MAT 447 Number Theory, # 25757, Spring 2005
Class
meets MW 17:30-18:45 in NSM D-129.
Instructor:
e-mail address: sraianu@csudh.edu, URL: http://www.csudh.edu/math/sraianu;
office hours: Monday, 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 Monday 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.
Makeup’s: 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:
M 1/24: 1.1 Divisibility: 3,4,5,6,7,8
W 1/26: 1.2 Prime numbers: 16,17,18,21
M
1/31: 1.3 Greatest
common divisors: 32,33,35,39
W
2/2: 1.4 The Euclidean
algorithm: 54,55,56
M 2/7: 2.1 Congruences:
1,2,4,5,6
W 2/9: 2.2 Linear congruences
in one variable: 28,29,30
M 2/14: 2.3 The Chinese Remainder Theorem: 33,34,35
W 2/18: 2.4
M 2/21: Presidents’ Day
W 2/23: Review
M 2/28: Exam I
W 3/2: 2.5 Fermat’s Little Theorem; Pseudoprime numbers: 50,51,52,54
M
3/7: 2.6 Euler’s
Theorem: 66,67,68
W 3/9: 3.1 Arithmetic functions; Multiplicativity: 3,4,5
M 3/14: 3.2 The Euler Phi-Function: 9,10,12
W 3/16: 3.3 The number of
positive divisors function: 29,30,31,32
M 3/21: 3.4 The sum of positive divisors function: 41,42,43
W 3/23: 3.5 Perfect numbers: 52,54
M 3/28: Spring
Recess
W 3/30: Spring Recess
M 4/4: 3.6 The Möbius Inversion Formula: 62,63,64
W 4/6: Review
M 4/11: Exam II
W
4/13: 4.1 Quadratic
residues: 1,2,3,4
M
4/18: 4.2 The Legendre Symbol: 12,13,14
W
4/20: 4.3 The Law of
Quadratic Reciprocity: 28,30,34
M
4/25: 6.1 Linear
Diophantine Equations: 1,2,3,5
W
4/27: 6.2 Nonlinear
Diophantine Equations; a Congruence Method: 11
M
5/2: 6.3 Pythagorean
Triples: 13,14; 6.4 Fermat’s Last Theorem: 21,22
W
5/4: Review 6.4 Fermat’s
Last Theorem: 21,22
M
5/9: Exam III
W
5/11: Review
Final
exam: Monday, May 16, 7:00 - 9:00 pm.