MAT 364 Fall 2019
MAT 364 Fall 2019 - Schedule always in construction

Section
Topic
HW due this week
# Notes
8/26 1.1

Open and closed sets

Fill this form 0
9/2 1.1 Open and closed sets, limit points, sequences. Work on these problems. (All are to be handed in)

1 9/2 Labor day
9/9 1.1

Definition of a topology on a set
History of Topology

Each Friday, submit only the problems in underlined boldface
Section 1.1: 3, 4, 5,  7, 8, 9, 10
Also, hand in a summary of all definitions and proposition we learned. Extra credit: write informal definitions.
2
9/16 1.1
Definition of topology (check this book, page 24)
Subspace topology
Section 1.1: 10, 12, 13, 14, 18.
3
9/23 1.1 Quotient topology (Here is a good set of notes about equivalence relations) All these problems (Note from 9/25, this is a new version of the same problems)
4
9/30 1.2
1.3
Continuous functions
Quotient topology
(Here is a good set of notes about images and inverse image of  functions)
Some topological properties
• Think of a topological description of (do not submit it... yet)
• Write down a summary of all propositions and statements that we studied until Friday Sept 27th, in your own words. (Advice: Save a copy of this summary and use it to study for the midterm)
• Section 1.1: 30, 31,
• Section 1.2: 1, 4.

5
10/7
Connectedness
Path connectedness
Compactness
There is no homework due this week. Here is a list of review problems (disregard the title, Homework 5)
6 Midterm is on Friday Oct 11th.
Here are a list of erratas of the book
10/14

Section 1.3: 19, 22, 23, 24.
7 10/14-15 Break
10/21
Definition of a manifold.
Definition of surface
Definition of surface with boundary
Connected sum construction
Section 1.3: 10, 11, 12, 13, 14, 16, 27, 28, 29, 30, 31, 34, 35
8
10/28
Plane models of surfaces
Orientability
Section 2.1: 1, 2.
Section 2.2: 2, 3, 4, 5, 6 (use the figure of the letters below), 7
Section 2.3: 1, 2, 3, Project 2.3.4.d,

Keep thinking of a topological description.
9
11/4
Classification of surfaces
Cell complexes and Euler characteristic
Section 2.3: 12, 13, 20, 21,  22, 23.
Prove Prop. 2.4.1.
Section 2.4:  2,  3, Project 4  (counts as two problems),
10
11/11
Cell complexes and Euler characteristic
Genus
Section 2.5: 3, 4
Section 2.6: 3, 4, 5, 6, 7,
Section 2.7: 3, 5, 6, 7
Write down a summary of all propositions and statements that we studied until Friday Nov 15, in your own words.
11
11/18
Review
Midterm: There is no homework this week.

12 Midterm 2
Friday Nov 22nd
List of topics and sample problems from the book
11/25
Maps and map coloring Thanksgiving: There is no homework this week. 13 11/27-29 Thanksgiving
12/2
Maps and map coloring Section 3.4: 2(explain your answer), 3, 7, 13,
Section 4.1: 8, 9, 10, 11, 12, 13, 14.

14
12/9
Maps and map coloring
15 12/9 Last day of classes

Final Wed. Dec. 18
2:15pm-5:00pm
List of topics for the final