Mathematics 35, Winter 2008

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 1/7	1.1	What is a real number?	1/11
#2	Wed 1/9	1.1	What is a real number? (contd.)	1/11
#3	Fri 1/11	1.2	Absolute values, intervals, inequalities.	1/18
#4	Mon 1/14	1.2, 1.3	Finite geometric sums; Upper and lower bounds, sups and infs, the completeness axiom.	1/18
#5	Wed 1/16	1.3	Logic, Archimedian Property, consequences.	1/18
#6	Fri 1/18	1.4	Countable, uncountable.	1/25
#7	Wed 1/23	1.4	Countable, uncountable (contd).	1/25
#8	Fri 1/25	1.4	Countable, uncountable (contd).	2/1
#9	Mon 1/28	2.1	Sequences.	2/1
#10	Wed 1/30	2.1	Sequences (contd).	2/1
#11	Fri 2/1	2.2	Monotone sequences and Cauchy sequences.	2/15
#12	Mon 2/4	2.2	Monotone sequences and Cauchy sequences (contd).	2/15
#13	Wed 2/6	2.2	Special sequences and nested intervals.	2/15
#14	Mon 2/11	2.3	Subsequences.	2/15
#15	Wed 2/13	3.1	The limit of a function.	2/15
#16	Fri 2/15	3.1	The limit of a function (contd).	2/22
#17	Mon 2/18	3.1	The limit of a function (contd).	2/22
#18	Wed 2/20	3.2	Continuous functions.	2/22
#19	Fri 2/22	3.3	Intermediate and Extreme Values.	2/29
#20	Mon 2/25	3.5	Monotone functions.	2/29
#21	Wed 2/27	3.4	Uniform continuity.	2/29
#22	Fri 2/29	6.1, 6.2, 6.3	Infinite series of numbers.	---
#23	Mon 3/3	7.1, 7.2	Sequences of functions.	---
#24	Wed 3/5	7.1, 7.2, 7.3	Infinite series of functions.	---
#25	Fri 3/7	7.3	Uniform convergence and inherited properties.	---