Wednesday, April 11th

For Wednesday:

  • On Monday, we did this worksheet on relations.  Finish it at home, and we will discuss it together in class.
  • There’s a 5% presentation/participation/groupwork grade in the class.  In light of the changes to our groupwork requirements in the second half of semester, I’m replacing the system with the following simpler, more generous system.  This should not hurt your grade.
    • You will get a full 5% if you present at least 2 times, and scribe at least 2 times for a group, and hand in at least 3 decent efforts at the individual works on canvas.
    • Your grade will otherwise be proportional to how many of the 7 tasks above you have done decently.
  • In light of the above, you may wish to volunteer to present on one of the two remaining presentation days, which are April 13th and 27th.  You can present any proofs that you wish, including proofs from groupwork or individual work.  The requirement is only that it be mathematically interesting and pertinent to the class.  Even if you have presented twice, you can volunteer, but those needing presentation credit will be given priority.
  • The remaining Logic and Proofs badges will only appear once more, next week.  After that they can be earned in office hour.  We will continue to have Functions, Relations and Synthesis on the badges quizzes.  Soon we will add the remaining badges also.
  • This coming Friday, I will ask you to prove something with functions in the abstract.  To study, I suggest you read the handouts about function having an inverse if and only if it is bijective (with slots, and filled).  The type of problems I may ask are similar to that, so study those carefully.

Additional:

  • You may be interested in CSCI 3434 Theory of Computation.  Here’s the blurb:
    • The theory of computation is the mathematical foundation of computer science, developed by mathematicians when computers were a mere thought experiment.  In fact, the theory of computation is not about computers at all, but about the nature of computation itself: what it means for a mathematical function to be amenable to calculation or computation.  Perhaps surprisingly, some simple functions cannot be computed.  Moreover, these incomputable functions are just the first floor of an infinite-story building; the second floor contains functions which cannot be computed even if one could compute the incomputable functions on the first floor, and so on.  For functions on the ground level, which can be computed, we further ask, how efficiently can they be computed.  CSCI 3434 is accessible to math majors, and the prerequisites will be waived for math majors having taken at least one proof-based course.  (If interested, email the instructor at raf@colorado.edu.)