Reflection #1 - Due Wednesday, January 22
We have touched on the question "What is mathematics?" this week and will continue to do so
over the course of this class. Talk about your own personal experience of mathematics.
Please be up-front and honest!
Some questions you may wish to talk about: Have you always loved math? Have you always hated math?
Did you use to love math, but then had a bad experience at some point? What are some of your earliest
memories about math (either good or bad!)? Are you excited about this class? What do you wish to get
out of this class?
Reflection #2 - Due Friday, January 31
In class, we talked about Fibonacci numbers and various places where they show up in nature. We
also used these numbers to generate the golden ratio, and we talked about golden rectangles and their
possible connection to art and architecture. My main question is, simply, "Do you believe any of this?"
Some questions you may wish to address: How can we explain the appearance of Fibonacci numbers in pineapples,
sunflowers, pinecones, etc.? Does nature understand mathematics? Is God a mathematician? Do Fibonacci numbers
really show up in nature more than other numbers? Can you find more examples of Fibonacci numbers in nature
that we didn't get to talk about in class? Are golden rectangles more "ideal" than other rectangles?
Do famous works of art and architecture really contain instances of golden rectangles?
Reflection #3 - Due Wednesday, February 12
We have seen two real mathematical proofs: a proof that there are infinitely many primes and a proof that
the square root of two is irrational. We also watched the BBC documentary called
"Fermat's Last Theorem" about Sir Andrew Wiles'
proof of this theorem. This reflection deals with your feelings about mathematical proof and your thoughts
about the movie we watched.
Some questions you may wish to address: Could you follow the proofs we did in class? Should we care at all about
"pure math" (math with no apparent connection to anything in real life)? Were you surprised at how emotional Wiles got
when he talked about his proof? Did the mathematicians in the movie fit your (or society's) stereotypes about
mathematicians?
Reflection #4 - Due Friday, February 28
Chapter 3 really stretches the mind. By thinking deeply about what it means to count, we learned how to
compare the sizes of infinite sets. We showed that there are different sizes of infinity, and we learned how to
create a larger set from any set. This means there are actually infinitely many sizes of infinity! We also
talked about the Continuum Hypothesis, which is neither true nor false! This reflection deals with your feelings
about all this craziness.
Some questions you may wish to address: Did this chapter interest you at all? Did you enjoy thinking about deep
philosophical/mathematical questions even though they have no direct bearing on your life? Were you surprised
that certain people personally attacked Cantor because of his ideas? Were you shocked to learn that there are
infinitely many sizes of infinity? Isn't it wild that certain mathematical questions are neither true nor false?