# 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 1/5 1.1 What is a proof? What is a real number? 1/9
#2 Wed 1/7 1.1 What is a real number? (contd.) 1/9
#3 Fri 1/9 1.2 Absolute values, intervals, inequalities. 1/16
#4 Mon 1/12 1.2, 1.3 Finite geometric sums; Upper and lower bounds, sups and infs, the completeness axiom. 1/16
#5 Wed 1/14 1.3 Logic, Archimedian Property, consequences. 1/16
#6 Fri 1/16
Mon: MLK Day
1.4 Countable, uncountable. 1/23
#7 Wed 1/21 1.4 Countable, uncountable (contd). 1/23
#8 Fri 1/23 1.4 Countable, uncountable (contd). 1/30
#9 Mon 1/26 2.1 Sequences. 1/30
#10 Wed 1/28 2.1 Sequences (contd). 1/30
#11 Fri 1/30 2.2 Monotone sequences and Cauchy sequences. 2/11
#12 Mon 2/2 2.2 Monotone sequences and Cauchy sequences (contd). 2/11
#13 Wed 2/4 2.2 Special sequences and nested intervals. 2/11
#14 Fri 2/6 2.3 Subsequences. 2/11
#15 Mon 2/9 2.3 Subsequences: liminf and limsup. 2/11
#16 Wed 2/11
No Class Fri 2/13
Winter Carnival
3.1 The limit of a function 2/20
#17 Mon 2/16 3.1 The limit of a function (contd). 2/20
#18 Wed 2/18 3.2 Continuous functions. 2/20
#19 Fri 2/20 3.3 Intermediate and Extreme Values. 2/27
#20 Mon 2/23 3.5 Monotone functions. 2/27
#21 Wed 2/25 3.4 Uniform continuity. 2/27
#22 Fri 2/27 6.1, 6.2, 6.3 Infinite series of numbers. 3/6
#23 Mon 3/2 7.1, 7.2 Sequences of functions. 3/6
#24 Wed 3/4 7.1, 7.2, 7.3 Infinite series of functions. 3/6
#25 Fri 3/6 7.3 Uniform convergence and inherited properties. ---
#26 Mon 3/9 - Review of course.
Course evaluations.
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