Math 502
Problem Set #10
Due week of Nov. 15, 2010, in lab.
Read Artin, Chapter 4, sections 6-7.
1. From Artin, Chapter 4, do these problems (pages 125-131):
6.4, 6.5, 6.8, 7.2, 7.4(a).
2. Let T : V V be a linear operator on a nite dimensional vector spac
Math 502
Sample Exam #1
October 2010
This exam consists of ten problems. Do them all, showing your work and explaining your
assertions. Give yourself 80 minutes.
1. Consider the system of equations
x 2y z = 5
x + 3y + 2z = 1
2x + y + z = c,
where c R. For
Math 502
Problem Set #9
Due week of Nov. 8, 2010, in lab.
Read Artin, Chapter 4, sections 3-5.
1. From Artin, Chapter 4, do these problems (pages 125-131):
3.1, 4.1, 4.3, 4.4, 5.1(a,c), 5.7. (In 4.1, prove in particular that V () is a subspace.)
2. Let T
Math 502
Problem Set #8
Due week of Nov. 1, 2010, in lab.
Read Artin, Chapter 4, sections 1-2.
1. Let V be the real vector space of polynomials f (x) of degree at most 3. Dene T : V V
1x
by T (f ) =
f (t) dt.
x0
a) Show that T is a linear transformation.
Math 502
Problem Set #7
Due week of Oct. 25, 2010, in lab.
Reminder: The rst exam will take place in class on Wednesday, October 27. It will cover
material up through section 3.5 of Artin. A sample exam is available on the Math 502 web
page.
Read Artin, C
Math 502
Problem Set #6
Due week of Oct. 18, 2010, in lab.
Reminder: The rst exam will take place in class on Wednesday, October 27.
Read Artin, Chapter 3, sections 1-3.
1. From Artin, Chapter 2, do these problems (pages 69-77):
9.2, 9.6, 9.7, 10.4, 11.4,
Math 502
Problem Set #5
Due week of Oct. 11, 2010, in lab.
Note: Fall break is Oct. 11-12. If you have a Tuesday lab, you may hand in this assignment
to your TA by Thursday.
Read Artin, Chapter 2, sections 8-12.
1. From Artin, Chapter 2, do these problems
Math 502
Problem Set #4
Due week of Oct. 4, 2010, in lab.
Read Artin, Chapter 2, sections 6-7.
1. From Artin, Chapter 2, do these problems (pages 69-77):
3.1, 3.2, 4.5, 5.1, 5.2, 5.4, 6.2, 6.3, 7.1.
2. Determine whether the following maps between groups a
Math 502
Problem Set #3
Due week of Sept. 27, 2010, in lab.
Read Artin, Chapter 2, sections 1-5.
1. From Artin, Chapter 2, do these problems (pages 69-77):
2.4, 2.6, 4.2, 4.3, 4.6.
2. For each permutation p of cfw_1, . . . , n, let Mp denote the associate
Math 502
Problem Set #2
Due week of Sept. 20, 2010, in lab.
Read Artin, Chapter 1, sections 4-6.
1. From Artin, Chapter 1, do these problems (pages 31-34):
1.6, 1.13, 2.6, 3.1, 4.4, 5.3, 6.2. In 1.13, also give an example of a non-zero nilpotent matrix
A,
Math 502
Problem Set #1
Due week of Sept. 13, 2010, in lab.
Read Artin, Chapter 1, sections 1-3.
For each of the following sets, determine whether it is a group, a ring, a eld, or a vector
space. (Some may be more than one.) Say under what operation(s) it
Math 502
Problem Set #13
Due the week of Dec. 6, 2010, in Tues. lab or in class.
Reminders: There will be an exam in class on Wed., Dec. 8. It will focus on material
beginning with section 3.5 of Artin, up through Chapter 8. The labs on Tues., Dec. 7 will
Math 502
Problem Set #12
Due week of Nov. 29, 2010, in lab.
Read Artin, Chapter 6, sections 9-11; and Chapter 7, sections 1-3 and 6-7.
1. From Artin, Chapter 7, do these problems (pages 221-228): 1.2, 2.2, 6.1, 7.2.
2. Dene the complex upper half plane H
Math 502
Problem Set #11
Due week of Nov. 22, 2010, in lab.
Note: Thanksgiving break is Nov. 25-26. If you have a Thursday lab, you may hand in
this assignment to your TA by Wednesday.
Read Artin, Chapter 5, sect. 1-4. Also read Chapter 6, sect. 1,7,8 (op
Math 502
Sample Exam #2
December 2010
This exam consists of ten problems. Do them all, showing your work and explaining your
assertions. Give yourself 80 minutes.
1. Let T : R2 R2 be the linear transformation such that T (x, y ) = (x + 3y, x y ).
a) Find