# Fall_2011_446_Syllabus

## Syllabus—Math 446, Fall 2011

Instructor:

Office:

Phone:

Mike “Quimby” Krebs

Simpson Tower F214

(323) 343-2166 from off campus, x 3-2166 from on campus mkrebs@calstatela.edu

e-mail:

Office hours:

Class location:

Days/times:

Textbook:

Tuesdays and Thursdays 10:30–11:30 a.m. in ST-F214

Mondays and Wednesdays 2:10–3:10 p.m. in SH-C357

SH-C266

MW 11:40 a.m.–1:20 p.m.

Number Theory: A Lively Introduction with Proofs, Applications, and Stories , by

Pommersheim, Marks, and Flapan (ISBN-10: 0470424133, ISBN-13: 978-0470424131)

Final exam period: Mon., Dec. 5 from 10:45 a.m. to 1:15 p.m.

General course description

Prerequisite: Math 325 with C or better. Description: In this course, we'll study properties of the integers.

Requirements

Basis for evaluation: There are two requirements: homework and tests. There will be three tests.

Student learning outcomes

Students who successfully complete this course will be able to:

 Prove combinatorial identities using induction and the binomial theorem.

Prove basic properties or integers using the division algorithm.

 Know and prove basic properties of primes.

Prove basic results on greatest common divisor and least common multiple and how the Euclidean algorithm is related to the greatest common divisor.

 Know how to apply the Fundamental Theorem of Arithmetic to other results in the theory of numbers.

 Recognize which linear Diophantine equations are solvable and which are not and how to obtain the general solution for a linear Diophantine equation given a particular solution.

 Know how to use congruences to obtain number theoretic results.

 Recognize when a linear congruence is solvable.

Know how to apply the Chinese Remainder Theorem.

Know how to apply Wilson's Theorem and Fermat's Little Theorem.

Know how to calculate the Euler Phi function for primes and prime powers and how to use these results to calculate Euler phi for a composite n given its prime power decomposition.

 Apply Euler's generalization of Fermat's Little Theorem.

Evaluate the tau and sigma functions.

 Prove basic results about order and primitive roots and how to apply them.

Know basic results on quadratic residues and quadratic congruences (Legendre symbol, Gauss' Lemma,

Euler Criterion).

Homework: 10%

Tests: 30% each

I will use plusses and minuses with the letter grades, when they’re warranted. Note: there is no A+ grade for any class. I will abide by CSULA’s policy on incomplete grades; see www.calstatela.edu/univ/advise/bb/Grade_Related_Information/incomplete.htm

Topical outline

The following is the preliminary day-by-day plan for the course.

Sept. 26

28

Oct. 3

3.1, 3.2

3.4, 3.5

3.6, 4.1

Oct. 31

Nov. 2

7

8.2, 8.3

Review

Test #2

5

10

12

17

4.2, 5.1

5.2, 5.3, 5.4

Review

Test #1

9

14

16

21

9.1, 9.2

9.3, 10.1

10.2, 10.3

10.4, 11.1

19

24

6.1, 6.2

7.1, 7.2

23

28

11.2, 11.3

Review

26 7.4, 8.1 30 Test #3

I will abide by the University Policy on academic dishonesty. In particular, all writing in this class should be your own. You do not need to do original mathematics—but you do need to write original sentences about mathematics.

Students with Disabilities

Reasonable accommodation will be provided to any student who is registered with the Office of Students with

Disabilities and requests needed accommodation.

Note: any of this could change at any time

I’ll let you know if it does. But if you’re not in class when I mention the change—or if you’re in class but spacing out—you’re still responsible for knowing about it.