Mathematics 5318 - Intermediate Analysis
I -
Spring 2003
Class Schedule and Homework Assigment
The problems without * will not be graded, they are meant for practice. You only need to turn in the problems with *. |
Class |   Date   | Day | Topic | Problems | ||
1 | Jan 15 | Wed | 1.1 | Sets and Elements | 1.1 # | 1 -- 4 |
1.2 | Operations on Sets | 1.2 # | 6, 7*, 8*, 9a)*,b)* | |||
2 | Jan 17 | Fri | 1.3 | Functions | 1.3 # | 2*,13 |
1.4 | Real-valued functions | 1.4 # | 1*,2*, 5 | |||
3 | Jan 22 | Wed | 1.5 | Equivalence, countability | 10.5 # | 3, 4, 5*, 8*, 9* |
4 | Jan 22 | Wed | 1.6 | Real Numbers | 10.6 # | 1*, 3*, 5 |
5 | Jan 24 | Fri | 1.7 | Least upper bounds | 1.7 # | 3*, 4*, 5* |
6 | Jan 24 | Fri | 2.1 | Sequences | 2.1 # | 2,3,5*,6* |
7 | Jan 27 | Mon | 2.2 | Limit of a sequence | 2.2 # | 7, 11 |
8 | Jan 27 | Mon | 2.3 | Convergent sequences | 2.3 # | 4, 5* |
2.4 | divergent sequences | 2.4 # | 2*, 3* (hint for 3: rationalize) | |||
9 | Jan 29 | Wed | 2.5 | Bounded Sequences | 2.5 # | 2*,3*,5 |
2.6 | Monotone sequences | 2.6 # | 10* | |||
10 | Jan 29 | Wed | 2.7 | Operations on convergents sequences | 2.7 # | 11* |
2.8 | Operations on divergent sequences | 2.8 # | 1, 2, 3 | |||
11 | Jan 31 | Fri | 2.9 | Limit superior and limit inferior | 2.9 # | 6* |
12 | Jan 31 | Fri | 2.9 | Limit superior and limit inferior (continued) | 2.9 # | 6* |
13 | Feb 3 | Mon | 2.10 | Cauchy sequences | 2.10 # | 1, 4*,6 |
14 | Feb 5 | Wed | 2.11 | Summability of sequences | 2.11 # | 3,5*,6 |
Feb 7 -- 14 -- No classes, will be visiting the MSRI in Berkeley. Corresponding topics were taught on Jan 22--29 extra sessions. | ||||||
15 | Feb 17 | Mon | 3.1 | Convergence and divergence of series | 3.1 # | 7* |
3.2 | Series with nonnegative terms | 3.2 # | 3* | |||
16 | Feb 19 | Wed | 3.3 | Alternating Series | 3.3 | 4* |
3.4 | Conditional convergence and absolute convergence | 3.4 | 5* | |||
17 | Feb 20 | Fri | 3.5 | Rearrangements of series | 3.5 | 4,5 |
18 | Feb 24 | Mon | 3.6 | Tests for absolute convergence | 3.6 | 6*, 12 |
19 | Feb 26 | Wed | 3.7 | Series whose terms form a nonincreasing sequence | 3.7 # | 4* |
3.8 | Summation by parts | 3.8 # | 1*, 2 | |||
20 | Feb 28 | Fri | 3.9 | (C,1) summability of series | 3.9 # | 1,5*,6 |
3.10 | The class l^2 | 3.10 # | 2*,3,4*,7 | |||
21 | Mar 3 | Mon | 3.11 | The real numbers | 3.11 # | 3* |
22 | Mar 5 | Wed | Problem Session I | |||
23 | Mar 7 | Fri | Test I: Chapters 1, 2 & 3 | |||
24 | Mar 10 | Mon | 4.1 | Limit of a function on the real line | 4.1 # | 1b), 2a), 12*, 14* |
25 | Mar 12 | Wed | 4.2 | Metric spaces | 4.2 # | 3*,7* |
Mar 14 -- No classes, gone for the Arizona Winter School. Corresponding topics were taught on the Jan 31 extra session. | ||||||
Mar 15 -- 23 -- Spring Break | ||||||
26 | Mar 24 | Mon | 4.3 | Limits in metric spaces | 4.3 # | 6*,7* |
27 | Mar 26 | Wed | 5.1 | Functions continuous at a point of the real line | 5.1 # | 3*,6* |
5.2 | Reformulation | 5.2 # | 1,2,3 | |||
28 | Mar 28 | Fri | 5.3 | Functions continuous on a metric space | 5.3 # | 5*,7,8*,9 |
5.4 | Open sets | 5.4 # | 1*,6* | |||
29 | Mar 31 | Mon | 5.4 | Open sets (continued) | 5.4 # | 1*,6* |
5.5 | Open sets | 5.5 # | 10*,13* | |||
30 | Apr 2 | Wed | 5.6 | Discontinuous functions on R^1 | 13.4 # | 3*,4* |
31 | Apr 4 | Fri | 5.7 | The distance from a point to a set | 13.5 # | 1* | 32 | Apr 7 | Mon | 6.1 | More about open sets | 6.1 # | 1*, 3* |
6.2 | Connected sets | 6.2# | 1*,3*,8 | |||
33 | Apr 9 | Wed | 6.3 | Bounded sets and totally bounded sets | 6.3 # | 7* |
34 | Apr 11 | Fri | 6.4 | Complete metric spaces | 6.4 # | 4*, 6* |
37 | Apr 14 | Mon | 6.5 | Compact metric spaces | 6.5 # | 8*,9*,10*,11 |
36 | Apr 16 | Wed | Problem Session II | |||
37 | Apr 18 | Fri | Test II: Chapters 4 & 5 | |||
Monday, April 21 -- Easter Holiday -- No classes | ||||||
38 | Apr 23 | Wed | 6.5 | Compact metric spaces (continued) | 6.5 # | 8*,9*,10*,11 |
39 | Apr 25 | Fri | 6.6 | Continuous functions on compact metric spaces | 6.6 # | 5* |
40 | Apr 28 | Mon | 6.7 | Continuity of the inverse function | 6.7 # | 4* |
41 | Apr 30 | Wed | 6.8 | Uniform continuity | 6.8 # | 5*,7* |
42 | May 2 | Fri | Problem Session III | |||
43 | May 5 | Mon | Problem Session IV | |||
May 9 | Fri | Final Exam, 10:30 a.m. - 1:00 p.m. |