Math 170: Ideas in Mathematics (Fall 2008)

Tuesday, Thursday 10:30 am - 12 pm DRL A8


Faculty: Nate Ackerman TA: David Favero TA: Donna Dietz
E-mail: nate AT math.upenn.edu E-mail: favero AT math.upenn.edu
E-mail: dietzd AT math.upenn.edu

This is the approximate schedule of what should be covered in class with the associated reading. Check back to this page for updates throughout the course. With regards to the reading column, Heart of Math refers to the textbook by Burger and Starbird while Magic Numbers refers to the textbook by Gross and Harris.

Topic
 Summary Reading
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, 12.1-2
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, 11.1-2, 11.4-5, 12.3-4, 13
4
Modular arithmetic
Roots
  Fermat's Little Theorem
Euler's Theorem
Heart of Math Chapter 2..4
Magic of Numbers Chapter 15-20
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
Heart of Math Chapter 3
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
Heart of Math Chapter 7

This page was created by Nate Ackerman, and last revised on September 2, 2008.