# 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 1/4 1.1 What is a proof? What is a real number? 1/13
#2 Fri 1/6 1.1 What is a real number? (contd.) 1/13
#3 Mon 1/9 1.2 Absolute values, intervals, inequalities. 1/13
#4 Wed 1/11 1.2, 1.3 Finite geometric sums; Upper and lower bounds, sups and infs, the completeness axiom. 1/13
#5 Fri 1/13
Mon: MLK Day
(no class)
1.3 Logic, Archimedian Property, consequences. 1/20
#6 Wed 1/18 1.4 Countable, uncountable. 1/20
#7 Fri 1/20 1.4 Countable, uncountable (contd). 1/27
#8 Mon 1/23 1.4 Countable, uncountable (contd). 1/27
#9 Wed 1/25 2.1 Sequences. 1/27
#10 Fri 1/27 2.1 Sequences (contd). Wed 2/8
#11 Mon 1/30
Midterm Exam this week 2/1-2/3
2.2 Monotone sequences and Cauchy sequences. Wed 2/8
#12 Wed 2/1 2.2 Monotone sequences and Cauchy sequences (contd). Wed 2/8
#13 Fri 2/3 2.2 Special sequences and nested intervals. Wed 2/8
#14 Mon 2/6 2.3 Subsequences. Wed 2/8
#15 Wed 2/8
No Class Fri 2/10
Winter Carnival
2.3 Subsequences: liminf and limsup. 2/17
#16 Mon 2/13 3.1 The limit of a function 2/17
#17 Wed 2/15 3.1 The limit of a function (contd). 2/17
#18 Fri 2/17 3.2 Continuous functions. 2/24
#19 Mon 2/20 3.3 Intermediate and Extreme Values. 2/24
#20 Wed 2/22 3.5 Monotone functions. 2/24
#21 Fri 2/24 3.4 Uniform continuity. 3/2
#22 Mon 2/27 6.1, 6.2, 6.3 Infinite series of numbers. 3/2
#23 Wed 2/29 7.1, 7.2 Sequences of functions. 3/2
#24 Fri 3/2 7.1, 7.2, 7.3 Infinite series of functions. ---
#25 Mon 3/5 7.3 Uniform convergence and inherited properties. ---
#26 Wed 3/7 - Review of course.
Course evaluations.
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