Syllabus & Homework
On this page you will find a short syllabus for Math 421 indicating
the topics and sections of the text we will cover. You should check
this page frequently to obtain your homework assignments.
Course Syllabus
The first half of the course will cover point set topology. We will not
strive for the utmost generality. We will give many examples. The
textbook for this part of the course is Willard.
The second half of the course will cover the topology of surfaces,
including basics of homology and homotopy theory. The textbook for this
part of the course is Henle.
Additional references:
- Algebraic topology: an introduction by Massey
- the first chapter on surfaces and the appendix on point
set topology are relevant
- Topology of surfaces by Kinsey
- Riemann surfaces by Ahlfors and Sorio
- the first chapter contains a proof that surfaces are
triangulable
- The Jordan-Schonflies theorem and the classification of
surfaces by Thomassen, American Math Monthly, vol 99
(1992) pp. 116 - 131.
- in addition to the title, you get a self-contained
proof that surfaces are triangulable
- Geometric topology in dimensions 2 and 3, by Moise
- everything you could want to know about surfaces,
and more
Homework Assignments
Homework problems marked in red will be
collected. I will write comments on your paper and return it. You
should then revise your solutions and resubmit. I will then grade
your solutions and return them to you.
The due dates below are targets for initial submission. According to
the above homework grading policy, you should, however, complete
everything by the end of the semester.
| Date |
Homework |
Comments |
| January 23 |
Willard: 2C.1-3, 2F --
3A.4, 3B, 3E -- 4A.2,3 |
?? |
| February 15 |
Willard: 3G,4B,4C --
6A.1,2,5 -- 7D |
?? |
| April 10 |
Willard: 9A.1-2, 9C.1-2 --
17B.5 -- 26D,
26B.4 (cool, but tricky) |
forget about 'semicontinuity' in 9A.2 |
| April 26 |
Henle p89:5,7,8 --
p96:10 --
p109:4abc 113:7a |
p89:7 -- two chains only |
Quiz & Exam Schedule
| Event |
Date |
Solution |
Comments |
| Quiz 1 |
March 6 |
in class |
none |
| Midterm Exam |
April 10 |
in class & take home |
none |
| Quiz 2 |
April 26 |
in class |
none |