MAT 333 Abstract Algebra, Section 01, CRN 42209, Fall 2019

Class meets MW 11:30 AM - 12:45 PM in LIB E133.

Instructor:  Serban Raianu

Office: NSM E-108; Office phone number: (310) 243- 3139

Office hours: Monday: 9:15 AM - 11:15 AM, Wednesday: 9 AM - 10 AM, Wednesday: in the Toro Learning Center: 10:15 AM - 11:15 AM, or by appointment.

Course Description: MAT 333, Abstract Algebra, covers material from the first two chapters of the textbook: sets, groups, rings, polynomial rings, fields.

Text: Algebra I: Groups, Rings, & Arithmetic, by Serban Raianu, PDF available online at https://math.csudh.edu/~sraianu/algebrabook.html

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 is due 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.

Accommodations 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 Student disAbility Resource Center (SdRC) 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 SdRC in WH D-180. 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 homework assignments

M 8/26: 1.1 Sets and functions: 1.1.2,1.1.6,1.1.7,1.1.8,1.1.11,1.1.12

W 8/28:  1.1 Sets and functions: 1.1.13,1.1.15,1.1.16,1.1.17

M 9/2:  Labor Day Holiday

W 9/4: 1.2 The integers: 1.2.3,1.2.4,1.2.6,1.2.9,1.2.12

M 9/9: 1.2 The integers: 1.2.14,1.2.16,1.2.17,1.2.18,1.2.26

W 9/11: 1.3 Equivalence relations and factor sets: 1.3.3,1.3.9,1.3.12,1.3.19

M 9/16: 1.4 Groups and morphisms of groups: 1.4.3,1.4.4,1.4.5

W 9/18: 1.4 Groups and morphisms of groups 1.4.6,1.4.7,1.4.8,1.4.11,1.4.13

M 9/23: 1.5 Subgroups and normal subgroups: 1.5.3,1.5.4,1.5.6,1.5.8

W 9/25: 1.5 Subgroups and normal subgroups: 1.5.13,1.5.15

M 9/30: Review

W 10/2: Exam I

M 10/7: 1.6 Factor groups: 1.6.2,1.6.4

W 10/9: 1.6 Factor groups: 1.6.16,1.6.17

M 10/14: 1.7 Finite groups and the Lagrange theorem: 1.7.3,1.7.7,1.7.8,1.7.10,1.7.11,1.7,12

W 10/16: 1.7 Finite groups and the Lagrange theorem: 1.7.14,1.7.19,1.7.20,1.7.21

M 10/21: Review

W 10/23: Exam II

M 10/28: 2.1 Rings and morphisms of rings: 2.1.2, 2.1.4

,2.1.6,2.1.7,2.1.8,2.1.13

W 10/30: 2.2 Subrings and ideals: 2.2.2,2.2.3,2.2.5,2.2.6

M 11/4: 2.2 Subrings and ideals: 2.2.7,2.2.8,2.2.10,2.2.12

W 11/6: 2.3 Factor rings: 2.3.4,2.3.6,2.3.8,2.3.10,2.3.11

M 11/11: Veterans Day

W 11/13: 2.3 Factor rings: 2.3.13,2.3.14,2.3.15,2.3.16

M 11/18: 2.4 Prime and maximal ideals: 2.4.2,2.4.3,2.4.5,2.4.10,2.4.12,2.4.15

W 11/20: 2.5 Rings of fractions: 2.5.2,2.5.10,2.5.11,2.5,12

M 11/25: 2.6 Polynomial rings: 2.6.3,2.6.6,2.6.7,2.6.9

W 11/27: 2.6 Polynomial rings: 2.6.10,2.6.11,2.6.12

M 12/2: Review

W 12/4: Exam III

M 12/9: Review

Final examination: Wednesday, December 11, 11:30 AM - 1:30 PM.

Important Dates: