Class Announcements Page for Math 187, Foundational and Discrete Math, Spring 2018

Welcome to the class

This is where homework assignments and other class resources will be posted and class announcements will be made. The most recent material will generally appear on top, except perhaps for a couple of commonly used resources. Here is the course syllabus, to start off with. See you on Monday!

  • General Information and office hours: My office is Mathematics 240A. My office telephone number is 426-3011. I am teaching Math 187 and Math 406 in Spring 2018. My classes are M187 9--9:50 MWF, M406 10:30--11:45 WF. I have the regular weekly PBC meeting 2-3 Tuesday, logic seminar 3-4 Tuesday. I am proposing to have an office hour wih my prospective graduate student 2-3 PM Monday, class office hours MWF 3-4 pm and TTh 10-11 am. At other times MWF from about 8:30 am until about 5 pm I'm very possibly to be found in my office. TTh I do not know what my routine will be (but I will be in in the morning since I have declared office hours then).

    Manual of Logical Style

    This is a document I will maintain in which our official proof strategies and logical rules will be recorded.

    Due Dates

    Your assignments are always due two class sessions after they are assigned, not counting dates of tests, unless I specifically say otherwise. If I do not state a due date, that is how you tell when it is due. I do usually say something about the due date when I assign it and even might remark on it when commenting on the due date, but if I do not do this, it is still due two sessions after it is assigned.

    Final examination and course grades

    Here are the final exam grades and course letter grades. Have a good summer!

    Study resources for final exam

    NEW The RSA worksheet now has solutions (and I fixed some dreadful typos). This is only relevant to an extra credit question on the final; the worksheet, without solutions, will be attached to your test for reference if you choose to work on the extra credit problem (which I wouldnt do unless you were done with everything else).

    NEW: Here are solutions to the modular exponential worksheet. If you turned in your section 37 and worksheet in class, you can pick up your paper with solutions attached (to selected 37 problems as well) at my office door.

    The first batch of posted stuff is copied from the Fall 2016 class page. The comments are from Fall 2016, too: I will probably update them as I look over these sample exams (and I will add the Fall 2016 final if I can find it. Please note that we do not cover permutations and we do not cover graph theory. We could almost do the Chinese Remainder Theorem, and I might actually show you how to do these problems, but it would be a stretch to introduce this at the very last minute. All of this is a function of the class having been reduced from 4 credits to 3 credits: I had a lot more time in those past years. I will also post your tests from this term as resources, and naturally you can use the old hour exams already posted as resources (they are still all on this page: I moved the review material for the old pages to the end).

    The hour exams this term are of course study resources for this test. Here is your Test I (speaking in Spring 2018). Here is Test II (in spring 2018). Here is Test III (Spring 2018). All of the old hour exams are study resources as well (see below). I am planning to find or make solution sets for the spring 2018 exams and post them here some time this week. You may expect that final exam questions on a topic covered on the hour exams will in general terms be similar to what I asked on the hour exams: I am not going to be dreaming up new tricky approaches.

    below this point copied from Fall 2016 final review: comments may be outdated

    The hour exams are of course study resources for this test. Here is a set of solutions to your Test I (speaking in Fall 2013). Here is Test II with solutions (in fall 2013). Here is Test III with solutions (Fall 2013). All of the old hour exams are study resources as well (see below).

    Here is the Spring 2013 final exam.

    Here is the Spring 2012 final exam. You will not have a proof question about graph theory.

    Comments on the following final papers were written in Spring 2012. Their coverage was not identical to yours but they should be useful.

    M187Su06final.pdf A good study resource for you – everything here is something I might ask. This particular test has some irritating typos in it.

    M187F06final.pdf we didnt do bubble sort; otherwise this is quite similar in coverage.

    M187S07final.pdf This is a nice study resource for you, too. Since it is a summer exam, it has quite a lot of the later material (it is also test 4, as it were).

    M187F08final.pdf Disregard the question about groups. This was from the semester where we were trying to save paper and made the students use blue books, so it doesn't have a separate page for each question.

    M187S10final.pdf Also a good test. Notice that problems in the same area are not always phrased the same in these exams; these tests are not clones (some questions are pretty stereotyped, of course).

