So here's the study material for thursday. the first section is about algebraic manipulation, so if you feel comfortable with exponents and the distributive property, feel free to skip it. Section 2 deals with the concepts of sets and functions, which will be essential tools/language for quantifying/describing the objects of our study (the set of congruence classes modulo p), so make sure you can understand the following notations:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

E = {2n: n is a member of Z} (even numbers)

For every x in Z, let f:Z->E be given by f(x)=2x (a function from the integers to the even numbers)

I={g:Z->Z, such that g(0)=0} (the set of functions (not numbers) from the integers to the integers (or a subset of the integers, like the even numbers) such that 0 maps to itself...note that f, as described above, is a member of this set since f(0)=2(0)=0)

the rest of the stuff is not necessary, but could be interesting to some...drop any questions on the wiki, and good luck

PROVISIONAL IDIOT

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things you should already know:

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distributive, associative, communitive properties

http://www.purplemath.com/modules/numbprop.htm

exponents, page 1&2

http://www.purplemath.com/modules/exponent.htm

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things to study for class:

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set notation

http://www.purplemath.com/modules/setnotn.htm

functions

http://www.purplemath.com/modules/fcns.htm (read the first part and study the pictures)

http://mathworld.wolfram.com/Bijection.html

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what we will learn

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http://www.ams.org/featurecolumn/archive/codes1.html

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other things of interest

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groups

http://en.wikipedia.org/wiki/Group_(mathematics)

http://en.wikipedia.org/wiki/Lagrange%27s_theorem_%28group_theory%29 (generalization of euler's theorem)

complexity theory

http://en.wikipedia.org/wiki/Computational_complexity_theory

http://en.wikipedia.org/wiki/Complexity_class

http://en.wikipedia.org/wiki/P_versus_NP

elliptic curves

http://en.wikipedia.org/wiki/Elliptic_curve_cryptography

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