Mathematics 3220-04: Foundation of Analysis I
Schedule: Monday, Wednesday, Friday at 4:35-5:55 PM (in JWB 206)
Text: Walter Rudin, Principles of Mathematical Analysis, Third Edition,
Office: LCB 104
Office hours: After classes or by arrangement.
Course Content: This is a Honors section of Math-3210. We use
a different, considerably more difficult, textbook than the regular
sections. Moreover, the exams are more difficult.
We plan to cover chapters 1 to 6 of the textbook.
Chapter 1: The Real and Complex Number Systems
Chapter 2: Basic Topology
Chapter 3: Numerical Sequences and Series
Chapter 4: Continuity
Chapter 5: Differentiation
Chapter 6: The Riemann-Stieltjes Integral
Goals and Objectives: The main objective of this course is to
learn rigorous foundation of calculus of functions of one variable, 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
First we shall study the basic notions of topology of metric spaces
(including compactness and conectedness) and continuous maps between
Then we shall apply these notions to study differentiability of
functions of one real variable. Finally we are going to study the
construction of Riemann integral of functions of one real variable.
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
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, August 11, 2017.