MAT 447 Number Theory, # 25588, Spring 2003
Class meets WF
Instructor: Prof.
e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu;
office hours: Wednesday
Course Description: MAT 447, Number Theory, covers
Chapters 1-4, 6 from the textbook: divisibility, congruences, prime number
theory, Diophantine equations and other selected topics from elementary number
theory.
Text: Elementary Number
Theory, by James K.
Strayer.
Objectives: After completing MAT 447 the student
should be able to: solve simple problems, do simple proofs and state basic
definitions and theorems involving: divisibility and congruences; The Euclidean
Algorithm, the Chinese Remainder Theorem; Fermat's Little Theorem, Euler's
Theorem, Wilson's Theorem, etc.; Important arithmetic functions,
multiplicativity, Möbius Inversion; Quadratic reciprocity; Diophantine Equations
and Fermat's Last Theorem.
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. W 1/29: 1.1 Divisibility: 3,4,5,6,7,8
2. F 1/31: 1.2 Prime numbers: 16,17,18,21
3. W 2/5: 1.3 Greatest common divisors:
32,33,35,39
4. F 2/7: 1.4 The Euclidean algorithm: 54,55,56
5. W 2/12: 2.1 Congruences: 1,2,4,5,6
6. F 2/14: 2.2 Linear congruences in one variable:
28,29,30
7. W 2/19: 2.3 The Chinese Remainder Theorem:
33,34,35
8. F 2/21: 2.4
9. W 2/26: Review
10. F 2/28: Exam I
11. W 3/5: 2.5 Fermat’s Little Theorem; Pseudoprime numbers: 50,51,52,54
12. F 3/7: 2.6 Euler’s Theorem: 66,67,68
13. W 3/12: 3.1 Arithmetic functions;
Multiplicativity: 3,4,5
14. F 3/14: 3.2 The Euler Phi-Function: 9,10,12
15. W 3/19: 3.3 The number of
positive divisors function: 29,30,31,32
16. F 3/21: 3.4 The sum of positive divisors
function: 41,42,43
17. W 3/26: 3.5 Perfect numbers: 52,54
18. F 3/28: 3.6 The Möbius Inversion Formula:
62,63,64
19. W 4/2: Spring Recess
20. F 4/4: Spring Recess
21. W 4/9:
Review
22. F 4/11: Exam
II
23. W 4/16: 4.1 Quadratic residues: 1,2,3,4
24. F 4/18: 4.2 The Legendre Symbol: 12,13,14
25. W 4/23: 4.3 The Law of Quadratic Reciprocity:
28,30,34
26. F 4/25: 6.1 Linear Diophantine Equations:
1,2,3,5
27. W 4/30: 6.2 Nonlinear Diophantine Equations; a
Congruence Method: 11
28. F 5/2: 6.3 Pythagorean Triples: 13,14
29. W 5/7: 6.4 Fermat’s Last Theorem: 21,22
30. F 5/9:
Review
31. W 5/14: Exam
III
32. F 5/16:
Review
Final exam: Monday, May 19,