All posts by profstange

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.)

Monday, April 9th

For Monday:

  • We will start relations in honest on Monday.
  • Badges quiz may include new relations Badges.
  • To prepare, you can read Hammack, Chapter 11, especially Sections 11.0 and 11.1, and do some exercises.  But don’t worry if anything is confusing — just bring your questions!  We will work on it in class.

Monday, April 2nd

I hope everyone is having a great break!  Please use break to catch up on anything you need, and plan ahead.

For Monday:

  • There will be a badges quiz.  It will cover Logic, Functions, Proofs, Synthesis.   It will include Logic I,II,IV, Proofs I,II for the last time.
  • You can earn badges in office hour (W/Th 1 pm):  you can earn any badge which has stopped appearing on the quiz, so Sets I-IV, Logic I,II,IV and Proofs I,II.  See this old post for details how to do this (it requires preparation).  Maximum one badge per week, so plan ahead.  This is an excellent way to bring your grade up by making an extra effort during the last weeks.
  • Look ahead:  the week following break will be another individual assignment due Friday.  I’ll post it shortly.  On that Friday we’ll have another induction proof quiz (because induction is so important).

Friday, March 23rd

For Friday:

  • Proof Quiz will be a proof that a function is/is not injective/surjective.  Read Hammack Section 12.2.  Examples 12.4 and 12.5 are ideal models, as are exercises 2-10 (where “verify” means “prove or disprove” (disprove means prove the negation).
  • Reminder that individual homework is due.  The assignment is under Resources (above) under Groupwork. (But you can do it individually.)  Hand in on canvas.
  • You can still earn badges in office hour Wed/Thur, as explained previously.
  • In class, we will continue talking about functions and cardinalities.

Wednesday, March 21st

For Wednesday:

  • Keep thinking about the relative cardinalities of the natural numbers, integers, rationals and reals.  Think about the cartesian product of the integers with itself, too.
  • Read Hammack, Section 12.2.  Do some exercises from 12.2 — maybe 5 of them.
  • Get a start on the Assignment for this week, which you’ll hand in on canvas.  It’s listed under the Groupwork section of Resources.  For more info on how this individual assignment replaces a groupwork, see the post on Monday.

Monday, March 19th

Thank you for your feedback on the midsemester survey!  It was very very helpful — thanks for writing so much.  Here’s what we will do:

  • We will have two more groupwork assignments with presentations, due/presented on April 13th and 27th.  We will mix up groups one more time beforehand.
  • On the non-groupwork weeks, I will still assign some proofs for everyone to write up individually and hand in on canvas.  You will be allowed to work with others, if you like.  They will also be handed in on canvas and I will assign a simple grade based on completeness, but can’t provide detailed feedback via canvas.  I can give one-on-one feedback by request in office hour.
  • On presentation days, I may choose from individual assignments and group assignments for presentations.

For Monday’s class:

  • I have posted an assignment (under groupwork on Resources) due for hand-in on canvas next Friday.  You may work with others if you like, but your write-up should be your own.  Some suggestions:
    • Look for other students in MARC, 6-8 pm Tuesday, Wednesday and Thursday.  (I’m just suggesting a general time, there’s no implied guarantee or requirement here.)  Note: MARC tutors don’t specifically cater to 2001, but it’s still a good place to meet.
    • Contact others via canvas.
    • Continue to work with your group or old group if desired.
  • Monday’s badges quiz will include the same topics as last time plus some Synthesis.  Synthesis badges are usually harder: they involve interesting combinations of your knowledge of other badges.
  • If you’re having trouble negating “if-then”, take a look at the video (see also Hammack 2.10).  If you’re having trouble with quantifiers, read Hammack, Chapter 2.7 and 2.9 and do exercises there.
  • The following badges will appear only two more times (last time is the Monday after break):  Logic I,II,IV, Proofs I,II.
  • Note: You can still earn Sets badges in office hour before break (see this old post for details).  After break, you can earn Logic/Proofs badges in office hour for a few weeks (but Sets will be finished).
  • I suggest that over the weekend you get a start on the assignment, and prepare for Monday’s badges quiz.

 

Friday, March 16th

Too bad it isn’t Pi Day forever.  I hope you all got some free pie.

For Friday:

  • The quiz will be on induction.  Please study for it, with the goal of understanding the main idea behind induction.  In the past few weeks of posts/materials you will find reminders and suggestions for problems/readings/study.
  • No presentations, since no groupwork.  We will, however, work on proofs.
  • If you haven’t already filled out the anonymous midsemester feedback survey on canvas, please please do so.

 

Wednesday, March 14th

Late addition!  Wednesday is Pi Day!  Some activities:

  • Please join your math community for free fruit pie and pi-related activities in the foyer of the Math building (near Math 175) from 9am until 4pm.
  • The next undergraduate Math Club talk for this Spring 2018 semester will be given by Dr. Robin Deeley, this Wednesday, March 14 from 5 – 6pm in MATH 350.  Title: Shift dynamics Abstract: Dynamical systems were introduce by Poincaré in his study of the behavior of the solar system. I will discuss a number of dynamical systems coming from linear algebra and calculus before moving to an introduction to shift spaces and their dynamics. The concept of sensitivity to initial conditions will be emphasized.  Free pizza-pi(e) and drinks will be provided.

For Wednesday:

  • Please fill out the anonymous midsemester feedback survey on canvas.
  • Review the terms on your Second Functions Worksheet, and make sure you have completed Problems 1 and 2 and feel confident about the answers.  In class Wednesday, we will finish this worksheet, so bring it back to class.
  • Read Hammack, Chapter 12 up to the end of 12.2 (pages 196-204).  This covers functions as we have been discussing them.  Note that Hammack uses the term “relation” in Definition 12.1 on page 197.  This really just means “subset of the Cartesian product”, as we discussed in class.  (No need to read Chapter 11 right now.)
  • Do some 12.1 and 12.2 Exercises — whatever you feel is interesting.
  • Do at least one inductive proof — I suggest Chapter 10, Exercise 10.