Mathematics 35, Winter 2012

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 1/4	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.	---