# 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 Wed 1/5 1.1 What is a proof? What is a real number? 1/14
#2 Fri 1/7 1.1 What is a real number? (contd.) 1/14
#3 Mon 1/10 1.2 Absolute values, intervals, inequalities. 1/14
#4 Wed 1/12 1.2, 1.3 Finite geometric sums; Upper and lower bounds, sups and infs, the completeness axiom. 1/14
#5 Fri 1/14
Mon: MLK Day
(no class)
1.3 Logic, Archimedian Property, consequences. 1/21
#6 Wed 1/19 1.4 Countable, uncountable. 1/21
#7 Fri 1/21 1.4 Countable, uncountable (contd). 1/28
#8 Mon 1/24 1.4 Countable, uncountable (contd). 1/28
#9 Wed 1/26 2.1 Sequences. 1/28
#10 Fri 1/28 2.1 Sequences (contd). 2/9
#11 Mon 1/31
Midterm Exam this week 2/2-2/4
2.2 Monotone sequences and Cauchy sequences. 2/9
#12 Wed 2/2 2.2 Monotone sequences and Cauchy sequences (contd). 2/9
#13 Fri 2/4 2.2 Special sequences and nested intervals. 2/9
#14 Mon 2/7 2.3 Subsequences. 2/9
#15 Wed 2/9
No Class Fri 2/11
Winter Carnival
2.3 Subsequences: liminf and limsup. 2/18
#16 Mon 2/14 3.1 The limit of a function 2/18
#17 Wed 2/16 3.1 The limit of a function (contd). 2/18
#18 Fri 2/18 3.2 Continuous functions. 2/25
#19 Mon 2/21 3.3 Intermediate and Extreme Values. 2/25
#20 Wed 2/23 3.5 Monotone functions. 2/25
#21 Fri 2/25 3.4 Uniform continuity. 3/4
#22 Mon 2/28 6.1, 6.2, 6.3 Infinite series of numbers. 3/4
#23 Wed 3/2 7.1, 7.2 Sequences of functions. 3/4
#24 Fri 3/4 7.1, 7.2, 7.3 Infinite series of functions. ---
#25 Mon 3/7 7.3 Uniform convergence and inherited properties. ---
#26 Wed 3/9 - Review of course.
Course evaluations.
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