This is the main page for section **57465** of **Math 365C**.

I am Andrew (Andy) Neitzke. You can contact me at neitzke@math.utexas.edu.
My **office hours** are **Tuesday 3:00-4:00p** and **Wednesday 2:00-3:00p** in **RLM 9.134**, or by appointment.

The teaching assistant is Pulak Goswami. His **office hours** cannot be posted on a public-facing
website, but have been announced in class; feel free to ask me if you need to know them.

Lectures are **Tuesday and Thursday**, from **11:00a to 12:30p**, in **RLM 6.114**.
There will be a total of 28 class days, of which 2 are taken up by midterm exams (see below), making 26 lectures.
My lecture notes will be posted here.

- Notes 1 (fields, ordered sets, and the real numbers)
- Notes 2 (functions, unions, intersections, finite and countable sets)
- Notes 3 (metric spaces, limit points, open and closed sets)
- Notes 4 (compactness)
- Notes 5 (connectedness)
- Notes 6 (convergent and Cauchy sequences)
- Notes 7 (series)
- Notes 8 (limits and continuity; these notes cover the guest lecture by Prof. Daniel Allcock)
- Notes 9 (continuity, continued)
- Notes 10 (differentiation)
- Notes 11 (the Riemann integral)
- Notes 12 (uniform convergence)
- Notes 13 (Stone-Weierstrass theorem)
- Notes 14 (equicontinuity and the Arzela-Ascoli theorem)
- Notes 15 (power series)

The main course text is *Principles of Mathematical Analysis, 3rd edition*, by Walter Rudin.
An alternate text which may be useful is *Introduction to Analysis*, by Maxwell Rosenlicht.

The course is intended to cover the material in Chapters 1-7 of the text. This amounts to a rigorous treatment of the real number system, metric spaces, continuity of functions in metric spaces, differentiation and Riemann integration of real-valued functions of one real variable, and uniform convergence of sequences and series of functions.

Problem sets will be assigned weekly, due on **Thursday at the beginning of class**,
*or* in the mail slot outside my office door (RLM 9.134) no later than 10:00a Thursday. You are strongly
encouraged to work together on the problems. However, you must write up your own solutions,
independently.

Late homework cannot generally be accepted, because it creates extra work for the already-overworked TA.

- Problem Set 1 (due Thu Sep 5)
- Problem Set 2 (due Thu Sep 12) (with solutions)
- Problem Set 3 (due Thu Sep 19) (with solutions)
- Problem Set 4 (due Thu Sep 26) (with solutions)
- Problem Set 5 (due Thu Oct 3) (with solutions)
- Problem Set 6 (due Thu Oct 10) (with solutions)
- Problem Set 7 (due Thu Oct 17) (with solutions)
- Problem Set 8 (due Thu Oct 24) (with solutions)
- Problem Set 9 (due Thu Oct 31) (with solutions)
- Problem Set 10 (due Thu Nov 7) (with solutions)
- Problem Set 11 (due Thu Nov 14) (with solutions)
- Problem Set 12 (due Thu Nov 21)
- Problem Set 13 (due Tue Dec 3)

There will be two in-class **midterm exams**. The first will be on the 11th class day,
**Thursday October 3**. The second will be on the 21st class day, **Thursday November 7**.

There will be a **final exam** which is comprehensive, covering all the material from the course;
this may be an in-class or take-home exam (to be decided depending on how the class goes.)

Here are some practice problems for the first midterm, and the first midterm itself with solutions.

Here are some practice problems for the second midterm with solutions, and the second midterm itself with solutions.

Homework will count 20%, each midterm 25%, and the final exam 30%. In addition, if the final exam grade is higher than at least one of the midterms, then I will replace your lowest midterm exam grade by your final grade in computing your average.

The mapping from averages to letter grades is not fixed in advance. I can promise that it will not be stricter than 90=A, 80=B, 70=C, 60=D, and there will be a curve as warranted.

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.