:10-3:30, 10 Evans.

Practice problems for final

Solutions to Practice problems

Solutions to the final

The final exam will be Monday, December 14, 12:30-3:30 pm, Room 70 Evans

Announcement: Office hours are changed from Wednesday 11/11 to

Thursday 11/12, 11-12 am, due to the veterans day holiday

Text:

C. Pugh, Real Mathematical Analysis, Springer, 2002.

Recommended Reading:

Rudin, Principles of Mathematical Analysis

Notes on Set Theory and Logic

Homework:

Homework will be due weekly on Thursdays, except

the weeks of exams and Thanksgiving.

Grading:

Each midterm is worth 20%

Homework is worth 30%

The final is worth 30%

Homework 1, due Thursday September 3:

pp. 41-42, Chapter 1, Exercises 2, 5

Update 9/1: save 9, 12, 13 for next week, since we didn't cover addition and

multiplication for Dedekind cuts yet.

Homework 2, due Thursday September 10:

Chapter 1, Exercises 9, 12, 13, 18, 19

Some solutions

Homework 3, due Thursday September 17:

Chapter 1, Exercises 31, 36, 41

Homework 4, due Thursday September 24:

Chapter 2, Exercises 12, 22, 23, 30(a)

Selected Solutions

Midterm 1 will be Thursday, October 1.

This midterm will cover only Chapter 1.

Practice problems for the midterm

Solutions to practice problems

Solutions to the midterm

Homework 5, due Thursday October 8:

p. 118, #34, p. 124, #81, p. 126, #89, p. 128, #97

Homework 6, due Thursday October 15:

p. 117, #27, p. 119 #41, p. 122 #71

(the 2-sphere S^2 is the set of all points in R^3 distance

1 from the origin)

Homework 7, due Thursday October 22:

p. 119 #40ab, p. 121 #59, p. 122 #68

Selected solutions to Homeworks 5-7

Homework 8, due Thursday October 29:

p. 186 # 5, #6, p. 187 #13

Midterm 2 will be Thursday, November 5.

This midterm will cover Chapter 2.

Practice problems for midterm 2

Solutions to practice problems for midterm 2

Solutions to midterm 2

Homework 9, due Thursday November 12

p. 187 #14, p. 192 #28(a)(b)

Remark: in problem 14, the sign of the exponent in part (d) should be + not -

e

Solutions to Homeworks 8 & 9

Homework 10, due Thursday November 19

p. 193 #33abc, p. 196 #51abde

Homework 11, due Thursday December 3

p. 195 #42, p. 197 #52, #57, #58

Solutions to Homeworks 10 & 11