Math 545

Analysis I (Real Analysis)

Instructor: Dr. Stefan Richter, 322 Ayres Hall, Tel.: 974-4286
e-mail: Richter at math dot utk dot edu
Class: MWF 9:05-9:55, room AH 121

Final exam: Friday 12/2, 8-10
Office hours this week: Wednesday, Thursday 2:30-3:30PM & by appointment

sample exam (Disclaimer: This was the final 2 years ago. Look at this for clues about format and length. It is not going to hurt to know how to do those problems, but understand that I'll make up a new exam for this year)

Lecture Notes

Homework #12, due Friday, 11-18 Solutions

Homework #11, due Friday, 11-1, Solutions

Homework #10, due Monday, 11-7, Solutions
Chapter 5, problems 3, 5, 8

Exam 1, Friday 10-28, Solutions, Solutions (Take home part)

Homework # 9, due Friday 10-28 Solutions Addendum to solutions
Chapter 5, Problems 4, 6

Homework # 8, due Friday 10-21 Solutions

Homework # 7, due Friday 10-14 Solutions
Chapter 3, Problems 6, 7, 8, Chapter 4, Problem 1

Homework # 6, due Friday 10-7 Solutions
Chapter 2, Problem 5, Chapter 3 Problems 1, 2, 3, 4, 5
(6 problems)

Homework # 5, due Friday 9-23 Solutions
Chapter 2, Problems 1, 2, 3, 4

Homework # 4, due Friday 9-16, Solutions
Chapter 1, Problems 11, 13, 14, 15

Homework # 3, due Friday 9-9, Solutions

Homework # 2, due Friday 9-2, Solutions

How many Borel sets are There? - a link I found on the internet. This is pure set theory, we will not go over this in class. The upshot is that compared to the collection of all subsets of the reals, there are relatively few Borel sets. And that is so even though it is hard to construct a set that is not a Borel set.

Homework # 1, due Friday 8-26, Solution problem 1, Solution problem 2

Background Check solutions
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Text: It should suffice to read the lecture notes that will be posted (and updated) here. The topics are roughly patterned after Chapters 1, 3 and parts of 4, 6, and 8 of the book Real & Complex Analysis, 3rd edition, by Walter Rudin, McGraw-Hill series in higher mathematics.

Abstract measure spaces, Borel and Lebesgue measures, measurable functions, convergence theorems (Fatou's Lemma, monotone and dominated convergence theorems), Hoelder, Jensen, and Minkowski inequalities, L^p-spaces, L^p-convergence, and completeness, Egoroff's theorem, elementary Hilbert space theory, Radon Nikodym theorem, product measures, Fubini's and Tonelli's theorems.
Differentiation and the Fundamental Theorem of Calculus, if time permits.

Class, test, and grading policies:

1. Attendance is mandatory.
2. Read the notes along with what we are doing in class.
3. There will be weekly assignments.
4. There will be one in class exam and a two hour comprehensive final exam.
Final exam: Friday 12/2, 8-10
5. Your final grade will be determined by use of the following key:
Homework 50%, Exams 50% (hour exam 16.6%, final exam 33.4%)