    Week Fifteen

    Week Fourteen

    Week Thirteen

    Week Twelve (or at any rate, the week after break)

  • Friday, April 4: Homework 22, due Wednesday before the exam, 26.1, 26.2, 26.4 (a trick question ;-), 26.9 (I will provide some guidance on 26.2 and 26.9, which are proofs, on Monday), 26.11 (hint: the answers are No, and you need infinite counterexamples); read the definition in 26.13 (but dont do 26.13) and do 26.14 (where section 23 will be useful).

    This is a demanding problem set, but notice that 26.1 is full of routine stuff you can do straightforwardly.

  • Wednesday, April 4: More fun with functions. Homework 21, due Monday: 24.7, 24.14, 24.16 (actually proving this is hard, but give as good an argument as you can), 24.17: hint, let A be the set of all natural numbers; 24.20, 24.21 (I've never asked this question before: I'm not sure how easy or hard it is; it is an application of counting methods we already have); 24.22 (again, familiar counting methods), 24.23 (this is very abstract, but it is important to understand this kind of extension of function notation in later mathematics). This is a quite tricky problem set!

  • Monday, April 2: discussed section 24 on Functions (I'm still in this section): a first batch of problems (homework 20 I believe) is: 24.1acegi, 24.2, 24.3, 24.4, 24.5 (in 3-5 you are writing down finite functions as sets of ordered pairs in list notation), 24.8. Due 4/6.

    Week Eleven

    Week Ten

    Week Eight

    Week Seven

    Week Six

    Week Five

    Week Four

    This week I am commenting a bit farther in advance than usual: comments on what we actually did and homework assignments will be added as we go through the week.

    Week Three

    Week Two

    Week One

    Test I will be Friday, February 9

    not Friday, February 2 as stated in the syllabus. Material covered by the end of class on Monday, February 5th, will be eligible to appear on the exam.

    Test I sample papers

    I may add some more recent papers, or comments on coverage, tonight or tomorrow (writing Monday afternoon). As I discussed in class, the 2013 papers are quite good models of sorts of things I may ask.

    Samples of Test I papers from previous terms: Spring 2010 Test I Spring 2007 Test I Fall 2008 Test I

    Fall 2006 Test I. Here is the Spring 2012 Test I paper.

    Here is the Spring 2013 Test I paper with solutions.

    Here is the Fall 2013 Test I paper with solutions.

    Two more test papers added Tuesday.

    Here is the Fall 2016 Test I paper with solutions.

    Here are the Fall 2017 Test I and II papers with solutions. These tests are rather different from yours; we were using a different book. There are some relevant questions in Test 1, and there are two formal proof questions in Test II.

    Test II Grades

    Here are the Test II grades posted by the ID number on your paper.

    Test II

    ... will be on March 9. I expect that it will cover sections 11 to 18. More details to appear. The last material to be included on the test will be whatever we cover on Monday, March 5.

    Sample Test II papers: Fall 2006 Test II; Fall 08 Test II; Spring 2007 Test II; Spring '10 Test II; Summer 06 Test II; an old Test II review sheet Spring 2012 Test II paper

    Here are the solutions to my Spring 2013 Test II.

    Here is a little sheet of counting problems which I gave my spring 2013 class. Some of them are good practice for the test (the simpler ones!)

    The tests do not all have identical coverage to ours. Questions that were on our Test I, or which mention things like Hasse diagrams and mathematical induction that we have not covered (yet), are not going to be on this test. The counting word problems are on this test (at least, fairly simple ones), and there are plenty of examples in these sample tests. I may have some more old tests on my office machine, but this should be enough to start with.

    Test I Grades Posted

    Here are your grades posted by the number on your exam paper.

    Test III Date

    Test III will occur on Friday, April 13th (ominous!). Details of coverage to be announced as we get closer.

    The exam covers sections 18-26 (the last section we covered was 25, but we covered 26 first). We did not explicitly talk about sections 19 or 20.

    Here I have copied my review material selection from Fall 2016:

    Here are solutions to Test 3 from Fall 2013.

    Here are solutions to Test 3 from Spring 2013.

    Other sample Test III papers: Fall 2006; Fall 2008; Spring 2007; Summer 2006; Summer 2007. Spring 2012 Some of these have different coverage from your test in ways which should be obvious.

    Test III has been marked and most papers have been returned. The class performance was very good.