Math 170 Topics (Fall 2007)

Math 170: Ideas in Mathematics (Fall 2007)

Tuesday, Thursday 12 pm - 1:30 pm DRL A1


Faculty: Nate Ackerman TA: Andrew Rupinski
E-mail: nate AT math.upenn.edu E-mail: rupinski 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.

Day of Week Date Topics Reading
Thursday September 6
Introduction, Explanation of Grading, Math Anxiety.
Heart of Math Chapter 1
Tuesday September 11
Natural Numbers
Pigeonhole Principle 
Heart of Math Chapter 2.1
Thursday September 13
Fibonacci Numbers
Continued Fractions
Golden Ratio
Heart of Math Chapter 2.2
Tuesday September 18
Prime Numbers
Proof of Prime Infitude
Definition of Relatively Prime
Fundamental Theorem of Arithmetic
Heart of Math Chapter 2.3
Thursday September 20
Basic Types of Codes
Problems With These Codes
RSA
Heart of Math Chapter 2.4
Tuesday September 25
Rational vs Irrational Numbers
Heart of Math Chapter 2.5, 2.6
Thursday September 27
Cardinality, Bijections, Injections and Surjections
Definition of Infinite
Definition of Countable, Rationals are Countable
All Line Segments In The Plane The Same Cardinality
Heart of Math Chapter 3.1, 3.2, 3.5
Tuesday October 2
Reals Are Uncountable
Order on Cardnalities
A <= B and B <= A implies A = B
Heart of Math Chapter 3.3
Thursday October 4
Powerset
Continuum Hypothesis
Heart of Math Chapter 3.4
Tuesday October 9
Pythagoras' Theorem
Golden Rectangle
Heart of Math Chapter 4.1, 4.3
Thursday October 11
Platonic Solids
Heart of Math Chapter 4.5
Tuesday October 16
Fall Break

Thursday October 18
Review

Tuesday October 23
MIDTERM

Thursday October 25
Discrete Dynamical Systems
Population
Spider Diagrams
Game of Life
Heart of Math Chapter 6.1, 6.2
Tuesday
October 30

Fractas
Sirpinski Gasket, Cantor Line
Self Similarity
Heart of Math Chapter 6.3
Thursday November 1
Complex Numbers
Fundamental Theorem of Algebra
Mandlebrot and Julia Sets
Chaos
Stable and Unstable Equilibrium
Heart of Math Chapter 6.4, 6.5
Tuesday November 6
Definition of Dimension
Heart of Math Chapter 6.6
Thursday November 8
Basic Probabilities
Lets Make A Deal
Birthday Question
Heart of Math Chapter 7.1
Tuesday November 13
How to Calculate Probabilities
Heart of Math Chapter 7.2
Thursday November 15
Coincidences
Infinite Monkey Theorem
 
Heart of Math Chapter 7.3
Tuesday November 20
Calculating Probabilities Of Multiple Events
Induction
Heart of Math Chapter 7.4
Thursday November 22
Thanksgiving

Tuesday November 27
      

Thursday November 29
      

Tuesday December 4
       

Thursday December 6
Review

Thursday
December 13
FINAL EXAM
 

This page was created by Nate Ackerman, and last revised on August 27, 2007.