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General Course Description
Math 402 is a continuation of Math 401 and is the second part of a first one-year course in Analysis. The course generalizes and extends the concepts of sequences, limits, compactness, and continuity to several variables and metric spaces. Other topics will include the interchanging of limit operations, series, power series, partial derivatives, and the fixed point, contraction mapping, implicit, and inverse function theorems.
Student Learning Outcomes (SLOs) and Rubric for Math 402
Textbook
Chapter 11 on the Riemann Integral in Analysis I by Terence Tao;
Terence Tao, Analysis II (Texts and Readings in Mathematics Book 38), Springer, 3rd Edition, 2016 (Required)
(Previous edtions will work as well.)
Terence Tao is an exceptional mathematician who won the 2006 Fields Medal. New York Times article about Tao.
Supplementary Readings
1) Introduction to Analysis by Maxwell Rosenlicht (Dover)
2) The Way of Analysis by Robert Strichartz.
3) Principles of Mathematical Analysis (3rd Edition) by Walter Rudin.
Homework
Homework problems come from the textbook. Note that the third edition of the book came out in October 2014, and the chapter numbering in Volume II now starts at 1. For Chapter N in the second edition with N > 11, it will be Chapter (N - 11) in the third edition.
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