Mathematics 35, Winter 2010

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