MAT 333 Abstract Algebra, Section 01, CRN
41797, Fall 2004
Class
meets MW
Instructor:
e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu;
office hours: MW:
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
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 three times, on the
days of the three exams, 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.
Students with Disabilities: Students who need special consideration
because of any sort of disability are urged to see me 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".)
Tentative schedule and homework
assignments:
M 8/30: 1.1. The Division algorithm: 1, 2, 3,
6, 8
W 9/1: 1.2. Divisibility: 1, 3, 5, 11, 17
M 9/6: Labor
Day
W 9/8: 1.3 Primes and Unique
Factorization:1,3,6,7,8,9,20,21,22
M
9/13: 2.1 Congruence and
Congruence Classes: 1, 3, 4, 5, 9, 11, 12, 13, 15
W 9/15: 2.2.
Modular arithmetic: 1, 2, 5, 6, 7, 8
M 9/20: 2.3 The structure of Zp when p is prime: 1, 5, 7
W 9/22: 3.1 Definitions and Examples of Rings:
1, 2, 3, 4
3.2
Basic Properties of Rings: 6, 9, 10, 13
M 9/27: 3.3 Isomorphisms
and Homomorphisms: 1, 2, 3, 7, 9
W 9/29: Review
M 10/4 : Exam
I
W 10/6: 4.1
Polynomial Arithmetic and the Division Algorithm: 1, 3, 4, 5, 6, 11, 12
M 10/11: 4.2 Divisibilty in F[x]: 1, 3, 5, 6, 7, 9
W
10/13: 4.3 Irreducibles and Unique Factorization: 1, 3, 5, 6, 9, 10,
11, 12
M 10/18: 4.4 Polynomial Functions, Roots, and Reducibility: 1, 2, 3, 4, 5, 6, 7, 8, 9
W
10/20: 5.1 Congruence in
F[x] : 1, 2, 3, 4, 5, 6, 9
M 10/25: 5.2 Congruence-Class Arithmetic: 1, 2,
3, 4, 5, 6, 7, 8, 9
W 10/27: 5.3 The structure of F[x]/p(x) When
p(x) is Irreducible: 1, 2, 3, 9
M 11/1: Review
W 11/3: Exam
II
M 11/8: 6.1 Ideals and Congruence: 1, 2, 3, 11,
12, 13, 14, 17
W 11/10: 6.2 Quotient Rings and Homomorphisms: 1, 3, 4, 5, 6, 8
M 11/15: 6.3 The Structure of R/I When I is
Prime or Maximal: 1, 2, 4, 5, 6, 7
W 11/17: 7.1 Definitions and Examples of Groups:
1, 2, 3, 4, 5, 6, 7, 9, 11
M 11/22: 7.2 Basic Properties of Groups: 1, 2,
3, 4, 7, 9
W 11/24: 7.3 Subgroups: 3, 5, 11, 12, 13, 21
M 11/29: 7.4 Isomorphisms and Homomorphisms: 1, 3, 4, 5
W 12/1: Review
M 12/6: Exam
III
W 12/8: Review
Final
exam: Wednesday, December 15, 17:30-19:30.