Syllabus

The following is a tentative syllabus for the course. Practice exercises are from the text and are not to be graded. It is good to choose a few practice problems from each set to check your understanding.

Week Lectures Sections in Text Brief Description Practice Exercises
1 9/16 Ch 1, 2 Introduction, Operations Chapter 2: A, B
9/18 Ch 3, 4 Groups Chapter 3: A, B, D
Chapter 4: C, D
9/19 (x-hour) Proof techniques (Practice) (Solutions)
9/20 Ch 5 Subgroups Chapter 5: A.1,4,6, B.1-3, C.1,4, E
2 9/23 Ch 6, 7 Functions, permutations Chapter 6: B.1-3, D.2, E.3,5
Chapter 7: B, D, F.2
9/25 Ch 7, 8 Permutations of a finite set Chapter 8: A.5,6, B.4,5, C.1, D.1-3
9/27 Ch 9 Isomorphisms Chapter 9: B.3, E.2,6
3 9/30 Ch 9,10 More on isomorphisms, order of group elements Chapter 10: B, C, F
10/2 Ch 11 Cyclic groups Chapter 11: A, B, E
10/3 (x-hour) Problem session (Practice) (Solutions)
10/4 No class today.
4 10/7 Ch 12 Partitions and equivalence relations Chapter 12: A.1-2, B.1-4, C.1-6
10/9 Exam 1 in-class portion Material through Ch 11. Take-home portion due 10/11.
10/11 Ch 13 Cosets and Lagrange's Theorem Chapter 13: A.1-2, B.3-5, C.4, E.1-3
5 10/14 Ch 14 Homomorphisms and normal subgroups Chapter 14: A.2,4, B.6, C.1-3, D.1-4
10/16 Ch 15 Quotient groups Chapter 15: A.1,5,6, B.1-3, C.1
10/18 Ch 16 Fundamental homomorphism theorem Chapter 16: A.1,4,5, C.1-3
6 10/21 Ch 16 More on FHT
10/23 Ch 17 Rings Chapter 17: A.1-7, C.1-3, H.1-3, I.1-4
10/24 (x-hour) Problem session (Practice) (Solutions)
10/25 Ch 18 Ideals and homomorphisms Chapter 18: A.3,6, B.1-4, C.1,3,4, E.1,3,4, G.5
7 10/28 Ch 19 Quotient rings B.1,3,4, C.1,2, E.2,6, F.1-4
10/30 Exam 2 in-class portion Material through Ch 18. Take-home portion due 11/1.
11/1 Ch 20 Integral domains Chapter 20: A.1,3,5, B.1, C.1, E.7
8 11/4 Ch 20 Finite fields Chapter 20: D.1-7, F.1-3
11/6 Ch 24 Polynomial rings Chaper 24: A.1,2,5, B.4, C.2,3
11/7 (x-hour) Special topic: elliptic curves Note: Not covered on the final exam.
11/8 Ch 25 Factoring polynomials Chapter 25: A.3, B.1-7, C.1
9 11/11 Ch 25 Factoring polynomials Chapter 25: D.3, F.1-4
11/13 Ch 26 Substitution in polynomials Chapter 26: A.1-4, C.1-4,7
11/15 Ch 26 Eisenstein's irreducibility criterian Chapter 26: B.1,5, E.1-4
10 11/18 Wrap-up Final Exam Study Guide