MATH 116 Basic Algebraic Structures (Spring 2002)

# MATH 116: Basic Algebraic Structures

• Announcements:
• Grades of the first midterm exam are announced now.
• Lectures:
• Section 01: (GE) Monday 13:40-15:30 (M-04) Friday 12:40-13:30 (M-103)
• Section 02: (EA) Monday 13:40-15:30 (M-07) Friday 12:40-13:30 (M-104)
• Section 03: (AB) Monday 12:40-14:30 (M-205) Friday 12:40-13:30 (M-105)
• Recitation: Monday 15:40-17:30 (HZ 1)
Wednesday 15:40-17:30 (P-1)
• Textbook. Elements of Modern Algebra, Jimmie Gilbert and Linda Gilbert, Brooks/Cole, fifth edition, 2000. (Five copies are available in the reserve section of the library.)

### Office Hours:

G�lin Ercan: Thursday
Ay�e Berkman: Monday 14:40 - 15:30
Ali Sait Diner: Thursday 10:40 - 12:30

### Exams:

Exam 1: 17 April 2003, Thursday 17:40 (Contents: TBA)
Exam 2: 15 May 2003, Thursday 17:40 (Contents: TBA)
Final: TBA (Contents: TBA)

Exam 1 - 30 points
Exam 2 - 30 points
Final - 40 points
Quizzes - 25 points

### Outline of the course:

 Weeks Topics Sections 1 Binary operations 1.4. 2 Matrices 1.5. 3 Integers 2.1-2.4 4 Congruence 2.5, 2.6 5 Groups, subgroups 3.1, 3.2 6 Cyclic groups, isomorphisms 3.3, 3.4 7 Permutation groups 4.1. 8 Normal subgroups, quotient groups 4.4*, 4.5** 9 Rings, integral domains 5.1, 5.2 10 Fields, ideals 5.2, 6.1 11 Quotient rings, ring isomorphisms 6.1, 6.2*** 12 Polynomials, divisibility 8.1, 8.2 13 GCD, factorization 8.2, 8.3 14 Zeros of a polynomial 8.4****

(*) 4.8, 4.9, 4.17, 4.19 and 4.20 will be skipped.
(**) Only 4.21 and 4.22.
(***) We will cover 6.6-6.9 (inclusive).
(****) 8.30 - 8.33 will not be covered.

### Exercises:

Solving exercises (NOT reading the solutions but really solving them) is an essential part of every math course and MATH 116 is no exception. Therefore to start studying for the exam the day before is not a good idea, because there is simply no time to work on all the exercises. We recommend you to solve the exercises of a section within the same week that the section is covered in the class. Good luck and have fun!

Some parts of certain sections were skipped in the class, the related information regarding the exercises is:

Section 4.4: Everything except 7, 25, 26, 28, 29, 30, 45, 46.
Section 4.5: Only 1, 2, 3, 4, 9, 13, 14, 15, 16, 20, 21, 22.
Section 6.2: 1, 2, 3, 7, 8, 10, 12, 13, 18, 19, 20. (In exercises 1, 2, 3 and 18, replace epimorphism with isomorphism.)
Section 8.4: TBA