MAT 333 Abstract Algebra, # 41086, Fall 2002
Class meets TTh
Instructor: Prof.
e-mail address: sraianu@csudh.edu, office
hours: Tuesday
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,