MTH 1321 - Groups and their Applications

Winter 2002

Course Information


Course:	MTH 1321, Groups and their Applications
Instructor:	Professor Andrei Zelevinsky
Time and Place:	Tue., Wed., Fr. 11:45 - 12:50 PM, in 205 RY
Office hours:	Tue., 10:30 - 11:30 AM; Wed., 1:00 - 2:30 PM, or by appointment
Textbook:	Joseph A. Gallian, Contemporary Abstract Algebra, 5th edition, Houghton Mifflin, 2002.

Course Description

The concept of groups is probably the most fundamental and successful of all mathematical abstractions. It provides mathematical foundation for the idea of symmetry and finds numerous applications in all branches of arts and sciences. The course starts from scratch and provides an introduction to basic properties of groups and some basic applications.
If time allows, we shall cover Parts 1 and 2 (Chapters 0 - 11) of the text. This is an ideal area for developing understanding and ability to do some rigorous mathematics. The grade in the course will be determined as follows: homework and class participation (35%), two one-hour tests (30%), and the final exam (35%).

If you have a concern about the course or the instructor that cannot be resolved by speaking with the instructor, then please see Professor D. King, 447 LA, x5679, donking@neu.edu.

It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.

Homework (the assignments to be collected in class are marked by !!):
Jan.4: read pp. 20-22 (Functions); pp. 31-34 (Symmetries of a square); p. 26, #50.
Jan.8: Chapter 1, pp. 37-39, #1-8; !! (due Friday, Jan.11) #2, 6, 8.
Jan.9: Chapter 2, pp. 54-55, #2, 6, 15-17.
Jan.11: p. 23, #9, 11, 13; pp. 54-55, #3, 8, 12, 18, 19, 20.
!! (due Friday, Jan.18): pp. 55-56, #24, 26, 36.
Bonus problem: consider a set S with a binary operation * satisfying the following property:
(a*b)*a=b for all a,b in S. Prove that a*(b*a)=b for all a,b in S.
Jan.15: pp. 55-56, #27-29, 33, 35.
Jan.16: Chapter 3, pp. 67-70, #6, 8-12.
Jan.18: pp. 68-71, #14, 15, 20, 21, 25, 32.
Jan. 22: pp. 70-71, #35, 37, 50, 52, 53.
Jan. 23: pp. 82-83, #1, 3, 5, 7, 13.
Jan. 25: !! (due Friday, Feb.1): pp. 83-85, #28, 54; p. 90, #6; bonus problem: p. 54, #9.
Jan. 29: pp. 82-83, #15, 19, 21.
Jan. 30: p. 84, #31, 36, 40, 41.
Feb. 1: Chapter 5, pp. 111-112, #3, 7, 9, 11, 15, 17, 18;
!! (due Friday, Feb.8): pp. 112-113, #24, 45, 46.
Feb. 5: pp. 112-113, #19, 26, 27, 31.
Feb. 6: p. 114, #49, 51.
Feb. 8: Chapter 6, pp. 129-131, #1, 3, 5, 7, 10, 17, 25.
Feb. 12: p. 131, #30, 32-34, 40, 43.
Feb. 13: pp. 145-146, #1, 2, 6, 9, 15-17.
!! (due Friday, Feb.22): p. 146, #28, 30, 33; bonus problem: p. 147, #38.
Feb. 19: pp. 146-147, #18, 21, 22, 31, 40.
Feb. 22: p. 162, #1, 2, 5, 7, 8, 14, 17.
!! (due Friday, Mar.1): p. 163, #26; pp. 169-171, #6, 34.
Feb. 26: pp. 162-164, #18, 24, 35, 43.
Feb. 27: Chapter 9, p. 186, #1, 3, 6, 7, 8, 10.
!! (due Friday, Mar.8): p. 187, #26, 30, 36; bonus problem: p. 190, #60.
Mar. 1: pp. 187-189, #32, 37-40, 46-48.
Mar. 5: p. 189, #49, 50, 53; Chapter 10, pp. 205-206, #5, 7-9.
Mar. 6: p. 206, #10, 14, 16, 18, 20.

Tests:
Jan.25: one-hour test (on the material in Chapters 0-4).
Feb.15: one-hour test (on the material in Chapters 3-6).

Final Exam:
Mar. 12 (Tuesday), 1:00 - 3:00pm, in 104 KA
(allowed: calculators, one sheet of notes).

GRADES

Department of Mathematics

Northeastern University
Boston, MA, 02115
Office: 431 LA
Phone: (617) 373-5648
Email: andrei@neu.edu

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Created: January 1, 2002. Last modified: March 6, 2002.