##
Home page for Math 508, Advanced Analysis

###
Fall 2017

**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 was planning to use as a text for the course The
Way of Analysis, by Robert Strichartz, but I noticed that the
price is now $263, so I don't think we'll use it. We are
likely to use Terry Tao's
Analysis I (first few chapters) as
the text. It can be purchased from the
AMS. Other good references
are **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.
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 Josh Rosenberg. He has office
hours from 4:00-6:00 on Wednesdays. His e-mail is rjos@math.upenn.edu.
- The TA's office is 3E2A in DRL and his phone number is 215-898-7836.

## Syllabus for the course

- 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
- Equicontinuity and compactness

- Elementary transcendental functions
- The basics facts of Fourier analysis

### Lecture Notes et al.

### Announcements

- The first class meeting will be on August 29, 2017 at 3:00.

#### Problem Sets

- Problem set 1 due September 12, 2017.
- Problem set 2 due September 19, 2017.
- Problem set 3 due September 26, 2017.