**Monday August 21 :**classes begin

**Math 187:**sections 1-3Read pp. 552-3;1.1; 2.1,2.2,2.4,2.6,2.8,2.9

**Math 502:**for day 1, read pp. 1-18.do at least one of 1.3, 1.4a, 1.5. do all if you can. 1.4a ia probably easiest.

**Tuesday August 22 :****Math 187:**sections 3-4just 3.1-5; we didn’t get to section 4.

**Math 502:****Wednesday August 23 :****Math 187:**section 44.1; 4.3-5,4.6,4.7,4.14,4.15 (for 4.14 and 4.15 truth tables might help)

**Math 502:**due next Wed, at least one of exercises 1.3, 1.4a, 1.5, carefully written up; preferably all of them. Due Fri, just for fun, formulas for bijections Z->N, N->NxN. The Z->N is pretty easy to define by cases: I got a definition using the floor and absolute value functions cunningly which is just a formula (no cases), which is amusing. To get the N->NxN you'll need to use the quadratic formula, the floor function and a little thought.**Friday August 25 :**last day to add without permission

**Math 187:**section 5, maybe 64.8, 4.10 (just to keep you thinking about proofs); 5.2,5.3,5.5,5.7,5.8,5.9.

**Math 502:**we talked about sections 2 and 3, pp. 13-18. For next time, read sections 4 and 5.Your homework exercises, due in a week, are found in this PDF file. If you have trouble printing it out, consult with me.

**Monday August 28 :**you need my signature to add during this week

**Math 187:**section 66.2, 6.3, 6.4, 6.7, 6.9, 6.11be, 6.14, 6.15, (6.16-19* )

**Math 502:**section 4, pp. 19-24. maybe section 5 too.Your homework, due Sept. 6, is found here.

**Tuesday August 29 :****Math 187:**section 77.2,7.4,7.5,7.7,7.9,7.11,7.14; Additional Boolean algebra notes and worksheet

**Math 502:****Wednesday August 30 :****Math 187:**sections 8, 98.1,8.4,8.5,8.7,8.8; 9.1, 9.2, 9.3, 9.4, 9.6.

**Math 502:**finished sections II 4,5 discussed III section 1no new assignment; please read through the definition of satisfaction on p. 33 at least, if not to p. 40.

**Friday September 1 :**add deadline

**Math 187:**section 1010.1, 10.2, 10.4, 10.5.

**Math 502:**intending to get through III section 3 if not section 4…exercises III.1.4.1.5,1.6 (if you don't have defs from abstract algebra, ask me), 2.1, 3.3, 3.4. read up to p. 40 for Wed.

**Monday September 4 :**Labor Day holiday

**Math 187:**holiday**Math 502:****Tuesday September 5 :****Math 187:**section 1111.1,3,5,8,9,13 (hint: think about an element in A but not B or vice versa),16,17 (I'll say more about 17 on Wed),19 (don't do full proof, just verify it for a reasonably complex example),22 (hint: you hve already proved that exclusive or is associative using truth tables),23 (this is quite hard to label clearly; see how clear you can make it...). You have an extra day to do this assignment: I'm still talking about it Wed.

**Math 502:****Wednesday September 6 :****Math 187:**section 1313.2,6,7,10,12,13; this and the section 11 homework are both due on Monday.

**Math 502:**no new assignment

**Friday September 8 :****Math 187:**sections 14,5314.1,2,4,6,11,12,13

**Math 502:**assignment due today has been extended to Monday! No new assignment given.

**Monday September 11 :****Math 187:**sections 14,5353.1-4, 53.8a-g I'm not altogether happy with the kinds of problems the book gives, but that's what I have to work with.

**Math 502:**assignment: III.4.9b and 4.11b due Friday (not Monday)

**Tuesday September 12 :****Math 187:**section s 54,55 (we are behind, of course, actually lecturing and assigning 14 and 53 today)assignments from 14 and 53 shown above are assigned today, due Monday

**Math 502:****Wednesday September 13 :****Math 187:**section 15no new assignment given

**Math 502:**4.14, 5.10a, both for Monday. In 4.14, for each group axiom, find a model of all group axioms except that one, and the same for equivalence relation axioms: the idea is to show that none of the axioms are redundant. In 5.10a see if you can define "x is less than y" (for real numbers x and y) using our formal language alone (using + and * only)

