Class Announcements Page for Math 187, Foundational and Discrete Math, Fall 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 275 in Fall 2018. My classes are M187 12--12:50 MWF, M275 9--10:15 MWF.
I am the coordinator for M488, the senior outcomes assessment activity, which meets once on a Saturday morning later in the semester in our computer lab Mathematics 136 (there will be two alternative dates TBA). I have the regular weekly PBC meeting at a time TBA, and logic seminar weekly at a time TBA. I am proposing to have time wih my graduate student 1-3 Thursdays, and class office hours MWF tentatively 10:30--11:30 pm and 3--4 pm. 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.
Manual of Logical Style
This is a document I will maintain in which our official proof strategies and logical rules will be recorded.
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.
Test IV, Final Exam, and Course Grades
Here are the indicated grades, posted by the ID on your Test IV and Final paper.
Test IV and Final Prep
and Here find all the readily accessible Test IV and final practice material. I scanned many tests into two large PDF documents.
Test I Solutions
Here are solutions to Test I. They do not include problem 5, which was disregarded because of a typo (you will see something like it again).
Test III Preparation
Test III is on Friday, November 9th. It covers sections 21 to 26 (excluding section 25).
A set of practice problems is here. This is a collection of the relevant problems from most of the tests I have, hand-numbered so you can tell me which ones you are asking about. Happy studying!
A solution set for Test III is here.
Test II Grades and Solutions
Here are the grades on Test II posted by the ID number on your test.
Here are the solutions to Test II.
Monday Dec 3 (last new lecture): RSA cryptosystem. Here is a tiny example with full step by step explanation.
Here find a handout of RSA calculations with solutions from last term. I don't promise no modular exponentiation by repeated squaring on your exam; that was last term (there won't be a lot of it, if any, but there might be a little).
Your actual homework is here: this handout has numerical answers, but you are assigned the task of doing the calculations to find those numerical answers.
Due at the final exam, and I will actually be willing to give some of these away in review on Friday.
- Friday November 30: lectured on modular exponentation. Your homework is this worksheet, due next Wednesday. Complete worked solutions will be posted for final review. DUE FRIDAY the 7th since this somehow wasnt posted until Monday.
- Wednesday November 28: lectured section 38 on the Chinese Remainder Theorem. Homework: 38.1, 38.3, 38.4 (arrr!), 38.6 (follow my lead in lecture and think about m=4, n=6). Their mysterious notation x ≡ y (n) means
x ≡ n y. DUE FRIDAY the 7th since this somehow wasnt posted until Monday. [it really was right there in the copy on my machine...sorry, I don't know what happened].
- Monday November 26: lectured section 37 on modular arithmetic. Homework, due Friday: 37.1 acegikmoq, 37.2, 37.3 (in this part there might be no solutions or more than one), 37.4 (different again), 37.5 is optional: I'll be impressed if someone comes up with the right conjecture, 37.14abc (not optional: this is importann).
- Friday Nov 16 (posted Friday the 23d): 39.1, 39.2, 39.3 (probably tricky to prove just because it looks so obvious), 39.9, 39.10 (we basically did this in class), 39.14 (you already know how to do this!). Due Wednesday. I hope your Thanksgiving was excellent!
- Wednesday, November 14: discussed extended Euclidean algorithm. Homework: 36.2, 36.12, 36.13, 36.18, 36.20, 36.21.
- Monday November 12: discussed section 35 on division and started section 36 on the Euclidean algorithm.
Homework is 35.1, 35.2, 35.3, 36.1. Due Friday (it's short, I think you can deal with it even though posted late).
- Monday Nov 5: Remember, remember the fifth of November...(why?)
I lectured on section 26 on composition of functions. Homework: 26.1, 26.7, 26.8, 26.9 (I did part of this in class. In part b, it should be "onto B", not just "onto"), 26.10, 26.12. For the test, focus on 26.1: the other questions are conceptual in nature, and the test question on this section will be computational. Nonetheless, it is useful to think carefully about these concepts.
Notice the review sheet for Test III is out, above.
- Friday 11/2: More chances to think about functions: 24.6, 24.8, 24.14, 24.17 (I did part of this, do you remember? -- and an assigned exercise does the other part, if you pay attention), 24.19 (hint: there is a bijection between two sets just in case they are the same size), 24.20.
Bonus question for class discussion (not graded, but think about it): suppose A has 10 elements and B has 3 elements. Without looking at the formula in the book (but using the example I did in class where B had 2 elements), how many functions are there from A to B which are onto B?
- Wednesday 10/31: homework 23.3, 23.7, 23.9, 24.1, 24.2, 24.3, 24.4, 24.5.
- Wednesday 10/24: first lecture on section 23: homework 23.1 ace, 23.2 acegikmo, 23.11, 23.14ae. If you can do any part of 23.15, I'll be impressed.
- Monday, 10/22: scary last induction lecture, no homework.
Friday Oct 19 (writing on Sunday): lectured more chapter 22, induction: second induction homework assignment
due next Friday (partly because I'm late posting it, but I think extra time is needed anyway): 22.5 all parts, 22.16 all parts (but I did one of these!), 21.3, 21.4, 21.7, 21.8 (chapter 21 problems to be done by chapter 22 methods; Ill talk about chapter 21's approach in the next lecture). Notice that Monday's assignment is not due until Wednesday: use the extra time to ask questions on Monday!
