MAT 333 Abstract Algebra, Section 01, CRN 41367, Fall 2009

Class meets MW 7:00 pm- 8:15 pm 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: TuTh 4:20 pm – 5:20 pm, 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 Monday, 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 Monday, 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 will be 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 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".)

Exam rules: Students must leave their CSUDH student ID on their desk for the duration of the exam. Cell phones, iPhones, iPods, or PDAs of any kind, as well as headphones, may not be used at all during a test. Students are discouraged from leaving the exam room during the period of the exam. Restroom breaks must be kept under five minutes and are limited to one/exam. You will be penalized 5 points if you are gone more than five minutes. No more than one student can be out of the room at any given time during an exam. If a student finds it necessary to leave the room under these circumstances, they are not permitted to access computer terminals, smoke, read notes/books, or talk with others. If a student is found engaging in this behavior, appropriate disciplinary action will be taken. Whenever a student leaves the room, they must turn their exam upside down on their desk. All book bags or similar items will be deposited in the front of the class for the duration of the test.

Tentative schedule and homework assignments:

M 8/31: 1.1. The Division algorithm: 1, 2, 3, 6, 8

W 9/2: 1.2. Divisibility: 1, 3, 5, 11, 17

M 9/7: Labor Day

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

M 9/14: 2.1 Congruence and Congruence Classes: 1, 3, 4, 5, 9, 11, 12, 13, 15

W 9/16: 2.2. Modular arithmetic: 1, 2, 5, 6, 7, 8

M 9/21: 2.3 The structure of Z_p when p is prime: 1, 5, 7

W 9/23: 3.1 Definitions and Examples of Rings: 1, 2, 3, 4

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

M 9/28: 3.3 Isomorphisms and Homomorphisms: 1, 2, 3, 7, 9

W 9/30: Review

M 10/5 : Exam I

W 10/7: 4.1 Polynomial Arithmetic and the Division Algorithm: 1, 3, 4, 5, 6, 11, 12

M 10/12: 4.2 Divisibilty in F[x]: 1, 3, 5, 6, 7, 9

W 10/14: 4.3 Irreducibles and Unique Factorization: 1, 3, 5, 6, 9, 10, 11, 12

M 10/19: 4.4 Polynomial Functions, Roots, and Reducibility: 1, 2, 3, 4, 5, 6, 7, 8, 9

W 10/21: 5.1 Congruence in F[x] : 1, 2, 3, 4, 5, 6, 9

M 10/26: 5.2 Congruence-Class Arithmetic: 1, 2, 3, 4, 5, 6, 7, 8, 9

W 10/28: 5.3 The structure of F[x]/p(x) When p(x) is Irreducible: 1, 2, 3, 9

M 11/2: Review

W 11/4: Exam II

M 11/9: 6.1 Ideals and Congruence: 1, 2, 3, 11, 12, 13, 14, 17

W 11/11: Veterans Day

M 11/16: 6.2 Quotient Rings and Homomorphisms: 1, 3, 4, 5, 6, 8

W 11/18: 6.3 The Structure of R/I When I is Prime or Maximal: 1, 2, 4, 5, 6, 7

M 11/23: 7.1 Definitions and Examples of Groups: 1, 2, 3, 4, 5, 6, 7, 9, 11

W 11/25: 7.2 Basic Properties of Groups: 1, 2, 3, 4, 7, 9

M 11/30: 7.3 Subgroups: 3, 5, 11, 12, 13, 21

W 12/2: 7.4 Isomorphisms and Homomorphisms: 1, 3, 4, 5

M 12/7: Exam III

W 12/9: Review

Final exam: Monday, December 14, 7:00 pm - 9:00 pm.