##
Home page for Math 508, Advanced Analysis

###
Fall 2018

**Instructor: **Charles L. Epstein
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### The Course

In this course we study the foundations of analysis. The goal of this
course is
to develop your skills and instincts as mathematical analysts. This
entails
understanding the basic concepts and techniques of analysis, as well as
developing intuition and proficiency in the construction of rigorous
proofs.
I like to use The
Way of Analysis, by Robert Strichartz as a text, but I noticed that the
price is now $263. A free pdf is readily available online. Other good books include Terry Tao's
Analysis I (it can be purchased from the
AMS), **Principles of Mathematical Analysis **by Walter Rudin,** A Consise Introduction to Analysis** by Daniel Stroock**,
**and
**Mathematical Thinking** by John P. D'Angelo and Douglas B. West. Another good text is Real Analysis and Foundations, 4th ed. by Steven Krantz.

A problem set will be assigned every week, on Tuesdays. We may have one or more midterms and a final.

- The class meets from 3:00 to 4:30 on Tuesdays and Thursdays in room A6 of DRL.
- My office hours are 3:00-5:00 on Mondays, no appointment is
required. Send e-mail if you have a
question
or would like to come see me at some other time.
- email: cle@math.upenn.edu.
Send e-mail or call if you need to see me at some other time.
- My office is DRL 4E7, my telephone number is: 8-8476.
- The TA for the course is Aline Zanardini. Her e-mail is
alinez@math.upenn.edu. Her office is 3N2A, and her office hours are Tuesday 1:30-2:30 and Friday 9:00-10:00.

## Syllabus for the course

- Integers, sets and rules of deduction

- The real numbers and topology of the real line

- Sequences and series of numbers
- Continuous functions
- Differential Calculus

- Integral Calculus

- Sequences and series of functions
- Approximation of Functions

### Lecture Notes et al.

### Announcements

- The homework due in class on Sept. 18 can be handed in on Sept. 20. I will
be in my office to answer questions on Sept. 20 from 11:00-12:00.
- Your lowest homework score will be dropped.
- The midterm will be in-class on October 18, 2018.
- The first class meeting will be on August 28, 2018 at 3:00.
- We will have a review session for the midterm exam on the evening of Tuesday, Oct
16 from 6:00 to 8:00 in A8 DRL.

- The final exam is scheduled for Decmeber 13, 2018 from 12:00-2:00PM, room TBA.

#### Problem Sets

- Problem set 1 due September 11, 2018.
- Problem set 2 due September 18, 2018.
- Problem set 3 due September 25, 2018.
- Problem set 4 due October 2, 2018.
- Problem set 5 due October 11, 2018.
- Problem set 6 due October 23, 2018.
- Problem set 7 due October 30, 2018.
- Problem set 8 due November 6, 2018.
- Problem set 9 due November 13, 2018.
- Problem set 10 due November 27, 2018.
- Problem set 11 due December 6, 2018.