Here you will find all the X-treme Thinking lesson notes and problem sets for Spring 2008.
Suggested Presentation Topics
These are some topics and subtopics that I really wanted to teach, but barely had time to mention them in the alloted class time, if at all. They would all make great presentation topics, and you can get your material by reading the notes and/or talking to me.
- Proofs
- Fundamental theorem of arithmetic
- Prove anything, it's all good
- Geometric constructions (compass and straightedge)
- How to construct an irrational value
- What's possible and impossible to construct
- Graph theory
- Graphs as visualizations of binary relations
- Proving some basic properties of graphs
- Mathematical Induction
- Mathematical induction vs. inductive (scientific) reasoning
- Strong induction
- Correctness of closed-form expression for Fibonacci sequence
- Strategy-Stealing Argument
- Why it's non-constructive
- Games it works on, games it doesn't
- Rational and Irrational Numbers
- Decimal representation
- Is there always one of each between any two real numbers?
- Proving that numbers are irrational (locking them into their cage in the irrational zoo)
- Counting
- Miscellaneous topics (I just think they're cool)
- The golden ratio
- Mental math tricks
- Pi, e
- Peano arithmetic
- Sequences (e.g. Fibonacci)
I will add more topics each week.
Note: You can do the presentation in a group of 2 or 3, or by yourself.
