MATH 338: Homework Assignments

Turn in your homework assignment to me (in class or my office) before 5:00 PM on the due date.

  • To receive full credit, homework sets must be handed in to me on time (either in class or my office.) Although it is not required, students should consider typesetting their homework using LaTeX. Turn in as much of the homework as you can by this deadline to receive partial credit. If you have a legitimate conflict you must tell me ahead of time.
  • You will work with a "homework partner" throughout the semester, and the two of you will turn in only one final version of each assignment. You are encouraged to work with other students on the assignments as much as possible, but each student pair must write up the answers in their own words. Each individual student is STRONGLY ENCOURAGED to think about and attempt the problems on their own before meeting with their partner. When you are about to tackle the homework assignment, you should use this strategy:
    THINK, PAIR, SHARE.
    • You are expected to be working on the homework assignments throughout the week.
    DO NOT WAIT UNTIL THE DAY BEFORE IT IS DUE TO START THE ASSIGNMENT!
  • In addition to learning wonderful mathematics this semester, we will also be working on three academic fundamentals that are vital to success in your education and in your career: Reading, writing, and communication.
    1. Reading the textbook is extremely important. It is required, NOT optional. I certainly won't be able to cover in class all the material you will be required to learn. As a result, you will be expected to do a lot of reading. The reading assignments will be on topics to be discussed in the following lecture to enable you to ask focused questions in the class and to better understand the material. Your chances of getting a good grade in this course are infinitesimally small unless you read the textbook in addition to attending lectures.
    2. Writing quality proofs is essential. You are expected to be able to effectively present mathematics with a well-organized, thoughtful, neatly written argument. What is a "quality proof"?
    3. Communication with your peers will be a focal point. In addition to working in pairs on your homework assignments, there will also be regular presentations given in class. Students will be asked to present their solutions to homework problems to the rest of the class. The best way to truly understand a concept is to be able to explain it to someone else. Talking about math is just as important as thinking and writing math. Our goal is to become more comfortable with the necessary communication.
UPDATED: Wednesday, November 28, 2012 at 12:47
Set Homework Problems Reading Assignment Due Date
0
None
Chapter 0
Friday, August 31
1
 Sec. 1.1: 1, 2, 3, 5, 6, 7, 9
Sections 1.1-1.3
Thursday, September 6
2
 Sec. 1.2: 10, 11, 12, 16, 17, 19
Sec. 1.3: 25, 27, 28, 33, 34, 36
Extra Problem/Note: I think the first part of #34 is a mistake. I.e. I'm certain that the only Hausdorff topology on any finite set is the discrete topology. Prove this for the five-point set.
Hints: (1) For 1.16 we showed T ' is contained in T in class.
(2) Don't make 1.17 too difficult. If p is a point on the line Ax+By=C and x is any point in R2, you may want to simply write that the distance between x and p is d(x,p).
(3) You may find DeMorgan's Laws useful. See page 13 of the textbook.
Sections 1.4, 2.1-2.2
Thursday, September 13
3
 Sec. 2.1: 1, 2, 6, 10, 11, 12
Sec. 2.2: 13, 17, 18, 20, 21
(For #1 and #13, just state the answers. No proof necessary.)
(Read #23. You don't have to do it, but it is a very good example of a limit point without a sequence that converges to it.)
Sections 2.3, 2.4
Friday, September 21
4
 Sec. 2.3: 24, 26, 28(Thm. 2.6 may help)
(For #24 and #26, just state the answers. No proof necessary.)
Sections 3.1
Thursday, September 27
Exam
 Exam 1 is on Thursday, Sept. 27: The exam will cover all of Sections 1.1-1.3 and 2.1-2.3 of the textbook. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know ALL of the relevant definitions and theorems.
Chapters 1 and 2
Thursday, September 27
Exam
Corrections
If you scored below an 80 on the midterm exam, you are REQUIRED to write up test corrections.
  1. All of you are allowed to do exam corrections, but you are only required to if you scored below an 80. These corrections will add points back to your exam, one half of the points taken off.
  2. You need to make corrections for all of the mistakes you made on the exam. Please provide the correct solution to EVERY problem that you did not get completely correct.
