Math 35
Real Analysis
Last updated July 18, 2017 09:28:22 EDT

## Syllabus

The following is a tentative syllabus for the course. In particular, the choice and ordering of topics beyond Chapter 3 is not set in stone. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

The Documents page has links to the questionnaire assigned on Monday, January 6, as well as the notes we used in class.
Lectures Sections in Text Brief Description
1/6 1.1 Introduction
1/7 (x-hour)   No class today
1/8 1.1 Axioms for the real numbers
1/10 1.2 Absolute value, intervals, and inequalities
1/13 1.3 Completeness
1/14 (x-hour)   Proofs using induction and completeness
1/15 1.4 Countable and uncountable sets
1/17 Chapter 1 Review and overview
1/20   No class; Martin Luther King, Jr. holiday
1/21 (x-hour) 2.1 Convergent sequences
1/22 2.1 Convergent sequences
1/24 2.2 Monotone sequences and Cauchy sequences
1/27 2.3 Subsequences
1/28 (x-hour)   Proofs involving sequences
1/29 2.3 Subsequences
1/31 Chapter 2 Review and overview
2/3 3.1 The limit of a function
2/3   Midterm exam distributed
2/4 (x-hour)   Limit proofs
2/5 3.2 Continuous functions
2/6   Midterm exam due 4 PM
2/7   No class; winter carnival holiday
2/10 3.3 Intermediate and extreme values
2/11 (x-hour)
2/12   Quantifiers and convergence
2/14 3.4 Uniform continuity
2/17 3.5 Monotone functions
2/18 (x-hour) optional Derivatives
2/19 Chapter 3 Review and Overview
2/21 6.1, 6.2 Infinite series
2/24 6.3 Absolute convergence
2/25 (x-hour)   Sequences of functions
2/26 7.1 Sequences of functions
2/28 7.2, 7.3 Uniform convergence
3/3 7.4 Power series
3/4 (x-hour) optional Riemann integrals
3/5 7.4 Power series
3/5   Take-home final exam distributed
3/7   Last day of class
3/10   In-class final 8 AM
3/11   Take-home final exam due at noon

Marcia J. Groszek
Last updated July 18, 2017 09:28:22 EDT