UWA Academy for Young Mathematicians Lecture Notes

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Below are Lecture Notes and Problems (with most solutions included) for some of the lectures Greg Gamble has given since 1995 to the UWA Academy for Young Mathematicians. For the 2005, 2006, 2007, 2008 lectures, only PDF files are provided (for earlier lectures I also provide DVI and PostScript formats - but these days most visitors to this site won't know what to do with those ;-).)

If you have a machine that is operating under some variety of UNIX then you may possibly have xdvi in which case you may be able to configure your web-browser to run that as an application on the .dvi links below; similarly, you may be able to configure ghostview to view the .ps links below. If you have a PostScript printer then downloading the .ps links and printing maybe your best option. Lastly, Acrobat Reader is available for most operating systems (and might be a plug-in of your web-browser) and can be used to read the .pdf links; use the v3.0 link if you have Acrobat Reader v3.0 and the v2.1 link if you have Acrobat Reader v2.1. (Later versions of Acrobat Reader seem o read the v3.0 links perfectly well.)

If none of the .dvi, .ps, .pdf links make the material below accessible to you send me an email explaining your problem and I'll see what I can do. If you find a mistake I'd certainly like to know, also. (Thanks to all those who have pointed out errors in the past.)

1995 Lectures

Number Theory I [numberI.dvi | numberI.ps | v3.0 numberI.pdf | v2.1 numberI.pdf ]
... topics: Divisibility, Index Laws, Prime Numbers, Important Polynomial Factorisations, Congruence modulo m.
- Problems with Solutions: [numberIprobs.dvi | numberIprobs.ps | v3.0 numberIprobs.pdf | v2.1 numberIprobs.pdf ]
Number Theory II [numberII.dvi | numberII.ps | v3.0 numberII.pdf | v2.1 numberII.pdf ]
... topics: Review of Primes (includes the Sieve of Eratosthenes), Transitivity,
Review of Divisibility and Congruence (includes Binomial Expansions), Fermat's Little Theorem,
Greatest Common Divisor (includes the Euclidean Algorithm), Least Common Multiple.
- Problems with Solutions: [numberIIprobs.dvi | numberIIprobs.ps | v3.0 numberIIprobs.pdf | v2.1 numberIIprobs.pdf ]

1996 Lectures

The Pigeon-Hole Principle [pigeonhole.dvi | pigeonhole.ps | v3.0 pigeonhole.pdf | v2.1 pigeonhole.pdf ]
More Number Theory and an Application to Cryptosystems [codes.dvi | codes.ps | v3.0 codes.pdf | v2.1 codes.pdf ]
... topics: Review (of Divisibility, Greatest Common Divisor), Prime Numbers, Congruence modulo m,
More about Primes (includes the Sieve of Eratosthenes), Cryptosystems.
- Problems with Solutions: [codesprobs.dvi | codesprobs.ps | v3.0 codesprobs.pdf | v2.1 codesprobs.pdf ]

1997 Lectures

Please use the .dvi, .ps or .pdf link instead of the hypertext link, if you can (where one exists), since, your browser will not render some of the text correctly if it is not capable of displaying subscripts, superscripts or tables.
Introductory Comments (half page advertisement of the lectures) [blurb.dvi | blurb.ps | v3.0 blurb.pdf | v2.1 blurb.pdf ]

Number Theory I [numberI.dvi | numberI.ps | v3.0 numberI.pdf | v2.1 numberI.pdf ]
... topics: Divisibility, Prime Numbers, Greatest Common Divisor (includes the Euclidean Algorithm).
- Problems with Solutions: [numberIprobs.dvi | numberIprobs.ps | v3.0 numberIprobs.pdf | v2.1 numberIprobs.pdf ]
Number Theory II [numberII.dvi | numberII.ps | v3.0 numberII.pdf | v2.1 numberII.pdf ]
... topics: Review of Primes (includes the Sieve of Eratosthenes), Congruence modulo m.
- Problems with Solutions: [numberIIprobs.dvi | numberIIprobs.ps | v3.0 numberIIprobs.pdf | v2.1 numberIIprobs.pdf ]
Number Theory III: An Application to Cryptosystems [numberIII.dvi | numberIII.ps | numberIII.pdf ]
- Problems with Solutions: [numberIIIprobs.dvi | numberIIIprobs.ps | v3.0 numberIIIprobs.pdf | v2.1 numberIIIprobs.pdf ]
- Links to other pages: If RSA codes interest you, you may like to check out the following PGP (Pretty Good Privacy) links:
  [ Pretty Good Privacy| The International PGP Home Page| PGP Documentation]