# Real Analysis

We will cover selected topics from the 8 chapters of the book by Gordon. See the Homework Assignments.

Syllabus and Daily Schedule
Lec Day SecTopicHwk Due
#1 Mon 1/7 1.1 What is a real number? 1/11
#2 Wed 1/9 1.1 What is a real number? (contd.) 1/11
#3 Fri 1/11 1.2 Absolute values, intervals, inequalities. 1/18
#4 Mon 1/14 1.2, 1.3 Finite geometric sums; Upper and lower bounds, sups and infs, the completeness axiom. 1/18
#5 Wed 1/16 1.3 Logic, Archimedian Property, consequences. 1/18
#6 Fri 1/18 1.4 Countable, uncountable. 1/25
#7 Wed 1/23 1.4 Countable, uncountable (contd). 1/25
#8 Fri 1/25 1.4 Countable, uncountable (contd). 2/1
#9 Mon 1/28 2.1 Sequences. 2/1
#10 Wed 1/30 2.1 Sequences (contd). 2/1
#11 Fri 2/1 2.2 Monotone sequences and Cauchy sequences. 2/15
#12 Mon 2/4 2.2 Monotone sequences and Cauchy sequences (contd). 2/15
#13 Wed 2/6 2.2 Special sequences and nested intervals. 2/15
#14 Mon 2/11 2.3 Subsequences. 2/15
#15 Wed 2/13 3.1 The limit of a function. 2/15
#16 Fri 2/15 3.1 The limit of a function (contd). 2/22
#17 Mon 2/18 3.1 The limit of a function (contd). 2/22
#18 Wed 2/20 3.2 Continuous functions. 2/22
#19 Fri 2/22 3.3 Intermediate and Extreme Values. 2/29
#20 Mon 2/25 3.5 Monotone functions. 2/29
#21 Wed 2/27 3.4 Uniform continuity. 2/29
#22 Fri 2/29 6.1, 6.2, 6.3 Infinite series of numbers. ---
#23 Mon 3/3 7.1, 7.2 Sequences of functions. ---
#24 Wed 3/5 7.1, 7.2, 7.3 Infinite series of functions. ---
#25 Fri 3/7 7.3 Uniform convergence and inherited properties. ---