# Journal entry about mathematics, writing help

**Question description**

One page is fine.

Write a journal entry about mathematics. You can touch on the material in this course or other mathematics that you have been thinking about. The idea is to give yourself a chance to think creatively, carefully, and deeply, rather than simply answering canned questions.

Here are some ideas to get you started. I'm not suggesting that you have to write about one of these (but you can if you want). Instead, I'm giving examples of the kinds of questions you might think about. You are free to be as creative (or eccentric) as you want. You can also drop a blob of barely-thought-about brain slobber, but then you are wasting your time and ours.

A few ideas for journal entries

- Simple: Write a vector class in a programming language of your choice. Medium-hard followup: would you use exact arithmetic or floating point arithmetic? What are the advantages and disadvantages of each? Harder followup: can everything you have learned about vectors so far be implemented on a computer? Is there a vector problem that cannot be done by a computer?
- Simple: What is the best quadratic surface approximation to the quad? How would you even think about constructing one? (You could just write an entry about how you would go about trying to do this.) Can you predict where a skateboard will end up if you drop it near the art building? Follow-ups: what about higher degree models (cubic equations)? When is a quadratic model better or worse than a linear model? What about making a lot of quadratic models for little patches of the quad and trying to glue them together?
- What is the history of the theory of vectors? Who invented them? Why? What are they used for outside of calculus?
- What are the real numbers? (This one is the most mathematically sophisticated -- but shortest -- question here!)
- What is a vector differential equation? Can you figure out the motion of a pendulum that is free to rotate with two degrees of freedom around its anchor point?
- Read part of Newton's original work about calculus. Does his definition of derivatives agree with ours? How does he deal with high-dimensional problems?
- And more!

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