Math 113, Fall 2014

Information for students

  • Syllabus for section 4 (9:30 am class)

  • Syllabus for section 5 (12:30 pm class)

  • 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
    Jason Ferguson is the GSI for 113. He has office hours (open to everyone) during the following times. His office is 1061 Evans.
    Monday 8:30-9:30, 4:45-6:15
    Tuesday 8:30-9:30, 4-5 note new time (again!)
    Wednesday 8:30-9:30, 4:45-6:15
    Thursday 8:30-9:30, 6-7
    Friday 8:30-9:30
    All times are Berkeley time; especially the MW 4:30-6 slots.

    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

Textbook

These 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 reading

Here 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.

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.

Review and solutions for tests and exams

  • Review for test 1

  • Solutions to test 1: *Version 1* *Version 2*
    Blank tests for extra practice: *Version 1* *Version 2*

    Statistics: The average (taken over all students who got at least a passing grade of 50%) for section 4 was 18.9/25, and for section 5 was 19.6/25.
    If you got a grade of 50% (12.5) or below, this indicates that you will have trouble with the rest of the course, and my recommendation is that you drop the class.

  • Review for the midterm

  • Notes on Sylow's theorem, by former 113 instructor S. Ma'u

  • Solutions to the midterm: *Version 1* *Version 2*

  • Review for test 2

  • Solutions to test 2: *Version 1* *Version 2*

  • Lecture notes from Thursday, November 20

  • Review for the final exam


  • More practice questions for the final exam

Problem sets

  • Problem set 0 due Tuesday, September 2

  • Problem set 1 due Tuesday, September 9. ( .tex file ) ( partial solutions )

  • Problem set 2 due Tuesday, September 16. ( .tex file ) ( partial solutions )

  • Problem set 3 due Tuesday, September 23. ( .tex file ) ( partial solutions )
    (here is the Super short homework handed out in class, due Thursday the 18th)

  • Problem set 4 due Tuesday, September 30. ( .tex file ) ( partial solutions )
    note -- there was a problem with question 3! see the solutions for a remark.

  • Problem set 5 due Tuesday, October 7. ( .tex file ) ( partial solutions )
    Alternative solution to 3.2.11 Many students tried to use a different strategy than the one I proposed. Here's how to do this correctly, written up by our grader.

    ** No problem set due October 14 (you have a midterm!) **

  • Problem set 6 due Tuesday, October 21. ( .tex file ) ( partial solutions )

  • Problem set 7 due Tuesday, October 28. ( .tex file ) ( partial solutions )

    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. This reading does 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. Reading this is optional, and of course you don't need to do the problems at the end, but I highly recommend reading it.

  • Problem set 8 due Tuesday, November 4. ( .tex file ) ( partial solutions )

  • Problem set 9 due Thursday, November 13. ( .tex file ) ( partial solutions )
    JUST FOR FUN: An example of a PID that is not a Euclidean domain. The example is a familiar object, but even the easiest proofs that this ring is a PID are somewhat difficult. DF gives a proof on page 282, but it's missing some details. Here are notes by C. Wong that give some more details (but are still a challenge).

    ** No problem set due November 18 **

  • Problem set 10 due Tuesday, November 25. ( .tex file ) ( partial solutions )

  • Problem set 11 due Tuesday, December 2 Thursday, December 4. ( .tex file ) ( partial solutions )