HOME COURSES NOTES EXAMS RÉSUMÉ

## MATH 250313 — NUMBER THEORY

Description
Course Syllabus (Second 2021/2022, pdf)
An introductory course in elementary number theory, covering topics in divisibility, prime numbers, congruences, primitive roots, quadratic residues, and the RSA algorithm of cryptography.

Textbook
Theory of Numbers (APR 2008, pbk)

Lecture Notes
Number Theory (JUN 2020, pdf)
Outline notes for this course.

The Primitive Root Theorem (APR 2012, pdf)
Notes for the supplementary lecture on the proof of the theorem.

The Quadratic Reciprocity Law (JAN 2019, pdf)
Notes for an independent reading on different proofs of the law.

Programming Notes
Trial Division To Twelve Digits (DEC 2011, html)
A JavaScript factorization program for integers up to one trillion, using trial division by prime numbers from 2 to 999,983.

Online Resources
Number Theory Web (ext)
A starting point for all number theory interests.

Sample Exams
Copies of past exams are available from the archive whose links are provided below. All problems are posted without solution and are intended for practice purposes only.

## MATH 250472 — COMPUTATIONAL NUMBER THEORY

Description
Course Syllabus (First 2010/2011, pdf)
A survey on the two main research topics in computational number theory: factorization and primality proving. Subtopics include the RSA cryptosystem, Fermat factorization, Pollard rho and p-1 methods, quadratic sieve, continued fraction method, Fermat, Euler and strong pseudoprimes, Lucas, Pocklington and Pepin tests, Fermat numbers, and Mersenne primes.

Recommended Textbook
Theory of Numbers (APR 2008, pbk)
Scroll up to Math 313 to see book description.

Lecture Notes
Factoring Composites Testing Primes (NOV 2018, pdf)
Outline notes for this course.

Programming Notes
Testing Primes To Nine Quadrillion (DEC 2011, html)
JavaScript primality testing algorithm based on the Miller-Rabin test.

Online Resources
ECM Factorization (ext)
Java applet for factoring large numbers via the elliptic curve method.

Sample Exams
Copies of past exams are available from the archive whose links are provided below. All problems are posted without solution and are intended for practice purposes only.
 First Second Final XXX F-2010/11 XXX F-2009/10 S-2008/09 S-2007/08 F-2007/08 F-2006/07 F-2011/12 F-2010/11 S-2009/10 F-2009/10 S-2008/09 S-2007/08 F-2007/08 F-2006/07 F-2011/12 F-2010/11 S-2009/10 F-2009/10 S-2008/09 S-2007/08 F-2007/08 F-2006/07