Monday Oct 15: lectured section 22 on math induction. We will be talking about this for several days!
first induction assignment: 22.4 parts a-d (as separate problems), 22.9, 22.10, 22.17, 21.2 (I did this in class, but it is good for you to write it out yourself), 21.6. Don't look at section 21; the 21 problems are to be done by 22 methods.
This is due a week from the test (Wednesday next week). I fully expect lots of questions on Friday!
- Friday Oct 12 (posted Monday before class, oops): lectured section 19 on inclusion exclusion.
Homework 19.1, 19.2, 19.3, 19.5, 19.7, due next Monday. Nothing about inclusion exclusion on this exam
except the three-compartment problems you see on the sample exams and possibly the formula for four sets,
since I flaked out on posting this...
- Wednesday Oct 10: covered section 18 and some general counting concepts. Homework from the chapter 3 review, page 118: 10,11,12 (this is a thinking cap question),13,15,17,20,21 (another thinking cap question). I really don't like the section 18 homework: you will need to read the section for an explanation of the stars and bars notation, though it is very similar to my bagel pictures! Do 18.1/2, 18.5, 18.7, 18.8 (I told you the answer), and look at 18.13 (put on thinking cap...). You might want to look for section 18 style counting problems in the sample tests. Sorry this is posted late: it's due Monday, and I'll have some comments Friday on it.
- Monday Oct 8: reviewed homework, no new assignment. Notice that I did post a section 17 assignment.
- Friday, Oct 5: section 17 lectured: 17.1, 17.2, 17.3, 17.4, 17.6, 17.7, 17.8, 17.10. Look at 17.14: Ill discuss this in class. Try 17.33 (but, like 17.14, it is not assigned): I am likely to count all the poker hands in a lecture.
These are due Friday Oct 12, since I didnt actually post them on Friday!
- Wednesday Oct 3: lecturing section 16 and assigning 15 and 16 homework due Monday: 15.3, 15.7, 15.9, 15.11, 15.14/15 (same problem, two different approaches), 15.16=16.1 (hint: these are exactly the same problem!), 16.2, 16.4, 16.7/8, 16.11, 16.12, 16.13.
- Monday Oct 1: lectured section 15 and forgot to post homework! Its posted Wed, combined with section
16, and due Monday.
Sorry, I was mostly asleep on Monday after my early morning airplane arrival in Boise.
- Friday, 21st Sept: Covered section 11 on quantifiers. Homework: 11.1 acegi; 11.2 acegi; 11.4, 11.5. Due next Wednesday the 26th.
- Monday and Wednesday, 17th and 19th: review for and administration of Test I. It should be graded and returned by Monday.
- Friday, Sept 7: The second exercise set in the manual of logical style will be assigned today and due next Friday, the 14th. Test I is delayed until the 19th. I'm giving you the extra day because Jean Schneider, who is lecturing on Monday, is probably not ready to answer questions about my formal logic setup -- you will be able to ask questions on Wednesday the 12th before the 14th when it is due. I think I said in class on the 12th that the logic exercises were due on Monday the 17th, so I'll let them go until then.
- Wednesday, Sept 5: No new assignment, as we are still working on new logic rules involving negation. You do have exercises to turn in Friday.
- Friday, 8/24/2018: section 5. Homework from section 5: 5.1, 5.2, 5.5, 5.6, 5.7, 5.9, 5.10, 5.13 (harder than the one we did in class!), 5.20 (read rules for inequalities in Appendix D carefully). I may do one or two of the earlier problems in class.
From the axioms given on page 482, prove that x0 = 0. This can be done but is surprisingly tricky. You aren't going to lose points in the course if you can't do it.
- Wednesday, 8/22/2018: section 4. Homework from section 4: 4.1, 4.3, 4.4, 4.5, 4.6, 4.10, 4.12 (an open ended exploration problem): of parts abcd, try at least two parts).
- Monday, 8/20/2018: section 3. Homework from section 3: 3.1, 3.2, 3.4 (your definition in 3.4 should use the notions of natural number and addition and nothing else to define the notion "the integer x is less (or equal to?) than the integer y"), 3.9 (they mean "on the line segment between A and B", to be defined in terms of distance), 3.12 (this one will definitely require some discussion on Wednesday :-)
This assignment is due on Friday the 24th. I won't always say when an assignment is due: the method of computing due dates is given above.
In addition, we define a natural number n as special just in case there is exactly one m strictly between 1 and n which is a factor of n. Compare with the definition of composite. Identify all the numbers between 1 and 50 which are special. Give a brief definition of special numbers in terms of familiar concepts.
Materials for Test I
Samples of Test I papers from previous terms: Spring
2010 Test I Spring
2007 Test I Fall
2008 Test I
2006 Test I. Here
is the Spring 2012 Test I paper.
is the Spring 2013 Test I paper with solutions.
is the Fall 2013 Test I paper with solutions.
is the Fall 2016 Test I paper with solutions.
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.
Here is the Spring 2018 Test I.
Test II preliminary announcement
Test II will be on Wed Oct 17, and I expect it to cover sections 11 through 19 (but in any case, whatever we have covered by Friday's class). I will post sample exams before Wednesday's class.
Fall '06 (everything but the last question)
Fall 08: everything is relevant (has solutions)
Spring 2010 all relevant
Spring 2012, no Hasse diagrams, no induction, otherwise relevant.
Spring 2013, relevant, solutions.
Spring 2018, all relevant.
Summer 2006, all but the last question.
just for the first question
just for the first two questions