Department of Mathematical Sciences, Northern Illinois University

MATH 420/520, Summer 2009

12:30-1:45, M T W Th, Davis Hall 116

INSTRUCTOR: Professor John Beachy, Watson 355, 753-6753, email: beachy@math.niu.edu

OFFICE HOURS: Mon - Wed 2:00-3:00, Thu 11:00-12:00, or by appointment.

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Exam 4     |     Exam 4 solutions



COURSE DESCRIPTION: Algebra I (3). Introduction to group theory. Properties of the integers, functions, and equivalence relations. A concrete approach to cyclic groups and permutation groups; isomorphisms and the theorems of Lagrange and Cayley.

TEXT: Abstract Algebra, 3rd Ed, by John Beachy and William Blair

        Study Guide for the 3rd edition (in pdf format)     |     OnLine Study Guide for the 2nd edition

SYLLABUS: Chapter One, Integers; Chapter Two, Functions; Chapter Three, Groups   |   Printed version

COURSE OBJECTIVES: The student is expected to acquire an understanding of the elementary theory of groups, together with the necessary number theoretic prerequisites. There will be some discussion of the computational aspects of these topics, but the main thrust of the course will be theoretical. The student will be expected not only to follow the proofs presented in class and in the text, but also to learn to construct new proofs. Proofs must be logically correct and care must be taken to write them precisely and in grammatically correct English.

COURSE PREREQUISITE: MATH 240, Linear Algebra. We will use matrices in some important examples, but the main reason for the requirement is to attempt to guarantee a certain level of "mathematical maturity."

GRADING: Final grades will be based on 500 points: 4 hour tests (400) and homework (100).
The homework problems are extremely important. In many ways the course is like an English composition course, since it requires you to write out very carefully the reasons for each step in your solutions of problems.

ASSIGNMENTS:

Assignment 1:  1.1, due 6/17, Wednesday, 5:00 pm    
Assignment 2:  1.2, due 6/22, Monday, 5:00 pm    Solutions
Assignment 3:  1.3, due 6/24, Wednesday, 5:00 pm
Assignment 4:  1.4, due 6/25, Thursday, in class     
  EXAM 1:      1.1-1.4, 6/29, Monday
Assignment 5:  2.1, due 7/06, Monday, 5:00 pm
Assignment 6:  2.2, due 7/08, Wednesday, 5:00 pm
Assignment 7:  2.3 #3,6,11-14; due 7/13, Monday, in class
  EXAM 2:      2.1-2.3, 7/14, Tuesday
Assignment 8:  3.1 #10,11,13,17,23,37,48;  
Assignment 9:  3.2 #8,9,19,21,22,24 
               Both due 7/20, Monday, 5:00 pm
Assignment 10: 3.3 #1,4,5,11,13; due 7/24, Thursday, in class
  EXAM 3:      3.1-3.3, 7/27, Monday
Assignment 11: 3.4 #10,13,15,18,22,24,50,52; due 7/30, Thursday, 5:00 pm
Assignment 12: 3.5 #2,3,11,16,18,36; due 8/4, Tuesday, 5:00 pm

SCHEDULE OF LECTURES:

       MONDAY   TUESDAY  WEDNESDAY  THURSDAY         M Tu  W Th  F
Week of                                         JUN     2009
 6/15   1.1       1.1        1.2      1.2           15 16 17 18 19
 6/22   1.3       1.3        1.4      1.4           22 23 24 25 26
 6/29  EXAM 1     2.1        2.1    HOLIDAY         29 30  1  2  3
 7/06   2.2       2.2        2.3      2.3       JUL  6  7  8  9 10
 7/13   3.1      EXAM 2      3.1      3.2           13 14 15 16 17
 7/20   3.2       3.2        3.3      3.3           20 21 22 23 24
 7/27  EXAM 3     3.4        3.4      3.5           27 28 29 30 31
 8/03   3.5       3.6        3.6     EXAM 4     AUG  3  4  5  6  7

REVIEW
Exam 1, Summer 2005     Exam 1, Summer 2007     Exam 1, Fall 2006     Exam 1, Fall 2006, solutions