09-240/Classnotes for Thursday September 10

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Date: Thurs. Sept. 10, 2009

  • Professor's name: Dror Bar-Natan
  • Solve systems of equations

  • how? when? one/many?
  • This describes the small-scale 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 long-term behaviour of almost anything...
  • Do all this without choosing coordinates.

2. Do everything over other “systems of numbers”

  1. real numbers
  2. rational numbers
  3. complex numbers (things like alternating current, circuit)
  4. {0,1} (binary, computer science)

3. Hidden Agenda

  • Learn the basic pure-math 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 09-240- or 09-240/
  • 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:


Aside: The character used for additon:

  • Prof. Dror asked why is sometimes written as ?