Day 13: mat385

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Today:

• Announcements:
  • First of all, let's push back the homework due today (section 3.3) until Monday. This is the last section covered on the upcoming exam, which covers sections 2.2, 3.1, 3.2, and 3.3.

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

  • In other homework news, let's just combine the two Section 4.1 assignments into one, which will be due the Tuesday after the exam.

  • You also have a project proposal due next week (let's make that Wednesday). This is a one page description of the project.

    This is a proposal: I'll get back to you on any concerns. It should be typed. I want to know that the project will 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).
    See the Project page. Remember that I encourage double-dipping: if you're doing a project in another course that can be piggy-backed with this one, all the better.

  • Homework 3.1 is graded: pp. 171--, problems 3, 17, 24

    Comments:

    • #3: no sweat there. I did write the closed form solution, which I think is pretty interesting.

    • #17: whoops! I did 17, but you all did 18. Well, that's okay, since 18 corresponded perfectly with 24. In the case of 18, you were to prove the result using the Fibonacci recurrence relation. This was no sweat for almost all.

    • #24: things got a little dicier here, because you were to prove it using the 2nd principle of mathematical induction. And because you require the result to hold for two of the previous cases, you need to prove the result for two base cases.

      That's what most people missed.

      Some of you presented it as an induction argument, but then repeated the work of #18! If you never invoke the inductive hypothesis, then you're not doing an induction proof....

  • We have an exam in a week. This new material will not be on the exam. However, don't slack off! I've nonetheless made the homework for this section due the Tuesday following the exam.

• Today: we'll finish section Section 4.1: Sets -- to infinity, and beyond!
  • First up: Binary and Unary operations on sets
  • Finally we finish section 4.1 with a bang:
    1. Motel $\infty$
    2. an infinite number of bigger and bigger infinities
    3. The marked up highlights pdf for Section 4.1;
    4. The pdf of "infinite school buses"; and the proof of larger infinities

• Links:
  • Nothing new to report.