Math 113, Fall 2015
Information for students
- DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.
Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities.
In particular, you must speak to the instructor before the end of the second week of classes.
- GSI Office hours
Shelly Manber is the GSI for 113. She has office hours (open to everyone) during the following times. Her office is 1043 Evans.
Monday 2-4 pm
Tuesday 2-4 pm
Wednesday 10 am-noon
Thursday 1:30-3:30 pm
Friday 2-4 pm
You are of course welcome to use my office hours as well, they are listed on the syllabus.
- Academic honesty in mathematics courses. A statement on cheating and plagiarism, courtesy of M. Hutchings.
- Policy on absences for tests and midterms.
- How to get an A in this class
TextbookThese are the authors of your textbook! (image from R. Foote's webpage)
Solutions to problems from the textbook:A google search will turn up many sets of solutions to problems from Dummit and Foote's book. It is to your benefit to use these only as a means of checking your answers. Homework is worth very little of your grade -- in order to do well, you need to use homework exercises as an opportunity to learn rather than copy. If you do want solutions to check your work, this solutions blog is very nicely organized. The few answers that I checked were correct and well done. I cannot vouch for the accuracy or coherency of all solutions; use at your own risk.
Supplementary readingHere are two general references that I recommend, if you're looking for something more like a novel and less like an encyclopedia.
1. (Only on groups) "Groups and Symmetry" by M. Armstrong.
2. "A Book of Abstract Algebra" by C. Pinter.
Also of interestNot directly related to our course, but you may enjoy doing an independent study through the Directed Reading Program .
Abstract algebra in the outside world:1. Braids and Knots and...DNA? Here's an expository paper (written by an undergraduate student I supervised in an REU) that proves that every knot can be made by joining the ends of a braid, as we talked about in class: Knots and Braids
Aside from being an interesting field of math, knot theory has a surprising new application: the knottedness of DNA
2. The Verhoeff check digit algorithm
Here's a nice description of the check digit problem, and Verhoeff's algorithm using D_8 and permutations.
Wikipedia has good entries on check digits and the more general checksum or "hash" that I mentioned in class.
3. The classification of finite simple groups
An accesible article on the classification of finite simple groups
Problem setsProblem sets will be posted here.
- Problem set 0 due Tuesday, September 1
- Problem set 1 due Tuesday, September 8.
- Problem set 2 due Tuesday, September 15.
( .tex file )
- Problem set 3 due Tuesday, September 22.
( .tex file )
- Problem set 4 due Tuesday, September 29.
( .tex file )
- Vocabulary to review for test 1 Not to hand in.
- Solutions to test 1
- Problem set 5 due Tuesday, October 6.
( .tex file )
- Review probelms for the midterm
(No homework is due Oct. 13, the day of the midterm)
- Possibly helpful: Notes on Sylow's theorem by former 113 instructor S. Ma'u
- Problem set 6 due Tuesday, October 20.
- Solutions to the midterm
note: either b or d was an acceptable answer to multiple choice I., depending on whether you interpreted |gN| to be the number of elements in the coset, or the order of it in the group G/N.
- Problem set 7 due Tuesday, October 27.
- Problem set 8 due Tuesday, November 3.
- Problem set 9 due Tuesday, November 10.
- no homework due Nov. 17 (you have a test).
Instead, here is a Review for test 2
Solutions to test 2
- Problem set 10 due Tuesday, November 24.
- Problem set 11 due Thursday, December 3.
- Review for the final exam
- Practice final exam
Here is some supplemental reading on the Field of Fractions of an integral domain. DF chapter 7.5 does a more general version of this than what I did in class or what I expect you to know. This reading does almost exactly what I did (you can ignore the part called Theorem 31.1, other than that it's exactly at the right level) and gives all the details. This reading is optional, and of course you don't need to do the problems at the end, but I recommend it.
And just for fun...