Mathematics 3220-03: Foundation of Analysis II



Schedule: Monday, Wednesday, Friday at 4:35-5:55 PM (in LCB 225)

Text: Walter Rudin, Principles of Mathematical Analysis, Third Edition, MacGraw-Hill

Contact:

Office: LCB 104

Phone: (801)581-5272

E-mail: milicic@math.utah.edu

Office hours: After classes or by arrangement.

Course Content: This is a Honors section of Math-3220 and continuation of Fall Semester Math 3210-04. We use a different, considerably more difficult, textbook than the regular sections. Moreover, the exams are more difficult.
We plan to cover chapters 7 to 11 of the textbook.

Chapter 7: Sequences and Series of Functions
Chapter 8: Some Special Functions
Chapter 9: Functions of Several Variables
Chapter 10: Integration of Differential Forms
Chapter 11: The Lebesgue Theory

Goals and Objectives: The main objective of this course is to learn rigorous foundation of calculus of functions of several variables, to learn how to do proofs and write them in mathematically precise form.
We will assume that students are familiar with routine calculations done in regular calculus courses, so these will be deemphasized in the course.
First we shall study the topology of spaces of continuous real functions on compact spaces including Stone-Weierstrass theorem.
Then we shall study local theory of differentialbe functions of several variables, including the inverse function theorem. This will be applied to develop the theory of differential forms and their integration. Finally we are going to prove the general Stokes' theorem.
At the end, we are going to sketch the theory of Lebegue integral.
Tests and Grading:
Homeworks will be assigned on regular basis, but not collected or graded. Some interesting homework problems will be discussed in class after students worked on them.
There will be three take-home midterm tests. They will be posted here on regular intervals.
The problems on these tests will be of different degree of difficulty. They will require from students to write up detailed proofs of various statements related to the material covered in class. The students will have about two weeks to work on each take-home exam.
The final grade will be based on the score on these three exams.
First Midterm Test
Second Midterm Test
Third Midterm Test


Last edit by dm, January 2, 2018.