Day 14, Mat385

• Quiz today is over sections 3.1 and 3.2: recursion and recurrence relations.

• We have an exam in a week. A little more info on that:
  • It will cover sections 1.1-1.4; 2.1&2.2; 3.1-3.3.
  • I'll have at least two problems straight off the homework.
  • There will be a problem you can drop (although there may be some that I require that you attempt).
  • Some old exams covering some of this material; here are some some old second exams, which will cover material which will not be on this exam.

• Come with your questions next time. I will give an overview as well.

• We wrapped up Section 3.3 (Analysis of Algorithms), spending some time with the Euclidean algorithm.

  It's a little mysterious until you see the geometry of the method -- recognizing that it can be considered a rectangle tiling problem -- and understand "the recursive idea". In the case of the Euclidean algorithm, it's about "casting out squares" to get to a smaller rectangle; then do it again.

  It also led us to understand the worst-case scenario -- casting out a single square each time. Working backwards from a single unit square, we could see that it is successive Fibonacci numbers which case the algorithm the most agonizingly slow convergence to its solution.

  Here's my work from that exercise.

We'll see how far we can get on Section 4.1 (Sets).

• Pi Day: How One Irrational Number Made Us Modern: The famous mathematical ratio, estimated to more than 22 trillion digits (and counting), is the perfect symbol for our species's long effort to tame infinity.