MTH435 - Mathematical Analysis and Topology I

Schedule

Here is a course timetable showing exactly where we are in class. I will attempt to update it at least weekly, to give you an idea of the reading you need to do to prepare for class that week.

Week beginning	Topics	Reading	Notes
09/04	Introduction Inequalities Properties of the Real Numbers	Chapter 1	First day of class on 09/06
09/11	2.2 Absolute Value and the real line 2.3 Completeness 2.4 Applications of Completeness	Chapter 2 up to p49
09/18	2.5 Intervals 3.1 Sequences and Limits 3.2 Limit Theorems 3.3 Monotone Sequences	pp40-77, excluding pp49-53	We may revisit binary and decimal expansions at a later date (time permitting).
09/25	3.2 Limit Theorems 3.3 Monotone Sequences 3.4 Subsequences	pp63-84
10/02	3.4 Subsequences 3.5 Cauchy Criterion 3.6 Properly Divergent Sequences	pp78-93
10/09	3.5 Cauchy Sequences 3.6 Properly Divergent Sequences	pp88-93	No class 10/09 (Columbus Day)
10/16	3.7 Introduction to Infinite Series 9.1 Absolute Convergence	pp94-100;pp267-269
10/23	Midterm I 9.2 Tests for Absolute Convergence	pp270-276	Midterm I on 10/23
10/30	9.3 Tests for Nonabsolute Convergence 11.4 Metric Spaces	pp277-280;pp341-345
11/06	4.1 Limits of Functions 4.2 Limit Theorems	pp102-115
11/13	Midterm II	Revision	No class 11/13 (Veteran's Day)
11/20	4.2 Limit Theorems	pp111-122	Optional Class on 11/22 (Q&A/Review session). Happy Thanksgiving!
11/27	4.3 Some Extensions of the Limit Concept 5.1 Continuous Functions 5.2 Combinations of Continuous Functions	p116-133