MAT 333 Abstract Algebra, # 41086, Fall 2002

Class meets TTh 19:00-20:15 in SBS A-232 on T, and in EAC 901 on Th.

Instructor: Prof. Serban Raianu, office: NSM A-135, office phone number: (310) 243-3139,

e-mail address: sraianu@csudh.edu, office hours: Tuesday 18:00-19:00 in the Math Lab SAC 1115; in my office: MWF: 12:30-13:30,  or by appointment.

Course Description: MAT 333, Abstract Algebra,  covers Chapters 1-7 from the textbook: arithmetic in Z and F[x], rings, ideals, groups, etc.

Text: Abstract Algebra, An Introduction (2nd edition), by Thomas W. Hungerford.

Objectives: After completing MAT 333 the student should be able to: state definitions of basic concepts (e.g., congruence, groups, rings, integral domains, fields, subrings, homomorphisms, ideals); understand and use the Euclidean algorithm; understand and use modular arithmetic; state major theorems (e.g., the division algorithm, the unique factorization theorem, the remainder theorem, the factor theorem, the isomorphism theorems) and be able to identify the structures to which each theorem applies (e.g. the integers, integral domains, polynomial rings F[x] where F is a field, groups, etc.) ; find examples of objects that satisfy given algebraic properties (a noncommutative ring, a commutative ring but not an integral domain, etc)

Prerequisites: MAT 271 or equivalent with a grade of "C" or better.

Grades: Grades will be based on three in‑class full‑period examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, and other assignments (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will be collected every class meeting, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every class meeting, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q. There are also 5 points awarded for attendance and class participation, this portion of the grade is denoted by A. The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F.

To determine your final grade  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.

Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with your instructor, who may then substitute the relevant score from your final examination for the missing grade.

Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see their instructor as soon as possible.

Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Technology: Symbolic calculators, such as TI-89 or TI-92 are acceptable for this course.

Tentative schedule:

T 8/27: 1.1. The Division algorithm: 1,2,3,6,8

Th 8/29: 1.2. Divisibility: (odd only) 1-13,17

T 9/3: 1.3 Primes and Unique Factorization:1,3,6,7,8,9,20,21,22

Th 9/5: 2.1 Congruence and Congruence Classes: (odd) 1-15

T 9/10: 2.2. Modular arithmetic: (odd) 1-9

Th 9/12: 2.3 The structure of Zp  when p is prime: 1,3,5,7,8,9,10,11

T 9/17: 3.1 Definitions and Examples of Rings: (odd) 1-11

3.2 Basic Properties of Rings: (odd) 1-15

Th 9/19: 3.3 Isomorphisms and Homomorphisms: (odd) 1-13

T 9/24: Review

Th 9/26 : Exam I

T 10/1: 4.1 Polynomial Arithmetic and the Division Algorithm: (odd) 1-9

Th 10/3: 4.2 Divisibilty in F[x]: (odd) 1-9

T 10/8: 4.3 Irreducibles and Unique Factorization: (odd) 1-15

Th 10/10:  4.4 Polynomial Functions, Roots, and Reducibility: (odd) 1-11

T 10/15: 5.1 Congruence in F[x] : (odd) 1-7

Th 10/17: 5.2 Congruence-Class Arithmetic: (odd) 1-11

T 10/22: 5.3 The structure of F[x]/p(x) When p(x) is Irreducible: (odd) 1-9

Th 10/24: Review

T 10/29: Exam II

Th 10/31: 6.1 Ideals and Congruence: (odd) 1-21

T 11/5: 6.2 Quotient Rings and Homomorphisms: (odd) 1-9

Th 11/7: 6.3 The Structure of R/I When I is Prime or Maximal: (odd) 1-9

T 11/12: 7.1 Definitions and Examples of Groups: (odd) 1-11

Th 11/14: 7.2 Basic Properties of Groups: (odd) 1-9

T 11/19: 7.3 Subgroups: 3,5,11,12,13,21

Th 11/21: 7.4 Isomorphisms and Homomorphisms: (odd) 1-9

T 11/26: Review

Th 11/28: Thanksgiving Day

T 12/3: Exam III

Th 12/5: Review

Final exam: Tuesday, December 10, 19:00-21:00.