MAT 333 Abstract Algebra, CRN 20559, Spring 2009

 

Class meets MW 10:00 a.m.-11:15 a.m. in NSM D123.

 

Instructor: Serban Raianu, office: NSM A-123, office phone number: (310) 243-3139,

e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu; office hours: Monday, Wednesday: 1:00 p.m.-3:00 p.m., 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 and attendance (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be gradedon a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will not be collected, but all problems on quizzes and exams will be similar to the problems in the homework.

5 to 10 minutes quizzes will be given in principle every Monday, with the exception of the review and exam days, and will be graded on a scale from 1 to 10. 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 will be divided by 8 and denoted by F.

To determine your final gradecompute E+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 me, and I may then substitute the relevant score from your final examination for the missing grade.

 

Accomodations for Students with Disabilities: Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.

 

 

 

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".)

 

 

Tentative schedule and homework assignments:

M 1/26: 1.1. The Division algorithm: 1, 2, 3, 6, 8

W 1/28: 1.2. Divisibility: 1, 3, 5, 11, 17

M 2/2: 1.3 Primes and Unique Factorization:1,3,6,7,8,9,20,21,22

W 2/4: 2.1 Congruence and Congruence Classes: 1, 3, 4, 5, 9, 11, 12, 13, 15

M 2/9: 2.2. Modular arithmetic: 1, 2, 5, 6, 7, 8

W 2/11: 2.3 The structure of Zpwhen p is prime: 1, 5, 7

M 2/16: Presidentsí Day Holiday

W 2/18: 3.1 Definitions and Examples of Rings: 1, 2, 3, 4

3.2 Basic Properties of Rings: 6, 9, 10, 13

M 2/23: 3.3 Isomorphisms and Homomorphisms: 1, 2, 3, 7, 9

W 2/25: Review

M 3/2 : Exam I

W 3/4: 4.1 Polynomial Arithmetic and the Division Algorithm: 1, 3, 4, 5, 6, 11, 12

M 3/9: 4.2 Divisibilty in F[x]: 1, 3, 5, 6, 7, 9

W 3/11: 4.3 Irreducibles and Unique Factorization: 1, 3, 5, 6, 9, 10, 11, 12

M 3/16: 4.4 Polynomial Functions, Roots, and Reducibility: 1, 2, 3, 4, 5, 6, 7, 8, 9

W 3/18: 5.1 Congruence in F[x] : 1, 2, 3, 4, 5, 6, 9

M 3/23: 5.2 Congruence-Class Arithmetic: 1, 2, 3, 4, 5, 6, 7, 8, 9

W 3/25: 5.3 The structure of F[x]/p(x) When p(x) is Irreducible: 1, 2, 3, 9

M 3/30: Spring Recess

W 4/1: Spring Recess

M 4/6: Review

W 4/8: Exam II

M 4/13: 6.1 Ideals and Congruence: 1, 2, 3, 11, 12, 13, 14, 17

W 4/15: 6.2 Quotient Rings and Homomorphisms: 1, 3, 4, 5, 6, 8

M 4/20: 6.3 The Structure of R/I When I is Prime or Maximal: 1, 2, 4, 5, 6, 7

W 4/22: 7.1 Definitions and Examples of Groups: 1, 2, 3, 4, 5, 6, 7, 9, 11

M 4/27: 7.2 Basic Properties of Groups: 1, 2, 3, 4, 7, 9

W 4/29: 7.3 Subgroups: 3, 5, 11, 12, 13, 21

M 5/4: 7.4 Isomorphisms and Homomorphisms: 1, 3, 4, 5

W 5/6: Review

M 5/11: Exam III

W 5/13: Review

Final exam: Monday, May 18, 10:00 a.m.-12:00 p.m.