  3. In addition to giving the correct solution, you must GIVE AN EXPLANATION for why your original solution is incorrect.
  4. The exam corrections must be submitted to me orally. Make an appointment or come by my office hours by Friday, October 12. (It is best if you do this AS SOON AS POSSIBLE, while the exam is still fresh in your mind. And I do NOT want everyone coming on the last day.)
DUE by
Friday, October 12
5
 Sec. 3.1: 2, 4, 5, 6, 7, 9, 10
(For #2, 4, 5 and 6, just state the answers. No proof necessary.)
(You may find homework problem 1.3 (Chapter 1) useful.)
Sections 3.2
Friday, October 5
6
 Sec. 3.2: 12, 16, 17, 18, 19, 21
Sections 3.3
Friday, October 12
7
 Sec. 3.3: 23, 25, 28, 30, 33
Sec. 3.4: 35, 37
(For one of the problems, I claim that this umbrella might be helpful.)
(Read but do not do #38 and #39. They are good problems to immerse your mind in...)
(For #35, remember that all 8 corners of the octagon are identified as a single point. Put this point on T#T and go from there.)
(Read #26. You may find it interesting. You can also go here to download a version of torus and klein bottle games for hours of distracting fun!)
Sections 3.4, 3.5, 4.1
Friday, October 19
8
 Sec. 4.1: 2, 4, 6(a), 7, 8, 14
(Read but do not do #13 and #16. These construct more continuous functions from known continuous functions.)
Sections 4.2, 4.3
Friday, October 26
9
 Sec. 4.2: 23, 25, 26, 29, 32, 33
(For #33, you may find Exercise 4.6 helpful.)
(Read but do not do #28 and #36.)
NOTE: Although we are skipping Ch. 5 on Metric Spaces, it is a very nice topic, and I encourage you to read it, especially if you are considering graduate school in mathematics.
Sections 6.1
Thursday, November 1
Exam
 Exam 2 is on Tuesday, November 6: The exam will cover all of Sections 3.1-3.4 and 4.1-4.2 of the textbook. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know ALL of the relevant definitions and theorems.
Chapters 3 and 4
Tuesday, November 6
Exam
Corrections
If you scored below an 80 on the midterm exam, you are REQUIRED to write up test corrections.
  1. All of you are allowed to do exam corrections, but you are only required to if you scored below an 80. These corrections will add points back to your exam, one half of the points taken off.
  2. You need to make corrections for all of the mistakes you made on the exam. Please provide the correct solution to EVERY problem that you did not get completely correct.
  3. In addition to giving the correct solution, you must GIVE AN EXPLANATION for why your original solution is incorrect.
  4. The exam corrections must be submitted to me orally. Make an appointment or come by my office hours by Friday, November 30. (It is best if you do this AS SOON AS POSSIBLE, while the exam is still fresh in your mind.)
DUE by
Friday, November 30
10
 Sec. 6.1: 1, 2, 3, 5, 7
Sec. 6.2: 18, 20(not c), 23, 26, 27, 29
(For #18, you may just draw pictures. For #20f, it may be both useful and fun to make a Mobius band out of paper and cut it as indicated.)
(See if you can do #22 as well, but you don't have to turn it in.)
Sections 6.2, 6.3, 6.4
Thursday,
November 15
Break
Thanksgiving Break: No classes, November 21-23.
STUDY ALL WEEK...
...Yeah right!
Have a great and safe break!
11
 Sec. 6.4: 39, 41, 42, 45, 46, 49
The exam is a "nonstandard" exam. Click here for more details.
Have your topic pre-approved by Friday, November 30.
Sections 6.5, 7.1-7.5
Thursday,
November 29
SOFI's
Student Opinion of Faculty Instruction
Please take the time to complete the SOFI for this course.
Log into KnightWeb to complete your SOFIs
Surveys must be completed by Tuesday, December 11
12
 Sec. 7.1: 1, 3, 5, 6
Sec. 7.5: 39, 40, 41
Sections 14.1-14.3
Thursday,
December 6
Final
Exam
 The Final Exam Presentations will be on Tuesday, December 18, 12:00-3:00 pm, in class (Sturges 208A). Click here for more details.
Chapters 1-14
Tuesday,
December 18