Text: Kenneth H. Rosen; Elementary Number Theory and Its Applications (fourth edition);
Addison Wesley, 2000 (544 pp.); (ISBN# 0-201-87073-8).

Grading Scheme:

• Midterm 1, Tuesday September 25, 20%
• Midterm 2, Thursday November 8, 20%
• Final, TBA, 40%
• Weekly Homeworks, 20% total.  The lowest two homework scores will be dropped.

Syllabus:
 

9/4	§1.1	Introduction, Calendar Mind Tricks
9/6	§§1.2,1.3	The Formula for Fibonacci Numbers
9/11	§1.4	Integers and Division
9/13	§2.1	Representing Integers
9/18	§§2.2,2.3	Computers and Integer Calculations (Rosh Hashana)
9/20	§3.1	Plenty of Primes, Review
9/25		Midterm 1
9/27		NOVA special about Fermat's Last Theorem (Yom Kippur)
10/2	§§3.2,3.3	GCDs and the Euclidean Algorithm (Sukkot)
10/4	§3.4	Factoring
10/9	§3.6	Change for a Dollar: integral solutions to equations (Shemini Atzeret)
10/11	§4.1	The Last Digit: working with congruences, Calendar revisited
10/16	§4.2	Dividing through congruences
10/18	§4.3	Chinese Remainder Theorem
10/23	§§4.4,4.6	Polynomial Congruences and Internet Security
10/25	§§6.1,6.2	Fermat's "Little" Theorem and prime imposters
10/30	§6.3	Miller-Rabin Test, Euler's Theorem
11/1	§7.1	The Euler "Totient" Function (Nifsu Sha'ban)
11/6	§7.2,7.3	Perfect Numbers: the oldest unsolved problem, Review
11/8		Midterm 2
11/13	§§7.4	Möbius Inversion
11/15	§11.1	Quadratic Residues: Congruence Squares
11/20	§11.2	Gauss' Golden Theorem
11/27	§11.5	Zero-Knowledge Proofs
11/29	§12.1	Decimal Expansions and Rational Numbers
12/4	§12.2	Continued Fractions
12/6	Handout	Irrationality of zeta(3)=1+1/8+1/27+1/64+1/81+1/125+....+1/n^3+.....
12/11		Review