Math 6342: Point-Set Topology, Fall
2015
Exams and Homework
Homework:
Due Wednesday, Dec. 9
To Be Handed In: Final Exam
End of the Semester Reading Assignments and Exercises
In the remaining weeks of the semester, we will cover the following topics, and you should read the appropriate sections of the book and notes that are provided.
Sec. 34 Urysohn's Lemma
Sec. 35 Tietze Extension Theorem
Notes on Locally Compact spaces (with versions of Urysohn's Lemma and the Tietze Extension theorem for locally compact Hausdorff spaces.)
Sec. 36 Imbeddings of Manifolds
Sec. 37 The Tychonoff Theorem
Sec. 38 The Stone-Cech Compactification
Notes on the Cantor Set
We will end with a 1-day summary of Chapter 7 emphasizing Ascoli's Theorem
The following problems are for your practice and do not need to be turned in:
Sec. 28 #1, 4, 5, 6, 7
Sec. 29 #1, 3, 5, 6, 7, 8, 10
Sec. 30 #1, 2, 5
Sec. 31 #1, 2, 3, 4, 5, 6, 7
Sec. 33 #3, 4, 5
Sec. 34 #1, 2, 3, 4
Sec. 35 #1
Sec. 36 #5
Sec. 38 #5, 6
Due Wednesday, Oct. 28
Reading Assignment: Sec. 32-33
To Be Handed In: Exam 2
Due Friday, Oct. 23
Reading Assignment: Sec. 30-31
To Be Handed In: Homework 5
Due Friday, Oct. 16
Reading Assignment: Sec. 28-29
There is nothing to be handed in this week. The following problems are for your practice:
Sec. 25 #1, 2, 3; Sec. 26 #1, 2, 3, 4, 5, 6, 7; Sec. 27 #1, 2, 3, 4
Due Friday, Oct. 9
Reading Assignment: Sec. 24-27
To Be Handed In: Homework 4
Due Friday, Oct. 2
Reading Assignment: Sec. 22-23
The following problems are for your practice and do not need to be turned in.
Sec.18 Exercises: 2, 3, 5, 7 (this is a good problem); Sec.19 Exercises:
6, 7, 8; Sec.20 Exercises: 6, 7
Due Wednesday, Sept. 23
Reading Assignment: Sec. 18-21
To Be Handed In: Exam 1
Due Friday, Sept. 11
Reading Assignment: Sec. 17
To Be Handed In: Homework 3
Due Friday, Sept. 4
Reading Assignment: Sec. 14--16
To Be Handed In: Homework 2
Due Friday, Aug. 28
Reading Assignment: Chapter 1 (most of this should be review) and Sec.
12--13
To Be Handed In: Homework 1
Exam Dates:
Exam 1 -- Due Wednesday, Sept. 23 at the beginning of class
Exam 2 -- Due Wednesday, Oct. 28 at the beginning of class
Final Exam -- Due Wednesday, Dec. 9 at Noon
Miscellaneous Resources
- It will be important for you to read your textbook in this course.
If you are unfamiliar with reading mathematics textbooks, here is a
collection of Tips for Reading Your
Mathematics Textbook that I have written.
- Here are some links to sites about point-set topology.
- The history of mathematics is an important subject. It gives a
context
in which to view the results that one learns in math classes.
Furthermore it shows that mathematics is, first and
foremost, a human activity. By looking at the historical development of
many areas of mathematics we see that it took a long time for many of its
ideas to be
rigorized. Like many areas of human understanding, the development of
mathematics was not a
careful march down a well-cleared highway, but rather a journey into a
strange wilderness, where the explorers often got lost and many wrong
turns were taken. If you find yourself struggling to understand the
concepts introduced in this course, then you are in good company. Many
of the greatest minds in mathematics struggled with these same concepts
over a period of thousands of years.
MacTutor
History of Mathematics Archive.
In particular, you can read about the
History
of Topology.