Math 306, Spring 2012
First Midterm Exam
Name:
Student ID:
Directions: Check that your test has 9 pages, including this one and the blank one on the bottom
(which you can use as scratch paper or to co
Math 306, Spring 2012
Final Exam Solutions
Name:
Student ID:
Directions: Check that your test has 12 pages, including this one and the blank one on the bottom
(which you can use as scratch paper or to
Math 306, Spring 2012
Homework 4, due Friday, February 24
(1) Find the minimal polynomials over the smaller eld of the following elements in the given extensions.
(a) in C : Q
3i
(b) 18 in R : Q
(c) e
Math 306, Spring 2012
Homework 5, due Friday, March 2
(1) (a) (3 pts) Find a linearly dependent set of three vectors in R3 , but such that any set of two of them is linearly
independent.
(b) (5 pts) L
Math 306, Spring 2012
Homework 3, due Friday, February 17
(1) Each of the following statements is false. Disprove each of them by providing a counterexample or by appealing
to the denitions.
(a) If K
Math 306, Spring 2012
Final Exam
Name:
Student ID:
Directions: Check that your test has 11 pages, including this one and the blank one on the bottom
(which you can use as scratch paper or to continue
Math 306, Spring 2012
Homework 1, due Friday, February 3
(1) Each of the following statements is false. Disprove each one by providing a counterexample or by appealing to
the denition.
(a) If R is a r
Math 306, Spring 2012
Second Midterm Exam, April 12, 2012
Name:
Student ID:
Directions: Check that your test has 8 pages, including this one and the blank one on the bottom
(which you can use as scrat
Math 306, Spring 2012
First Midterm Exam Solutions
Name:
Student ID:
Directions: Check that your test has 9 pages, including this one and the blank one on the bottom
(which you can use as scratch pape
Math 306, Spring 2012
Second Midterm Exam Solutions
Name:
Student ID:
Directions: Check that your test has 8 pages, including this one and the blank one on the bottom
(which you can use as scratch pap
Math 306, Spring 2012
Homework 6, due Friday, March 16
(1) (5 pts/part)
(a) Prove that cos(2/5) = 51 . (Hint: Using the equation (cos(2/5) + i sin(2/5)5 = 1, rst show that
4
= cos(2/5) is a root of 1
Math 306, Spring 2012
Homework 2, due Friday, February 10
(1) (5 pts) Suppose that R is an integral domain that is not a eld. Prove that R[x] is not a principal ideal domain.
(Hint: Let c R be nonzero