06-240/Final Exam Preparation Forum

If you have questions, ask them here and hopefully someone else will know the answer. (Answering questions will probably help you understand it more).

Since many of us (including me) don't really know how to use Wiki's, I suggest that we keep the formatting simple: I will post a template at the top of this page, and if you want to add something just click on the "edit", copy the template, and insert your question. Order the questions with the newest at the top, except for the template question. Finally, once a question is solved, put "SOLVED" in the title and move it below the unsolved questions. In general, I wouldn't retype the question if it's from the book because that's tedious and we all have the book. (By the way, I think you leave a space between lines in the code to make a new line; that is, simply pressing enter once will not make a new line. Also, you can press a button at the top of the math page that lets you put in simple equations.)

Hopefully I won't be the only one using this...

Question Template

Q: How many ways are there to get to the nth stair, if at each step you can move either one or two squares up?

A: This question can be easily modeled by the Fibonacci numbers, with the nth number being the ways to get to the nth stair. This is because, to get to the nth stair, you can come only from the n-1th or the n-2th. This is exactly how the Fibonacci numbers are defined; the proof is simple by induction.

Sec. 1.6, Ex. 29 a.

Q: Does anyone know an efficient way of doing this?

Sec. 1.3 Thm 1.3 Proof

Q: In the first paragraph of the proof, it says "But also x + 0 = 0 , and thus 0'=0." How do we know 0 (that is 0 of V) even exists in W? I understand that we know some zero exists (0'), but not why the zero (0) exists.