1

Natural
Numbers 
Pigeonhole
principle 
Reducing
to
a previously solved problem 
Proof
by
induction 
Definition
by Recursion 
Multiplication,
Exponential, Factorial 
Division,
Rational Numbers 

Heart of Math
Chapter 2.1

Magic of Numbers Chapter
1, 2.2, 2.4, 7.2  7.4, 12.12


2

Fibonacci Numbers

Continued Fractions

Golden
Ratio


Heart of Math
Chapter 2.2, 2.4


3

Prime
Numbers 
Proof There Are Infinitely
Many Primes 
Fundamental
Theorem of Arithmetic 
Factorization

Greatest
Common Divisor 
Relatively
Prime

Euler's
Function


Heart of Math
Chapter 2.3

Magic of Numbers Chapter
10, 11.12, 11.45, 12.34, 13


4

Modular
arithmetic 
Roots 
Fermat's
Little Theorem 
Euler's
Theorem 

Heart of Math
Chapter 2..4

Magic of Numbers Chapter
1520 

5

Basic Types of Codes:
Permutation, Cyclic, The Unbreakable Code

Problems With These Codes

Difficulties Because
of Computers

RSA


Heart of Math
Chapter 2.5

Magic of Numbers Chapter
21, 22


6

Rational vs Irrational
Numbers

Decimals

Square
Root of 2 Is Irrational


Heart of Math
Chapter 2.6

Magic of Numbers Chapter
12.6, 14


7

Cardinality, Bijections,
Injections and
Surjections

Definition of Infinite 
Definition of
Countable,

Rationals are
Countable 
All
Line Segments In The Plane The Same
Cardinality 
Reals
are Uncountable



8

Platonic
Solids 
Pythagoras
Theorem 

Heart of Math
Chapter 4.1, 4.5


9

Discrete
Dynamical Systems 
Models
of Population 
Spider
Diagrams 
Stable,
Unstable Equilibrium 
Chaos 
Game
of Life 

Heart of Math
Chapter 6.2, 6.5


10

Fractals

Self
similarity 
Definition
of Dimension


Heart of Math
Chapter 6.1, 6.3


11

Complex
numbers

Fundamental
Theorem of Algebra

Mandlebrot
and Julia Sets 

Heart of Math
Chapter 6.4


12

Basic
Probabilities, Lets make a deal, the Birthday Question

What
are probabilities? How to Calculate them. 
Multiple
Events, Dependent and Independent Eventa 
Coincidences
and the Infinite Monkey
Theorem 

