Day 15: mat385

Last time

Next time

Today:

• Announcements:
  • Section 3.3 homework; graded two, 14 and 38 (with 26 from 3.1 thrown in for good measure).

    General comments:

    • #14: Best case is an already sorted list; worst case is a reversed list. In the best case there's not an exchange; in the worst, there's an exchange for each comparison.

    • #38: I took the instructions to mean that you could assume both #37, and #26 from section 3.1. A lot of you thought you'd better do #26; so I did, too.

      The biggest thing I saw was that you forgot what you were to show. Read the questions, and make sure that you respond to what's asked.

    • #26: You need two base cases and to use the second principle of mathematical induction to prove this one. Study this example (in my on-line version above), if you don't understand those ideas.

    • In the links below is a sample of bubble sort in action, programmed in lisp. Too much fun not to do it.

      I love recursion!

  • Today is a review, for exam 2 this weekend, covering sections 2.2, 3.1-3.3.

    Exam 2 will operate about like the prior exam. You'll be allowed a one-page sheet of notes you can use. You'll take it using a lock-down browser.

    The exam will open at 5:00 pm on Friday, and close at 9:00 pm on Sunday. It should take about an hour.

  • Previous Exam 1s and 2s from other years (these may cover more or less material -- and typically we had more time -- 75 minutes):?

    1. Here are some first exams from years past.
    2. Here are some second exams from years past. (Lots of this material we haven't covered yet!)

  • The two Section 4.1 assignments can be combined into one, which is due next Tuesday after the exam.

  • Your project proposals will be evaluated soon, and I'll let you know if I have any concerns. I'll be making everyone an account on the wiki.

    This is a proposal: I'll get back to you on any concerns. The project should be

    • interesting to you (and nice if it's of interest to others, as well!);
    • not overwhelming;
    • doable within the time frame (projects are due April 23).

• Today: I'll go over some highlights from the four sections covered on the exam.
  • Section 2.2: Induction
  • Section 3.1: Recursive Definitions}
  • Section 3.2: Recurrence Relations}
  • Section 3.3: Analysis of Algorithms
  • A stroll through the sections.

• Links:
  • 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).

    Since I had to grade a bubbleSort problem, I couldn't resist coding it up.

  • I've discovered a really interesting fellow, James Tanton, who makes a fascinating presentation on Exploding Dots!

    James shows us how to conceive of different bases, algebra as arithmetic, the geometric series as infinite algebra, and the Fibonacci numbers as an infinite sequence of dots -- all this, via the magic of exploding dots! Very entertaining.

    We'll probably try to invite this guy to campus -- hopefully this fall. I'm working on that!