AMCS 601, Fall 2009


Dr. Jim Haglund, jhaglund@math.upenn.edu
Course webpage: http://www.math.upenn.edu/~jhaglund/601/

Office hours : T 10-11am, F 3-4pm in DRL 4E2B.
Office Phone: 215-573-9093

Lecture: MW 10:30am-12noon in Benn 141 (Fisher-Bennett Hall at corner of 34th and Walnut)

Homework Assignments: There will be recommended HW assignments (not to be turned in) and some required HW assignments (to be turned in and graded). The assignments will be posted at the bottom of this web page. You will occassionally be required to present solutions to select homework problems before the class.

Course: Algebraic Techniques for AMCS I: We begin with an introduction to group theory. The emphasis is on groups as symmetries and transformations of space. After an introduction to abstract groups and the basic facts about finite groups, we discuss finite fields and applications to coding theory.

Text:We will be using Lecture Notes for "Algebra and Applications" by Robert Calderbank of Princeton University, copies of which will be passed out the first day of class.

Exams and Grades: There will be two hour exams and a final exam. Each hour exam counts 25% of your grade, and the final exam counts 35%. HW and presentations count 15%. Hour exam 1 will be on Wednesday, Oct. 14 from 10:30am-12noon in Benn 141, and Hour exam 2 will be on Wednesday, Nov. 18, also from 10:30am-12noon in Benn 141. The final exam may be a take-home exam.

Midterm 1: Covers material from Lectures 2 through 7 in "Algebra and Applications" lecture notes by R. Calderbank, except pages 10-12 from Lecture 4, and pages 2-5 from Lecture 6. Also includes discussion of the RSA cryptosystem handout, Mobious Inversion, and the regular representation.

Midterm 2: Covers material from Lectures 8 through 14 in "Algebra and Applications" lecture notes by R. Calderbank, except pages 8-12 from Lecture 10, and page 8 from Lecture 13. Also includes discussion of the q-binomial theorem and the number of k-dimensional subspaces of an n-dimensional vector space over a finite field with q elements.

Final: There will be a take-home final exam.

Important Dates:
Hour Exam 1: Oct. 14, 10:30am-12noon in Benn 141.
Fall Break: Oct. 17-19 (No Class on OCt. 19)
Hour Exam 2: Nov. 18, 10:30am-12noon in Benn 141
Thanksgiving Break : Thursday, Nov. 26-Sun. Nov. 29
Last Day of Classes: Thursday, Dec. 10.
Final Exam: ??.

Homework Assignments:
HW1, due Monday 9/28: Problem set "Introduction to Finite Groups", problems 1-4. (Do the challenge problem for extra credit).
HW2, due Monday 11/16: Problem set "Finite Group Rotations and the Sylow Theorems", problems 1-7. (For problem 1, you only need to do parts (a), (d). Do the challenge problem for extra credit).