Math 402 Algebra (Fall 2010)

Breaking News: Midterm I have started writing up some answers and comments on the recent midterm (Fall 2010): click here . Although I have finished grading everything but the True/False questions you will have to wait until Wednesday to get your overall scores.

Group Theory: The topic for the course is Group Theory. For most of you this will be your first course in abstract algebra. It is very different from anything you have encountered before. It will strike you as very abstract at first, and you will need to look at lots of examples and do lots of exercises to make the abstract ideas come alive and have real meaning. You need to develop some intuition otherwise it will all remain a foreign language and difficult. There is only one way to do that---work with concrete examples. It might be a smart idea to google "group theory" and read some of what is out there---there is lots, some of it of an introductory nature and it might help you. Group theory is about symmetry. All mathematics related to symmetry uses group theory extensively.

The textbook for this course is Abstract Algebra , Third Edition, by D.S. Dummit and R.M. Foote, and published by John Wiley and Sons. We will cover most of Chapters 1 through 5. Together they total 160 pages. There are 28 lecture days so we will have to cover about 6 pages a day. That's a lot, and I won't be able to say everything in class. I rely on you to read the book too. For the most part the lecture content is the course. You need to take good notes---your notes will comprise the course. There are many books in the library that provide an introduction to group theory. I advise you to consult those books. They have a lot to offer---different perspectives, different examples, different emphases.

Course Notes: Here are notes for the course. I wrote some notes about group theory a while ago. They might be of some use. Of course, Rotman is our primary text.

Important dates: There will be a midterm on Wednesday November 3. The final is 8:30-10:20 a.m. on Wednesday, December 15. You must use a blue book for exams.

Office Hours: Tuesday 3:30--4:30 and Wednesday 2:30--4:00 in Padelford C-418, and by appointment.

Grades. Your grade will be based on the homework, the midterm, and the final. Your homework scores will contribute 25%, the midterm will contribute 25%, and the final will contribute 50%.

Homework. Every ten days or two weeks I will give you a list of problems. Of those, four will be graded; each question is worth 4 points. The grader will give you a score out of 20, the 4 additional points being at her discretion will be based on how neat and tidy your homework is (stapled together, no raggedy pages), how clear your answers are, how legible your handwriting is, how efficient your solutions are, et cetera.

Homework 1: due October 11.

  • Section 1.1: 1, 2, 6, 7, 9, 11, 17, 18, 20, 21, 22, 23, 26, 27, 28, 30, 31, 32, 36.

    • Homework 2: due October 25

  • Section 1.3: 2, 3, 5, 9, 19
  • Section 1.4: 11
  • Section 1.6: 1, 2, 3, 4, 5, 6, 8, 11, 12, 15, 17

    • Homework 3: due November 12

  • Section 1.6: 18, 19, 21, 26
  • Section 2.1: 1d, 1e, 2e, 8
  • Section 2.3: 3, 13, 20
  • Section 3.1: 5, 6, 7, 8, 9

    • Homework 4: due December 8

  • Section 2.2: 7, 10,
  • Section 4.1: 1, 2, 4, 5
  • Section 4.2: 3, 4, 7, 10,

    • Practice Questions This contains some questions that I consider fair game for quizzes, midterms, and the final. If you can answer all these you are
    Practice Questions This contains some questions that I consider fair game for quizzes, midterms, and the final. If you can answer all these you are getting to grips with the material.

    An old midterm.

    How to succeed. You want a good grade and I would like to give you a good grade. I will do that if you demonstrate some degree of mastery of elementary group theory. Learning math requires much more than reading books, or re-reading the notes you take in class; that is necessary of course, but not sufficient. You learn math by solving problems, doing exercises, both those I assign, and those you find yourself in books on elementary group theory. You will not master the material in this course if you do only those homework problems that I assign. Solving problems is the only way to learn mathematics. So, do hundreds during this course. Yes, hundreds. I know your time is precious and that there are many demands on your time. But that cannot change the fact that to master 3 hours of lecture material you probably need to do at least twenty problems; not just twenty variations on the same problem, but twenty different problems. You also need to be absolutely honest with yourself, uncovering your own weaknesses and seeking help when you need to. There is no shame in struggling. I failed my first group theory course (!!) because I was afraid to say "I don't understand" and ask for help---I took a group theory course my first year at university and was 3 or 4 years younger than everyone else in the class, all of whom had already spent at least one year at university, and I just assumed they all knew much more than me and that they would think I was very thick if I asked a question! Now I know better---I was probably as smart as anyone in the class, just more afraid than others to admit I was lost. So, I hope you are better than me at asking for help. I am happy to give it. It might be helpful for you to study with others. Check each other's solutions to problems, talk about the theorems and results.