Homework Assignments

Math 252

Professor Sands


 If you have questions, you can contact me using email: sands@math.uvm.edu
Problems in parantheses are required for graduate students and optional for undergraduates. However, they are still recommended reading as preparation for later sections.

#      Due                      Homework                                        Topic
 
  1  Jan. 26
 
7.4 #8,10,(12,15)
7.6 # (5a)
Properties of Ideals 
The Chinese Remainder Theorem
 2 Feb.  2 8.1 #1a,2a,3, (8,one value for each part), 10, (11)
8.2 #1,(2),3
Euclidean Domains
Principal Ideal Domains
 3 Feb. 9 8.3  #5 with n odd,(6c)
9.1 #2,5,6,(7)
9.2 #1,2,5,(7),8
Unique Factorization Domains
Basics of polynomial rings R[x]
F[x]
 4 (Holiday Feb. 16)
Feb. 18
9.3 # (1), 2, 3, (4)
9.4 # 1,2, (3), first half of 5, 11, (19d), 20
Factorization in Polynomial Rings
Irreducibility Criteria
 5 (Take-home test due 2/23)
Mar. 2
10.1 #1,2,5,(6),7,8a,(9,10),11,19
10.2 # (2),3,8,(12)
Basics of Modules
Quotients and Homomorphisms
 6  (Break Mar. 9-13)
Mar. 18
10.3 # (2),4,6,(7)
12.1 # 6
Free Modules
Modules over PIDs
 7 Mar. 23 11.1  # 8, (9)
11.2  # 8 
See handout for other homework problems
11.4 # 5
Vector Space Basics
Matrices
Linear Transformations
Determinants
 8 (Take-home test due 3/ 30)
April 6

12.2 # (9), (10)
12.3 # (6), (21)
13.1 #1,4, (6)
Rational Canonical Form
Jordan Canonical Form
Field Extensions
 9 April 13
13.2 #1,2,(4),5,(9),10,(11),12,13,16
Algebraic Extensions
 10 April 20
13.3 # 4, 5
13.4 # 1
13.5 # 1, (6)
13.6 # 2, 10, (11)
Constructibility
Splitting Fields
Separability
Cyclotomic and Finite Fields
 11 April 27
13.2 # (18)  14.1 # 4,(6),7,(8)
14.2 # 1,4
Elements of Galois Theory
Galois Groups
 12 May 4 (In my mailbox)

14.2 # 3,5,6,15,(17)

Fundamental Theorem of Galois Theory