Math 413 Analysis I
Fall 2003
Instructor: David Marker
Call Number: 67387
Class Meets: 1200 MWF 220 SH
Office: 411 SEO
Office Hours: M 1:30-3, W 9-11, Th 10:30-12
Finals Week Office Hours T 12-3, Th 10:30-12, 1-3
phone: (312) 996-3069
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math413
Text
- S. Abbott, Understanding Analysis, Springer.
- Quick Tour of the topology
of R,
Supplementary notes on the topology of the reals for Math 413-414
(pdf file).
Prerequisites
Grade of C or better in Math 215 Introduction to Advanced Mathematics, or consent of instructor.
Description
The main purpose of Math 413--414 is to rigorously revisit many of the ideas and results
from Calculus I and II, including:
- Properties of the Real Numbers
- Sequences
- Elementary topology of the real line
- Limits and Continuity
- Differentiation
- Integration
- Series and Power Series
As time permits, additional topics may include metric spaces,
differential equations and Fourier series.
Here is a detailed week-to-week syllabus.
Problem Sets
As in all advanced mathematics courses, homework problem sets are an essential
part of the course. There will be weekly homework assignement.
You may discuss homework problems with other students, but you must write
up your solution independently. All proofs should be written neatly
with complete gramatical sentences. Each problem should be submitted on
a separate page.
Late homework will be accepted only in exceptional circumstances.
Grading
- There will be two midterm exams. The best of your two scores
will count for 30% of your final grade. The midterm exams will
be on Friday October 17 and Wed November 26.
- The final exam will count for 40% of your final grade. Part of the final
may be a take home exam.
The final exam will be Friday December 12 at 8:00 am.
- Homework will count for 30% of your final grade. The three
lowest homework scores will be dropped.
Homework Assignments
Bonus Problems
- Bonus Problem 1: The continued fraction expansion of
the square root of 2. (Turn in by 10/3) Note: There was a typo
on this problem.
- Bonus Problem 2: Every sequence has a stricly
monotonic subsequence. (Turn in by 10/3)
- Bonus Problem 3 A sequence with subsequences
converging to every possible limit. (Turn in by 10/3)
- Bonus Problems 4 & 5 Fat Cantor Sets,
Limits of limits (Turn in by 10/31)typo corrected
- Bonus Problem 6 Exercise 4.3.9 (Turn in by 10/31)
- Bonus Problem 7 Exercises 4.6.4 and 4.6.5 (Turn in by
11/14)
- Bonus Problem 8 (Turn in by 12/5)
Links
David Marker's homepage
Last revised: 12/12/03