| Date |
Sections
Covered |
Suggested assignments | Comments |
| Jan. 07 |
1-3. Sets, Functions, Relations |
Sect. 1 - #2 h-m, 4, 5, 6, 9 Sect. 2 - #1-5 Sect. 3 - #1-9, 13, 14 |
Besides the problems suggested
on the left, you should also try to do all exercises suggested in class |
| Jan. 09 |
7. Countable &
Uncountable sets |
Sect. 7 - #1-5, 6* |
|
| Jan. 14 |
12&13 Topological space,
Basis + Def. of metric space and metric topology (see p. 119, 120) |
Sect. 13 - #1-8 |
Starting
this week, my office hours are changed permanently to Thursdays 1-4 pm. No office hours on Tuesdays. |
| Jan 16 |
More on Basis Convergence in a topological space (see def. on page 98) |
Class exercises |
Homework 1 due
Wednesday, Jan. 23 To avoid deductions, your homework should be stapled, neatly written, and, most of all, correct mathematically. You are allowed to discuss the problems, but each of you should write the solution independently. |
| Jan. 21 |
No class - MLK day |
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| Jan. 23 |
14, 15, 16 Order, Product,
Subspace Topology |
Sect. 16 - #1-6, 8-10 |
The deadline to Hwk1 is extended
to Monday, Jan. 28. No extra problem. Try not to miss any details especially on 2(b). |
| Jan. 28 |
17 Closed sets and Limit Points |
Sect 17 - #8-16, 19, 21* |
Homework 2 due
Monday, Feb. 4. |
| Jan. 30 |
18 Continuous Functions |
Sect. 18 - #2, 3, 5-9 |
|
| Feb. 4 |
19 Product spaces |
Sect. 19 - #3-8, 10 |
|
| Feb. 6 |
Problem solving |
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| Feb. 11 |
20 Metric topology |
Sec. 20 - #1-7, 11 |
Homework 3 due
Monday, Feb. 18 |
| Feb. 13 |
21 Metric topology |
Sec. 21 - #1, 3, 5-10 |
Exam 1 on Mon. Feb. 25 (note the
new date) covers
all sections done up to (and including) Sect. 21. |
| Feb. 18 |
Problem solving Review for Exam |
For the exam, you should know
well the definitions of all concept discussed. Most problems you'll have will be common sense proofs that should come naturally from the definitions. Most of the theorems that we've done so far fall into this category. All suggested exercises and the hand-in homework problems could serve as exam subjects as well. |
|
| Feb. 20 |
22 Quotient Topology |
Sec. 22 - #1-4, 6 |
This section is not covered on
exam1 |
| Feb. 25 |
Exam
1 |
Handout
on the problem I failed to do in class. Fill in the details. It's
good review! |
|
| Feb. 27 |
22 Quotient Topology2 |
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| Mar. 3 |
23 Connectedness |
Sec. 23 - #1-12 |
|
| Mar. 5 |
24 Connectedness2 |
Sec. 24 - #1-7 |
Homework
4 due Wednesday, March 12 |
| Mar. 10 |
finish section 24 |
Sec. 24 - #8, 10 |
|
| Mar. 12 |
25 Path Connectedness |
Sec. 25 - #1, 2, 4 |
Homework 5 due Monday,
March 24 Pbs 6 and 11 page 152 textbook Pbs 2 and 4 page 158 textbook |
| Mar. 17 |
Spring break |
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| Mar. 19 |
Spring break | Have a good spring break! | |
| Mar. 24 |
26 Compactness |
Sec. 26 - # 1-9 |
|
| Mar. 26 |
27 Compactness2 | Sec. 27 - # 2-6 |
|
| Mar. 31 |
27 Compactness 3 |
Sec. 27 - # 2-6 | Pb.
2 page 177, Teams: (RJM) Rafael, Jorge, Matias (JID) Jose, Ish, David Each team should hand in one written solution by Mon. Apr. 7 |
| Apr. 2 |
28 Compactness 4 |
Sec. 28 - #1-7 |
Pb. 2, above, is now part of
your exam 2 . Each one of you should individually submit solution for it. |
| Apr. 7 |
51 Homotopy of paths |
Sec. 51 - #1-3 |
Exam 2 - take home - Due Mon. Apr. 21 No delays admitted! |
| Apr. 9 |
52 Fundamental group | Sec. 52 - #1-5 | Take home part of the final exam - Due Mon.
Apr. 21 No delays admitted! |
| Apr. 14 |
55 Retractions and Brouwer Fixed
Pt. Thm |
Sec. 55 - #1, 3 |
|
| Apr. 16 |
54 Pi_1(S^1) = (Z,+) |
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| Monday Apr. 21 |
Final
Exam 18:30-20:30 (Note the time!) |
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