Mathematics 35, Winter 2011

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	Sec	Topic	Hwk 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.	---