MAT 364:
Fall 2012
Schedule and Homework Assignements

## Tentative Schedule and Homework

This schedule is, as the title indicates, tentative. It is updated up to (and including) the homework due the next week but future assignments may be modified if the progress of the class requires it. It is your responsibility to check it weekly.

Homework is a mandatory part of the course. Homework assignments are due each week at the beginning of the Monday's class. Under no circumstances will late homework be accepted.

The numbering in the schedule below refer to the course textbook Introduction to Topology, pure and applied by Colin Adams and Robert Franzosa.  The extra-credit homework (denoted by EC in the schedule below) is optional but you are encouraged to work on them.

It is allowed (and encouraged) to discuss the problems with other students in the class, however you (and only you and nobody else but you) are responsible for the write up. All the work you hand in should be your own, not copied from someone else  work. You should list all your sources and collaborators.  Suspiciously similar solutions will receive no credit and will be reported to the Academic Judiciary.

New material is presented every week. You should read the corresponding section of the textbook before the class.

##### Remarks
8/27
1.1
Introduction
Topological spaces
0-1
HW 0
1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9,
9/5
Do not forget hw0!
9/3
1.2
1.3
1.4
Basis for a topology
Closed sets
Examples
2
1.10, 1.11, 1.13, 1.14, 1.16, 1.17
1.25, 1.26, 1.28, 1.31 1.34,1.36
1.39 (1.39 is extra credit)
9/12
Monday Sept. 9th,
Labor Day, No Class.
9/10
2.1
2.2
2.3
Interior and closure of sets
Limit Points
The boundary of a set
3
2.1, 2.2, 2.3, 2.4, 2,7,2.8, 2.9,2.11, 2.12
2.13, 2.14,  2.16, 2.18, 2,19, 2.21, 2.22, 2.23
2.24, 2.26, 2.28
9/19

9/17
3.1
3.2
3.3
The subspace topology
The product topology
The quotient topology
4
3.1, 3.2, 3.4, 3.6, 3.9, 3.10, 3.11
3.12, 3.13, 3.14, 3.15, 3.17, 3.18, 3.19, 3.20,  3.22

9/26

9/24
3.4
4.1
The quotient topology
Continuity
5
3.24, 3.25, 3.26, 3.27, 3.28, 3.29, 3.30, 3.31, 3.33.
4.1, 4.3, 4.5, 4.6, 4.8, 4.10, 4.13, 4.14, 4.16
Play torus games, get them here.
10/3

10/1
4.2
Homeomorphisms
Review
6
4.22, 4.23, 4.24, 4.25, 4.28, 4.29, 4.31, 4.33, 4.37
10/10 Working on the set of problems due next week will help you review for the midterm. (Note that there are no new topics)
10/8
5.1
Metric Spaces
7
Change in homework assignements:  As usual, problems in bold letters are mandatory. Problems underlined are for students who aspire to an A, or A- in the class. (Everybody can try it but it is very important that you are able to solve ALL the non-underlined problems before trying underlined ones).
5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.10, 5.11, 5.12, 5.13, 5.14, 5.16 (the correct version of 5.14 is here, page 6).
Extra hw about functions and relations here (due 10/24) for students who got 20 or less in the midterm.
10/17 Monday Oct 8 Midterm 1:
Topics Chapters 1 to 4. (including 4)
10/15
5.3
6.1-6.2
Metric Spaces
Connectedness
8
5.23, 5.24, 5.26, 5.27, 5.28, 5.29, 5.30
6.1, 6.2, 6.4, 6.5, 6.6, 6.76.8, 6.9,  6.10
10/24
10/22
6.2
6.3
Connectedness
9
6.17, 6.18, 6.19, 6.20, 6.21, 6.25, 6.26, 6.276.28, 6.32, 6.33, 6.34, 6.35, 6.38,
Extra homework for students who got 20 or less in the midterm here
11/7
10/29

11/5
6.4
7.1

Path connectedness
Compactness

10
6.39, 6.40, 6.41, 6.42, 6.43, 6.44 6.45 , 6.46, 6.48, 6.50, 6.51, 6.52

11/14
11/12
7.2 Compactness

No hw due on 11/21!! Monday Nov 12 Midterm 2
Midterm Topics: Metric Spaces and Connectedness.
11/19
7.3

Compactness
11 7.1, 7.2, 7.3, 7.5, 7.6, 7.8, 7.10, 7.11, 7.12, 7.13
7.14, 7.16, 7.17, 7.18, 7.19, 7.20, 7.21
11/28 Thanksgiving Break, Nov. 21st - Nov 25th
11/26
7.3
14.1
14.2
Compactness
Surfaces

12
7.22, 7.23, 14.10,14.11,14.12, 14.13, 14.14.
There is no homework due next week, but BEWARE!! Very similar problems to ALL of those listed in this column will appear in the final.

12/3

Special topic
Review
13

Dec 7th, last day of classes.
12/10

12/17

Final Exam: Thursday Dec. 13th, 5:30pm-8pm

 Section Topic (in bold letters what we will cover). Other topics might be covered. 9 14 12 Other sources Homotopy and degree theory Manifolds and cosmology Knots Hyperbolic geometry.