
NUMBER THEORY COURSE PAGE
250313 — NUMBER THEORY
Description
Course Syllabus (Second 2022/2023, 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)
Published by BookSurge, this affordable book may be purchased online from Amazon.com. The first six chapters, which pretty much span the entire course, can be downloaded for free as pdf files following the above link.
Lecture Notes
Number Theory (APR 2023, 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.
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 p1 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 MillerRabin 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.
Copyright © 2002–2023 Amin Witno
This page belongs to the personal folder of Amin Witno and does not necessarily represent the philosophy and values of Philadelphia University or the Department of Basic Sciences in particular.

