MAT 447 Number Theory, CRN 20562, Spring 2009

Class meets MW 5:30 p.m.-6:45 p.m. in SBS B203.

Instructor: Serban Raianu, office: NSM A-123, office phone number: (310) 243-3139,

e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu; office hours: Monday, Wednesday: 1:00 p.m.-3:00 p.m., or by appointment.

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 and attendance (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 not be collected, but all problems on quizzes and exams will be similar to the problems in the homework

5 to 10 minutes quizzes will be given in principle every Monday class meeting, with the exception of the review and exam days, and will be graded on a scale from 1 to 10. 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+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.

Accomodations 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 Disabled Student Services (DSS) 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 DSS in WH B250. 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 schedule:

M 1/26: 1.1 Divisibility: 3,4,5,6,7,8

W 1/28: 1.2 Prime numbers: 16,17,18,21

M 2/2: 1.3 Greatest common divisors: 32,33,35,39

W 2/4: 1.4 The Euclidean algorithm: 54,55,56

M 2/9: 2.1 Congruences: 1,2,4,5,6

W 2/11: 2.2 Linear congruences in one variable: 28,29,30

M 2/16: Presidents’ Day Holiday

W 2/18: 2.3 The Chinese Remainder Theorem: 33,34,35

M 2/23: 2.4 Wilson’s Theorem: 42,43,44,45

W 2/25: Review

M 3/2: Exam I

W 3/4: 2.5 Fermat’s Little Theorem; Pseudoprime numbers: 50,51,52,54

M 3/9: 2.6 Euler’s Theorem: 66,67,68

W 3/11: 3.1 Arithmetic functions; Multiplicativity: 3,4,5

M 3/16: 3.2 The Euler Phi-Function: 9,10,12

W 3/18: 3.3 The number of positive divisors function: 29,30,31,32

M 3/23:  3.4 The sum of positive divisors function: 41,42,43

W 3/25: 3.5 Perfect numbers: 52,54

M 3/30: Spring Recess

W 4/1: Spring Recess

M 4/6: 3.6 The Möbius Inversion Formula: 62,63,64

W 4/8: Review

M 4/13: Exam II

W 4/15: 4.1 Quadratic residues: 1,2,3,4

M 4/20: 4.2 The Legendre Symbol: 12,13,14

W 4/22: 4.3 The Law of Quadratic Reciprocity: 28,30,34

M 4/27: 6.1 Linear Diophantine Equations: 1,2,3,5

W 4/29: 6.2 Nonlinear Diophantine Equations; a Congruence Method: 11

M 5/4: 6.3 Pythagorean Triples: 13,14; 6.4 Fermat’s Last Theorem: 21,22

W 5/6: Review

M 5/11: Exam III

W 5/13: Review

Final exam: Wednesday, May 20, 5:30 p.m.- 7:30 p.m.