Homework Assignments

Math 251, Fall 2017, University of Vermont

Professor Sands

Homework is ordinarily due on Wednesdays at the beginning of class.
If you have questions, you can contact me using email: sands@cems.uvm.edu

Problems listed on this page are for practice and need not be handed in. The problems to be handed in are found by following the links.
Problems in parantheses are required of graduate students and optional for undergraduates, but recommended as preparation for later sections and tests.

Note: Remember to click "refresh" or "reload" on your browser to be sure you have the most recent version of this page.

HOMEWORK MUST BE:
  1. Prefaced by a signed statement that the work on the assignment is your own.
  2. Written in your own words, without any references in front of you other than the textbook and notes from class. Cite any other resources you consult, so as to give credit and allow the reader to locate the exact source.  Use of solutions written by others is not allowed, and is a violation of academic integrity.  
  3. Legible, complete and concise. (Typeset is ideal!)
  4. Written in complete grammatical English sentences. 
  5. Explained fully and logically with reasoning behind each step. When using a theorem or proposition, say so explicitly.  Show all work required to arrive at your answer.
  6. Self-contained: explain the use of any symbols or terms not introduced in class.  Prove any results you use that have not been established in class. 

#      Due Date           Homework Assignment                            Topic
Follow the links for problems to be handed in. Problems listed below are for practice.
 1 Sept. 6First  Problem Set: Follow this link.
 Solutions
 0.1 Basics
 0.2 Properties of the Integers
 2   Sept. 13 0.3 #  3, (5), 6, 7, (8), (12)     HW2 link
1.1 #   1abc, 2abc, 4, 6abc      Solutions
0.3 #15a, 15b,
Z/nZ, modular arithmetic 
Intro. to groups
Inverse of an element
 3  Sept. 20 1.1 # 13, 14, 16, 19, 22, 24, 35  HW3 link
 1.2 #1, (4,5), 9, (13)                   Solutions
1.3 # 1, 4, 5, (10), 19, (20)
Order of an element 
Dihedral Groups
Permutations and Symmetric Groups
 4  Sept. 27 1.4 #  2, 3, 10, (11abc)       HW4 link
1.5 #  1                                Solutions
1.6 # 1, 2, 3, 8, 9, 10, 17 (19)
Matrix Groups 
Quaternions
  Homomorphisms 
Test Oct. 4 Chapters 0-1     Practice             Hints
 5
 Oct. 11
2.1 # 3, (4), (6), 8, 10, 12   HW 5 Link  Solutions
2.3 #  2, 3, 10, 11, (12), 16, (20), (21), (26) 
Subgroups
Cyclic Groups
 6  Oct. 18 2.5 #  2, 9, (12)     HW 6 Link
3.2 #  2, (4), 5, 8, (11), 22 Solutions
Lattice of Subgroups
Cosets and Lagrange's Thm.
 7  Oct. 253.1 #  1, 3, 4, 5, 6, 7, 11, (14), 20, 22a, (32), 42
 3.3 #   2 (choose 3 parts), 3  HW 7 Link
3.4 #  1                         Solutions
Quotient Groups
Isomorphism Theorems 
Simple Groups
Test Nov. 1 Chapters 2-3   Practice    Hints
     Test Solutions
 8  
 
Nov. 8
3.5 #   2, (3), (4), 7, 9, (17)   HW 8 Link
4.1 #   1, 4                             Solutions
4.2 #   3, (11)
4.3 #   2c, (5) , 8, 11b, 11c, (20)  
Alternating Group
Group Actions 
Cayley's Theorem
Class Equation  
 9
  Nov. 15
4.5 #  6, (18), 13, (22), (32)   HW 9
5.1 #  1 (for n=2) , 5, 14 (for n=2)
5.4 #  (10), 13              Solutions
Sylow Theorems
Direct Products (External)
Direct Products  (Internal)
Break week of Nov. 22
  Test Nov. 29
 Chapters 4-5     Practice Problems     Hints
                      Test solutions
 10  Dec. 6  5.2 #  1a                 HW 10 Link
7.1 #  5abef, 6abce    Solutions
7.3 #  6, 7, 10
Finite Abelian Groups
Rings 
Homomorphisms and Quotients
 FINAL EXAM
 Dec. 11