# M365C: Real Analysis I

## Announcements

I posted solutions to the final exam. Enjoy the holidays!

## Basic Information

Professor: Dan Freed, RLM 9.162

Lectures: Tuesdays and Thursdays
9:30 - 10:45, RLM 5.114

Office Hours: Wednesdays 2:00 - 4:00

TA: Lingfan Chen, RLM 13.156

TA Office Hours: Mondays 2:30 - 3:30
and Thursdays 2:00 - 3:00

For more details, see the First Day Handout.

## Homework

The solutions will appear on the web only
after the assignment is due!

Homework #1 due September 1 [solutions to some of the
problems]

Homework #2 due September 8 [solutions to some of the
problems]

Homework #3 due September 15 [solutions to some of the
problems]

Homework #4 due September 22 [solutions to some of the
problems]

Homework #5 due September 29 [solutions to some of the
problems]

Homework #6 due October 6 [solutions to some of the
problems]

Homework #7 due October 13 [solutions to some of the
problems]

Homework #8 due October 20 [solutions to some of the
problems]

Homework #9 due October 27 [solutions to some of the
problems]

Homework #10 due November 3 [solutions to some of the
problems]

Homework #11 due November 10 [solutions to some of the
problems]

Homework #12 due November 17 [solutions to some of the
problems]

Homework #13 due December 1 [solutions to some of the
problems]

##
Tests

Solutions to Test 2

Solutions to Final Exam

## Additional Material

Chapter 1 of Rudin, *Principles of Mathematical
Analysis, 3rd edition*. No other chapters will be posted; this is just
to give you time to purchase the book.

Notes on sets, functions, logic, and other
background topics. These are extracted from old course notes by Joel
Robbin.

Article on the history of the notion of compactness.

Note on lim sup and
lim inf.

Article on the history of the real numbers.

Schoenberg on the Peano curve.

Note on uniformity and
differentiation.

Note on uniformity and
integration in a tricky case.

## Poincare Conjecture and Ricci Flow

Numberphile
video on Poincare conjecture

Numberphile
video on Ricci flow

Curve shortening demo

Ricci flow demo

You should visit the Numberphile video
homepage for many more short videos on interesting and fun math topics