INSTRUCTOR: Professor John Beachy, Watson 355, 753-6753, email: beachy@math.niu.edu
OFFICE HOURS: W Th 12:00-1:50, or by appointment.
My faculty homepage | My personal homepage
Thursday morning (12/14/2006) Exam scores and semester grades have been posted on Blackboard. Final exam 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 600 points:
3 hour tests (300), homework (100),
and a comprehensive final exam (200).
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.
Note that the last day for an undergraduate to withdraw from the course without
penalty is Friday, October 20.
FINAL: The final exam for Section 1 is scheduled for Monday, December 11, 10:00-11:50 a.m.
REVIEW: Sample Exam 1 questions | Sample Exam 2 questions | Exam 2, Fall 1995 | Review of groups | Previous final exams
EXAMS: Exam 1 Solutions | Exam 2 Solutions | Exam 3 Solutions | Final Exam Solutions
ASSIGNMENTS:
Friday, 12/8 Optional Homework: 3.5 #4,10,11,18 If you decide to turn in these problems, I will use your score to replace the lowest homework or quiz score that you have. Since I do not plan to drop any of these scores, if you missed a quiz or homework assignment, replacing a 0 is high priority. Monday, 12/4 Exam 3 3.1-3.4 Monday, 11/20 Hmwk 10: Hand in 3.3 #2,5,8,11 Friday, 11/17 Quiz 7 Definitions and statements of results only! But covering 3.1, 3.2, and 3.3.1-3.3.4 Friday, 11/10 Quiz 6 on Sections 3.1, 3.2 Know the definitions and statements of results!! Suggested problems for the quiz: 3.1 #1-3,6-8,15,23 3.2 #1,4,5,7,11,12,14,15 Hmwk 8,9: Hand in 3.1 #10-13; 3.2 #6,8,19,24 Friday, 10/27 Exam 2 on sections 2.1-2.3 Wednesday, 10/25 Hmwk 7 Section 2.3 #3,6,13,14 Friday, 10/20/06 Quiz 5 over section 2.2 Suggested problems: 2.2 #1-6,10 Study guide: #13-16,21 Friday, 10/13/06 Quiz 4 over section 2.1 Quiz problems: 2.1 #1-10 Wednesday, 10/11/06 Hmwk 6 Section 2.1 #11,12,15,16 Friday, 10/6/06 NO QUIZ Monday, 10/2 Exam 1 on sections 1.1-1.4 Friday, 9/27/06 Exam 1 postponed to Monday Hmwk 5 Section 1.4 #3d,9,12,27 Friday, 9/22/06 Quiz 3 Hmwk 3,4 Section 1.2 #23,25 Section 1.3 #13,17,24,27 Section 1.4 #2,4 Monday, 9/11/06 Quiz 2 Hmwk 2 Section 1.1 # 13,20 1.2 #12,14 Friday, 9/1/06 Hmwk 1 Section 1.1 #7, 10, 16, 21 Quiz 1 (on Section 1.1 #2, 7-10, 15-18, 21)
SCHEDULE OF LECTURES AND EXAMS (TENTATIVE):
MONDAY WEDNESDAY FRIDAY M Tu W Th F Week of 2006 08/28 1.1 1.1 1.1 AUG 28 29 30 31 1 09/04 HOLIDAY 1.2 1.2 SEP 4 5 6 7 8 09/11 1.2 1.3 1.3 11 12 13 14 15 09/18 1.3 1.4 1.4 18 19 20 21 22 09/25 1.4 2.1 TEST I 25 26 27 28 29 10/02 2.1 2.1 2.2 OCT 2 3 4 5 6 10/09 2.2 2.2 2.3 9 10 11 12 13 10/16 2.3 2.3 3.1 16 17 18 19 20 10/23 3.1 3.1 TEST II 23 24 25 26 27 10/30 3.2 3.2 3.2 30 31 1 2 3 11/06 3.3 3.3 3.3 NOV 6 7 8 9 10 11/13 3.4 3.4 3.4 13 14 15 16 17 11/20 3.5 THANKSGIVING HOLIDAY 20 21 22 23 24 11/27 3.5 3.5 TEST III 27 28 29 20 1 12/04 3.6 3.6 3.6 DEC 4 5 6 7 8 12/11 FINAL 11 12 13 14 15 FINAL EXAM Monday 12/11/2006 10:00-11:50 a.m.