09240/Classnotes for Thursday September 10
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WARNING: The notes below, written for students and by students, are provided "as is", with absolutely no warranty. They can not be assumed to be complete, correct, reliable or relevant. If you don't like them, don't read them. It is a bad idea to stop taking your own notes thinking that these notes can be a total replacement  there's nothing like one's own handwriting!
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Date: Thurs. Sept. 10, 2009
 Professor's name: Dror BarNatan
 Solve systems of equations
 how? when? one/many?
 This describes the smallscale behaviour of almost everything that has a mathematical description.
1. A matrix is a square or rectangular array of numbers.
 we will learn addition, multiplication, and powers of matrices
 describes the approximate longterm behaviour of almost anything...
 Do all this without choosing coordinates.
2. Do everything over other “systems of numbers”
 real numbers
 rational numbers
 complex numbers (things like alternating current, circuit)
 {0,1} (binary, computer science)
3. Hidden Agenda
 Learn the basic puremath processes of: abstraction, generalizations, definitions, theorems, proofs, notation logic
4. Administration
 can add things to wiki (so long as relevant to course material)
 any page added to wiki must start with 09240 or 09240/
 HW assigned on Tuesday, due in tutorial 9 days later.
 HW graded and returned by following tutorial
5. Classwork done today
 The Real Numbers: a set with two binary operations , (2 inputs, one output) and also with two distinguished elements with the following properties:
R1
Aside: The character used for additon:
 Prof. Dror asked why is sometimes written as ?
 This is a Jewish tradition that dates back to at least the 19th century, and is still used today in Israeli elementary schools. It avoids the writing of the symbol, which resembles a Christian cross. (reference: http://en.wikipedia.org/wiki/Plus_and_minus_signs#Alternative_plus_sign)