# Math 61CM Analysis (aka Modern Mathematics: Continuous Methods)

### Lectures:

MTWTh 9:30-10:20am, Section: Friday 9:30-10:20am, all in in 380Y.
For the first six weeks, we plan to have lectures on analysis on Monday and Wednesday, and
on linear algebra on Tuesday and Thursday. The linear algebra lectures will be in 380C.
After that, we will have lectures on analysis on all four lecture days in 380Y.

### Instructor: *Lenya Ryzhik*

*Office:* 382U in Building 380
*Office Hours:* TW 1:30-3:00PM and by appointment (email me).
*Office Phone:*
650-721-2113
*e-mail:*
ryzhik@stanford.edu

### Course Assistant: * Cedric de Groote*

*Office: 381H*
*Office Hours:* M10:30-11:30 and 3:00-4:00 and Th 6-8pm, tentatively
*e-mail:*
cedricd "at" stanford.edu.

### Textbooks:

L. Simon "An Introduction to Multivariable Mathematics" (the main text),
an electronic version
V. Zorich "Mathematical Analysis I" (supplementary but likely to be used a lot, available online at Stanford Library)
W. Rudin "Principle of Mathematical Analysis" (supplementary, a classic text)
Lecture notes on analysis,
Lecture notes on linear algebra,
both
to be more or less continuously updated.

### Material from Sections:

Section 1
Proof writing Section 1
Section 2
Proof writing Section 2
Section 3
Section 4
Proof writing Section 3
Section 5
Section 6
Section 7
Solutions to sections problems
Section 8
Section 9
Section 10
Answers to sections problems

### Exams:

There will be two midterms, the first on October 16, and the second on November 13,
both 7:00-10:00pm, and a final on Monday, December 10, also 7:00-10:00pm. Any need for an alternative
arrangement should be discussed at least two weeks in advance of the exam.
Homeworks will be
due on Fridays.
Practice Midterm 1
Solutions to Midterm 1
Practice problems for Midterm 2
Solutions to Midterm 2
Practice problems for the final

### Grading:

Midterm 1: 20%
Midterm 2: 20%
Homework: 30%
Final: 30%

### Homeworks:

Note: The homework problems form an integral part of the course and the most reliable check of
your progress. It is fine, and even encouraged, for you to discuss the problems in general terms with your peers.
However, it is expected that what
you hand in is your own work. The lecture notes contain some exercises that are not part of the homework
and you do not need to turn them in. You are very much encouraged to think about the exercises daily
as you review the lecture notes and make sure you
know how to do them - this is a good check of your grasp of the material of the lecture.

### Homework 1 (Due Monday, October 1)

Read the lecture notes: Sections 1.1-2.2, this material corresponds
to Simon: Lecture 1 in Appendix and Zorich: Chapter 2, until (and including) Section 2.3.2. Zorich has
more material than we have covered, please read as much as you can. Linear algebra material is in the lecture
notes until p.9.
Do as many exercises in the lecture notes
as you can, but you do not need to turn them in.
Homework 1 problems
Homework 1 solutions
### Homework 2 (Due Friday, October 5)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 2 problems
Homework 2 solutions
### Homework 3 (Due Friday, October 12)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 3 problems
Homework 3 solutions
### Homework 4 (Due Friday, October 19)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 4 problems
Homework 4 solutions
### Homework 5 (Due Friday, October 26)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 5 problems
Homework 5 solutions
### Homework 6 (Due Monday, November 5)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 6 problems
Homework 6 solutions
### Homework 7 (Due Friday, November 9)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 7 problems
Homework 7 solutions
### Homework 8 (Due Monday, November 26)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 8 problems
Homework 8 solutions
### Homework 9 (Due Friday, November 30)

Read the lecture notes, Simon and Zorich (the contraction mapping principle is both in Simon and Zorich Volume II).
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 9 problems
Homework 9 solutions
### Homework 10 (Due Friday,December 7)

Read the lecture notes, Simon and Zorich.
Do as many exercises in the lecture notes as you can, but you do not need to turn them in.
Homework 10 problems
Homework 10 solutions