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