Course Description:
This is the second course in the basic algebra sequence. This sequence
covers groups, subgroups, and permutation groups; rings and ideals; some
work on fields; vector spaces, linear transformations and matrices, and
modules; and canonical forms of matrices, quadratic forms, and
multilinear algebra.
Required text:
A First Course in Abstract Algebra, Fraleigh
Abstract Linear Algebra, Curtis
Homework:
There will be weekly homework assignments. You are encouraged to
work together but all students must independently write up their
solutions. All homeworks
are due at the beginning of class unless otherwise noted.
Homework 1 Due Wednesday Jan. 17th, From Fraleigh: Section 26:
17,22,30,34,35(Give a solution different from that in the back of the
book) Section 27: 4,30,33 Section 29: 12,16,30. Homework 2 Due Monday Jan. 22nd, From Fraleigh: Section 29: 33 Section
30: 4,24,27 Section 45: 10 Homework 3 Due Monday Jan. 29th, From Fraleigh: Section 29: 14
Section 30: 10, Section 46: 4,18 Section 45: 8,31 Reminder: Midterm is next Monday Jan. 29th in class Homework 4 Due Wednesday Feb. 7th, From Curtis: Page 20: 3, 5 Page 27: 6 Page 55: 3, 4 Homework 5 Due Monday Feb. 19th, From Curtis: Read pages 66 and
67. Page 61: 1, Page 65: 2,3, Page 69: 6,7 Homework 6 Due Monday Feb. 26th, From Curtis: Page 69: 3,8 Page 86: 8 -
There is a typo in this problem. The image of e_3 = e_1 - 2e_2 + 4e_3,
Additional problems: (1) Prove that the characteristic polynomial is in fact a
monic polynomial. (2) Prove that the dimension of the kernel of a linear map A is
equal to the number of rows of zeros in R, where R is the reduced echlon form of
A. Homework 7 Due Monday March 5th, From Curtis: Page 93: 9, Page 106:
2(i,ii,iii) 4,9. Final Exam: Friday, March 16, 10:30-12:30.
It is the policy of the Department of Mathematics that the following
rules apply to final exams in all
undergraduate mathematics courses:
1. The final exam must occur at the time and place designated on the
College Final Exam Schedule. In
particular, no final examinations may be given during the tenth week of
the quarter, except in the case
of graduating seniors.
2. Any student who wishes to depart from the scheduled final exam time
for the course must receive
permission from Paul Sally (office is Ry 250, phone is 2-7388, email is
sally@math.uchicago.edu). Instructors
are not permitted to excuse students from the scheduled time of the
final exam except in the
cases of an Incomplete.