1. What is chaos theory? What is the Lorenz attractor; be able to draw it. Using examples, what does chaos theory suggest about the limits of mathematical knowledge. Is there order in chaos? Explain.
2. What is meant by calling mathematics a language? What does it describe? How well does it interact with our spoken or written language?
3. Illustrate how mathematics can be superior to common sense in certain cases.
4. How does one prove a theorem? How many cases must be tested in order to "prove" the validity of the theorem?
5. What are Fibonacci numbers? Give some examples from nature. What did Fibonacci numbers suggest about mathematics and nature? What is the golden ratio (PHI) ? Relate the golden ratio of Fibonacci to beauty.
6. What is non-Euclidean geometry? Which postulate of Euclid is questionable? What implications does this have for the structure of the universe? Who formulated these alternate views?
7. How supportable is the claim that mathematics is infallible? Does 1 + 1 = 2 ? How does mathematics fit in with 'the real world'.. Link this to review question #3. What are non-linear equations? Give examples of non-linear systems in society.
8. Explain how mathematics produces a unique kind of knowledge using axioms and deductive reasoning. What are the other essential elements of mathematics? They are: 1. use of basic concepts (like: point, number, line, complex and negative numbers....). 2. abstraction. 3. idealization. 4. use of symbols. 5. seems to describe nature.
9. How can statistics be manipulated? Give strengths and weaknesses of the types of stats (Unscaled scores. Scaled scores. Position rank scores) we crunched in class.
10. Be aware of the contents of the articles as given by the presenters in class: They were - Dark Matter, Dark Energy, God Particle, ESP, Quantum Computers, Brain Microtubules, Pollock & Chaos, Godel, String Theory, Paul Erdos.
11. Be able to explain any of the "new physics" terms: double slit experiment, particle-wave duality, Copenhagen Interpretation, quantum, Schrodinger’s cat, particle accelerators like CERN and Fermilab, quantum logic/ polarized light, implications of Relativity, twin paradox, Heisenberg Uncertainty Principle, EPR thought experiment, Bell’s theorem, quantum non-locality, entanglement.
12. Explain what Godel’s theorem is and its implications for mathematics.
13. Know the questions from the article: 'Weirdness Makes Sense'.
14.From the YouTube videos called "The Elegant Universe" - Have a basic idea of how string theory tries to unify quantum mechanics and relativity but has problems being believed.