MAT 333 Abstract Algebra, # 25585, Spring 2003
Class meets MWF
Instructor: Prof.
e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu;
office hours: Wednesday
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 date of each
midterm exam, 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 Friday 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 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".)
Technology: Symbolic calculators, such as TI-89 or
TI-92 are acceptable for this course, but they will not be
needed.
Tentative schedule:
1. M 1/27: 1.1. The Division algorithm: 1,6,8
2. W 1/29: 1.2. Divisibility: 1,3,5,11,17
3. F 1/31: 1.3 Primes and Unique
Factorization:1,3,6,7,8,9
4. M 2/3: 1.3 Primes and Unique
Factorization:20,21,22
5. W 2/5: 2.1
Congruence and
Congruence Classes: 1,3,4,5
6. F 2/7: 2.1 Congruence and Congruence
Classes: 9,11,12,13,15
7. M 2/10: 2.2. Modular arithmetic: 1,2,5
8. W 2/12: 2.2. Modular arithmetic: 6,7,8
9. F 2/14: 2.3 The structure of Zp
when p is
prime: 1,5,7
10. M 2/17: Presidents’ Day
11. W 2/19: 3.1 Definitions and Examples of
Rings: 1,2,3,4
12. F 2/21: 3.2 Basic Properties of Rings: 6,9,10,13
13. M 2/24: 3.3 Isomorphisms and Homomorphisms:
1,2,3,7,9
14. W 2/26: Review
15. F 2/28: Exam I
16. M 3/3: 4.1 Polynomial
Arithmetic and the Division Algorithm: 1,3,4,5
17. W 3/5: 4.1 Polynomial Arithmetic and the Division Algorithm: 6,11,12
18. F 3/7: 4.2 Divisibilty in F[x]: 1,3,5
19. M 3/10: 4.2 Divisibilty in F[x]: 6,7.9
20. W 3/12: 4.3 Irreducibles and Unique
Factorization: 1,3,5,6
21. F 3/14: 4.3 Irreducibles and Unique
Factorization: 9,10,11,12
22. M 3/17: 4.4 Polynomial Functions, Roots, and
Reducibility: 1,2,3,4
23. W 3/19: 4.4 Polynomial Functions, Roots, and
Reducibility: 5,6,7,8,9
24. F 3/21: 5.1 Congruence in F[x]
: 1,2,3,4
25. M 3/24: 5.1 Congruence in F[x]
: 5,6,9
26. W 3/26: 5.2 Congruence-Class
Arithmetic: 1,2,3,4
27. F 3/28: 5.2 Congruence-Class Arithmetic: 5,6,7,8,9
28. M 3/31: Spring Recess
29. W 4/2: Spring Recess
30. F 4/4: Spring Recess
31. M 4/7: 5.3 The
structure of F[x]/p(x) When p(x) is Irreducible: 1,2,3,9
32. W 4/9:
Review
33. F 4/11: Exam
II
34. M 4/14: 6.1 Ideals and Congruence: 1,2,3,11
35. W 4/16: 6.1 Ideals and Congruence: 12,13,14,17
36. F 4/18: 6.2 Quotient Rings and Homomorphisms:
1,3,4
37. M 4/21: 6.2 Quotient Rings and Homomorphisms:
5,6,8
38. W 4/23: 6.3 The Structure of R/I When I is Prime
or Maximal: 1,2,4
39. F 4/25: 6.3 The Structure of R/I When I is Prime
or Maximal: 5,6,7
40. M 4/28: 7.1 Definitions and Examples of Groups:
1,2,3,4
41. W 4/30: 7.1 Definitions and Examples of Groups:
5,6,7,9,11
42. F 5/2: 7.2 Basic Properties of Groups: 1,2,3,4,7,9
43. M 5/5: 7.3 Subgroups: 3,5,11
44. W 5/7: 7.3 Subgroups: 12,13,21
45. F 5/9: 7.4 Isomorphisms and Homomorphisms:
1,3,4,5
46. M 5/12:
Review
47. W 5/14: Exam
III
48. F 5/16:
Review
Final exam: Wednesday, May 21,