Mathematics 35, Winter 2009

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	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.	---