University of Rhode Island MTH435: Mathematical Analysis and Topology I
Fall 2017


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 beginningTopicsReadingNotes
Properties of the Real Numbers
Chapter 1First day of class on 09/06
09/112.2 Absolute Value and the real line
2.3 Completeness
2.4 Applications of Completeness
Chapter 2 up to p49
09/182.5 Intervals
3.1 Sequences and Limits
3.2 Limit Theorems
3.3 Monotone Sequences
pp40-77, excluding pp49-53We may revisit binary and decimal expansions at a later date (time permitting).
09/253.2 Limit Theorems
3.3 Monotone Sequences
3.4 Subsequences
10/023.4 Subsequences
3.5 Cauchy Criterion
3.6 Properly Divergent Sequences
10/093.5 Cauchy Sequences
3.6 Properly Divergent Sequences
pp88-93No class 10/09 (Columbus Day)
10/163.7 Introduction to Infinite Series
9.1 Absolute Convergence
10/23Midterm I
9.2 Tests for Absolute Convergence
pp270-276Midterm I on 10/23
10/309.3 Tests for Nonabsolute Convergence
11.4 Metric Spaces
11/064.1 Limits of Functions
4.2 Limit Theorems
11/13Midterm IIRevisionNo class 11/13 (Veteran's Day)
11/204.2 Limit Theoremspp111-122Optional Class on 11/22 (Q&A/Review session). Happy Thanksgiving!
11/274.3 Some Extensions of the Limit Concept
5.1 Continuous Functions
5.2 Combinations of Continuous Functions