Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 115A: Number Theory
Approved: 2003-03-01 (revised 2011-08-01, )

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Rosen’s Elementary Number Theory and Its Applications, 6th Edition; Addison-Wesley; Priced with amazon.com at $99.79 to $137.00
Search by ISBN on Amazon: 9780321500311

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-3

ch 1.1-1.4

Well-ordering principle, induction, divisibility, prime numbers

4-5

ch. 3.1-3.3

Greatest common divisor, Euclidean algorithm

6-7

ch. 3.4

Fundamental theorem of arithmetic

8

ch. 3.5

Factorization methods, sieve methods, Fermat numbers

9-10

ch. 3.6

Linear Diophantine equations

11-12

ch. 4.1-4.2

Congruences

13-15

ch. 4.3

Linear congruences, Chinese remainders theorem

16-18

ch. 6.1

Fermat’s little theorem, Wilson’s theorem

19-20

ch. 6.3, ch. 7.1

Euler’s theorem, Euler-Phi function

20-22

ch. 8.1, 8.4, 8.5

Public-key encryption (RSA)

Additional Notes:

Essentially covers Rosen Ch. 1, 3-6, 8

Have students use Mathematica, Maple or the open source computer algebra system SAGE to explore concepts such as the Carmichael numbers, the distribution of primes and the RSA algorithm.

Learning Goals:

A goal of this course is to ensure students learn to write rigorous proofs and how to communicate mathematical concepts using language. Have students regularly practice writing formal proof that emphasize course content and mathematical thinking using language.