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
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.