Day 13, Mat385

Last time

Next time

Announcements
- The Zooms continue
  A menu of our past zooms...
- I hope that you'll have a nice spring break!
- When you come back, we'll be starting section 4.1.
- Your project proposal is due by the Tuesday after spring break (3/15).
  Your proposal is just a one-page description of what you'd like to do. Then we'll no doubt iterate!:)
- This from NKU's President, RE Covid:
  Effective Tuesday, March 8, masks will be optional on campus, with these exceptions:
  - Masks are required during class meetings in classrooms and lab spaces, through Monday, March 21.
  - Masks are required in NKU Health, Counseling and Student Wellness facilities.
  - Masks are required for at least five days following diagnosis of or exposure to COVID-19, per CDC policy.
  - Individual employees may continue to require masks in individual private offices where they meet with students, other employees or visitors.
  So one more week, following Spring break, we wear the masks; and then I think that I will be maskless in class.
Last time:
- We wrapped up Section 3.2 (Recurrence Relations), and
- Started on Section 3.3 (Analysis of Algorithms)
Today: We'll
1. wrap up Section 3.3 (Analysis of Algorithms). In particular, we'll spend a little more time with the Euclidean algorithm.
  The Euclidean algorithm is ancient, and yet it has a fundamental connection to the Fibonacci numbers.
  When it comes time, we're going to be doing a little drawing with some graph paper. If you're attending on-line, you'll want to grab some of your own, or print some off.
  Here's our work from that session:
  1. Figuring out the algorithm as tilings of rectangles, and recursion.
  2. Worst-case scenario: a Fibonacci spiral
2. A graph I'll refer to in a bit:
  
  This has to do with how many searches you need to do before it becomes more useful to sort your list with a mergesort and binary search, rather than to simply sequential search.
Links:
- Recursive computation of Fibonacci numbers (in lisp)
- Recursive computation of rows from Pascal's triangle (in lisp)
- "String exponention" (in lisp)
- Here is the recursive selection sort algorithm, in lisp:
- Here is a recursive binary search algorithm in lisp:
- Closed-form computation of Fibonacci numbers (in lisp)
- Some examples of the Euclidean algorithm:
  1. Simple and clean recursive Euclidean Algorithm in lisp:
  2. Written as a while loop, using the recurrence relation:
- Here is a recursive bubbleSort algorithm in lisp
  
  (coded up following our author's algorithm, in section 3.3, p. 214, as closely as possible).

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