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.
Class website: Follow the link from www.calstatela.edu/faculty/mkrebs
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.
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
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.

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
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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.
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
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).
Grading system
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
for more information.
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
Academic Dishonesty
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.