| Monday |
January 8 |
| Introduction, Explanation of Grading, Math Anxiety. |
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Begin Coincidences, Birthday Problem
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| Math Jazz: Chapter 1 |
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Magic Numbers: Chapter 5
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| Wednesday |
January 10 |
| Related and Unrelated Events |
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Monte Hall Game
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How to Calculate Probabilities
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| Friday |
January 12 |
| More Coincidences |
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Finishing up with Probabilities
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Calculate Probabilities
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| Monday |
January 15 |
Martin Luther King Jr. Day (no class)
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| Wednesday |
January 17 |
| Chaos, Iterations and Small Variations. |
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Butterfly Effect
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Rounding Error
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| Population Formula |
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| Wednesday |
January 24 |
| Complex numbers, Complex plane |
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Mandelbrot and Julia sets
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Coastlines of infinite length
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| Wednesday |
January 31 |
| Fractals |
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Sierpinski Gasket
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Cantor Line
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Definition of Dimension
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| Monday |
February 5 |
| Definition by recursion |
| Factorial |
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Proof by Induction
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| Wednesday |
February 7 |
| Fibonacci numbers |
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Breeding Rabbits
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| Friday |
February 9 |
| Golden Ration |
| Relationship between Squares and Rectangles
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| Beauty and the Ancient Greeks
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| Monday |
February 12 |
| Golden Ration and Fibonacci numbers |
| Continued Fractions |
| Limits, Cauchy Sequences, Real numbers
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| Rational and Irrational numbers
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| Equivalence classes
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| Friday |
February 17 |
| Pascal's Triangle |
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Some Nice Properties
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Sierpenski's Gasket and Pascal's Triangle
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| Monday |
February 20 |
| Binomial Formula |
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Expanding out (x + y)^n
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Prove by induction that this corresponds to Pascal's Triangle
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| Wednesday |
February 22 |
| Prime numbers |
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Relative Prime Numbers
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Divisibility
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| Friday |
February 24 |
| Rational numbers |
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Square root 2 is not rational
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| Irrational Numbers
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| Friday |
February 24 |
| Modular Arithmetic |
| Examples of Clocks and Computers
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| Operations in modular arithmetic
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| Friday |
February 24 |
| Show that Z/(p) is a field when p is prime (but
don't define field) |
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Explain difference between Z/(p) and Z/(m) where m is not prime
|
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| Magic of Numbers: Chapter 17 |
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| Monday |
February 26 |
| Basic Codes |
| (Possibly) Talk about Enigma
|
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| Magic of Numbers: Chapter 21 |
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| Wednesday |
February 28 |
| Fermat's Little Theorem |
| Taking kth Roots |
|
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| Friday |
March 2 |
| Public Key Cryptography |
| RSA |
|
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| Monday |
March 12 |
| Limits on Public Key Cryptography |
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Limits of Computer Power
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| Wednesday |
March 14 |
| Primitive Recursive Functions |
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Encoding Primitive Recursive Functions
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| Friday |
March 16 |
| Halting Problem |
| Non-Primitive Recursive Functions |
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Cantor's Diagonal Argument
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| Monday |
March 19 |
| Recursive/Computable Functions |
| mu Operator |
| Church-Turing Thesis |
|
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| Wednesday |
March 21 |
| Recursive/Computable Sets |
| Recursively/Computably Enumerable Sets |
|
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| Monday |
March 26 |
| Turing Degrees/Reducibility |
| Recursive Relative to a Function |
| Turing Jump |
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| Wednesday |
March 28 |
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| Wednesday |
February 28 |
| Connections to Modern Computers |
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Churches Thesis
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| Friday |
March 2 |
| Encoding Computer Programs as Numbers |
| Computer Programs Which Run on Programs |
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| Monday |
March 12 |
| Halting Problem |
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Why it isn't a solution to Churches thesis
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Difference between Computable and Computably
Enumerable
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|
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| Wednesday |
March 14 |
| Definition of Size of a set |
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Monte Hall Game
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Calculate Probabilities
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|
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| Friday |
March 16 |
| Related and Unrelated Events |
|
Examples of finite and infinite sets
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|
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| Monday |
March 19 |
| Operations on Infinite Sets |
| +, *, Exponent |
|
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| Wednesday |
March 21 |
| There are more reals than natural numbers |
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| Friday |
March 23 |
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| Monday |
March 26 |
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| Wednesday |
March 28 |
| Topology |
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Equivalence with Clay
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| Friday |
March 30 |
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| Monday |
April 2 |
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| Wednesday |
April 4 |
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| Friday |
April 6 |
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| Monday |
April 9 |
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| Wednesday |
April 11 |
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| Friday |
April 13 |
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| Monday |
April 16 |
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| Wednesday |
April 18 |
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| Friday |
April 20 |
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