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

Office hours : W, F 2-2:50pm in DRL 4E2B.
Office Phone: 215-573-9093

Lecture: MWF 3-4pm in DRL 4C6

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, copies of which will be passed out the first day of class. A companion text is "Algebra", 2nd edition, by Michael Artin, which is on reserve in the math/physics library, 3rd floor DRL.

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 40%. HW and presentations count 10%. Hour exam 1 will be on Wednesday, Oct. 12 from 3-3:50pm in DRL 4C6, and Hour exam 2 will be on Wednesday, Nov. 16, also from 3-3:50pm in DRL 4C6. The final exam may be a take-home exam.

Midterm 1: Covers material from Lectures 2 through 9 in "Algebra and Applications" lecture notes by R. Calderbank, except pages 10-12 from Lecture 4, and pages 2-7, 9-12 from Lecture 6, page 13 from lecture 8, and pages 7-14 of lecture 9. Also includes discussion of the RSA cryptosystem handout.

Midterm 2: Covers material from Lecture 11 through page 7 of Lecture 16 in "Algebra and Applications" lecture notes by R. Calderbank, except 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.

Important Dates:
Hour Exam 1: Oct. 12, 3-3:50pm in DRL 4C6
Fall Break: Oct. 8-11 (No Class on Oct. 10)
Hour Exam 2: Nov. 16, 3-3:50pm in DRL 4C6
Thanksgiving Break : noon, Wednesday, Nov. 23 - Sun. Nov. 27
Last Day of Classes: Friday, Dec. 9.
Final Exam: Take home exam.

Homework Assignments:

HW1, due Monday 9/26: Problem set "Group Theory and Finite Lattices", problems 1-5.

HW2, due Wednesday, Oct. 19: Problem set "Finite Groups acting as permutations of sets", problems 1, 3, 4, 5, 6, 9. Also, prove Proposition 9.4 in Lecture 9 of Calderbank, possibly by filling in the details of his argument, or by writing a computer program and using alanytic geometry as in class. If you do this, turn in the computer program and the output.

HW3, due Monday, Nov. 14: Problem set "Euclidean Domains, Finite Fields, and Algebraic Error Correcting Codes", problems 1, 2, 3, 4, 5.