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PHILADELPHIA UNIVERSITY



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LECTURE NOTES AND E-BOOKS FOR SELF-STUDY

Programming Notes

A Bisenary Number System
Last updated: November 2013
A guided project to switch integer representations between base-10 and base-36 number systems. A JavaScript applet is provided for the conversion from decimal to bisenary.

Testing Primes To Nine Quadrillion
Last updated: January 2012
Primality testing algorithm based on Miller-Rabin test to the bases 2, 3, 5, and 7. Written in JavaScript, where integer upperbound is 53 bits.

Trial Division To Twelve Digits
Last updated: December 2011
JavaScript factorization program for integers up to one trillion, using trial division by prime numbers from 2 to 999,983. (Note: While these notes have not been updated, the prime database has recently been expanded to 10^7, so we can now factor integers up to 14 digits.)

Textbooks

Discrete Structures in Five Chapters
14.49US$, 198pp, July 2010
Strongly recommended for Discrete Structures Comp 104, Discrete Mathematics Eng 204, as well as a reference text for Set Theory Math 251 and Graph Theory Math 351. Printed by CreateSpace, the pdf softcopies of the five chapters remain available for free download.

Theory of Numbers
14.49US$, 144pp, April 2008
Recommended text for both Math 313 Number Theory and Math 472 Computational Number Theory. Published by BookSurge.

Lecture Notes

These works are licensed under a Creative Commons License.
Creative Commons License

From Groups to Galois
300kb, 54pp, June 2017
Required notes for the Abstract Algebra series of Math 342–442, containing some extra sections on a sketchy introduction to Galois Theory for independent studies.

Discrete Structures
155kb, 24pp, May 2016
The original revision notes and problem sets for Discrete Structures Math 104, now updated again to supplement the main text.

Infinite Countable Sets
80kb, 7pp, January 2013
Extra lecture notes to supplement Homework Set #10 for the Set Theory (Math 251) course, dealing with the total ordering of cardinal numbers.

Finite Abelian Groups
92kb, 10pp, May 2012
Supplementary lecture notes for Abstract Algebra 1 (Math 342) discussing the proof and applications of the fundamental theorem of finite abelian groups.

The Primitive Root Theorem
94kb, 9pp, April 2012
Supplementary lecture notes for Number Theory (Math 313) providing the details of the proof of the primitive root theorem.

Computational Number Theory
229kb, 25pp, January 2011
Required notes for Math 472. The contents are structured in a way that also accomodates students who have not taken the Number Theory course of Math 313.

Logic & Set Theory
199kb, 24pp, December 2010
The old revision notes for Math 251 course.

Number Theory
227kb, 25pp, December 2006
Outdated lecture notes for Math 313. No longer used.

Graph Theory
183kb, 16pp, May 2006
Revision notes from Math 351. Incomplete.

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