**Friday September 15 :**Test 1

**Math 187:**Test 1Here find the summer 2006 version of Test I. Also look at problems 1 and 7 in the summer Test II.

**Math 502:**Test I in M502 deferred to Sept. 22III4.9b and 4.11b due; new assignment is to write out the proof of Lemma 5.5 on page 42 in detail. Their hint that you can follow the structure of the proof of the Isomorphism Lemma is a good one, but remember that the relation between the structures A and B is not the same in the isomorphism proof; the proof will be parallel in structure but it will differ in local details. This is due on Monday after the test (the 25th); I want to see and go over drafts of it with each of you in my office sometime during the week next week, and the visit to show me the draft is worth two points on MTh, one point on Friday :-) [if you show up completely puzzled you get the points and some guidance...] The purpose of the exercise is to get some handle on these induction arguments on terms and formulas... Due date for this changed to Wed instead of Mon, and you can see me on Friday after the test if you prefer (and on Monday if you are a severe procrastinator with 1-point penalty...)

**Monday September 18 :****Math 187:**section 16 [really covered 54,55 and 15]54.2-4; 55.1,3; 15.1,2,4,7,8,11,12,13. Some of the section 15 problems call for additional discussion tomorrow.

**Math 502:**Attempt formal proofs of 3.5 and 3.6 on p. 65; a writeup of all of these in a week is expected, but work with the idea that you might be asked to present any proofs you have in class tomorrow.

**Tuesday September 19 :****Math 187:**section 17 [actually covering section 16]16.2,3,4,6,10,12,14,28

**Math 502:****Wednesday September 20 :****Math 187:**section 1817:1,2,3,4,5,6 (some word problems are needed);18.1,2; chapter 3 self-test 18, 19, 20. Sorry I posted these late: I don't really like the selection and will look for some different problems. That was my remark last semester; this semester, still sorry about the 17 problems late (again) and you get an extra day to do them :-)

**Math 502:****Friday September 22 :****Math 187:**section 19for section 18 problems see just above.

**Math 502:**Test 1 in M502Practice Test here are the solutions.

**Monday September 25 :****Math 187:**sections 20 and 21photocopied handout with counting word problems

**Math 502:**two formal proofs specified in class due on Friday (I see no reason for a week turnaround time); I have now posted extensive notes on this lecture (with extra stuff I didn't say in the lecture!) which include description of these two formal proofs.

**Tuesday September 26 :****Math 187:**sections 20 and 21 [actually section 19]19:1,3,4,6,7,8,11

**Math 502:****Wednesday September 27 :****Math 187:**section 22**Math 502:****Friday September 29 :****Math 187:**section 2320.2,3,4,6; 21.3, 21.4, 21.6, 21.8, 21.9. Dr. Kaiser will be lecturing on further chapter 20 and 21 material on Monday; I will not be on campus. Please turn in section 19 on Tuesday (to me, not Dr. Kaiser).

**Math 502:**I'm putting this note in Friday midafternoon: notes on sequent calculus with exercises will appear--if they don't appear today look for them in this space on Sunday (not Saturday as I said in class; don't know what I was thinking).Here are the notes with exercises.

**Monday October 2 :**drop deadline

**Math 187:**section 24**Math 502:****Tuesday October 3 :****Math 187:**section 25**Math 502:****Wednesday October 4 :****Math 187:**section 26 (maybe 27 too)**Math 502:****Friday October 6 :**Test 2

**Math 187:**Test 2for test 2 review see the summer Test II, except for problems 1 and 7., and the summer Test III, problem 1, all three parts. Solutions!

**Math 502:**Test 2 (not!) seriously, not for a bit.**Monday October 9 :****Math 187:**section 2822.1; 22.2 parts (b), (e), (i), (k); 23.1, 23.2-4, 23.6, 23.8, 23.9, 23.13, 23.14.

**Math 502:**Propositional logic lab exercises Watch this space for notes on the completeness theorem.

**Tuesday October 10 :****Math 187:**section 34**Math 502:****Wednesday October 11 :****Math 187:**section 3522 due; new assignment is 24.2, 24.3, 24.4, 24.5, 24.9, 24.10; 25.1 all parts; for finite examples draw diagrams; 25.2, 25.9a (I'll do at least one of these proofs in class later); 25.10, 25.11 (the answer is different depending on whether A is finite or not)

**Math 502:**notes for the Completeness Theorem to be read for Friday's class (which will not be lab). Quantifier and equality lab problems will appear shortly.

**Friday October 13 :****Math 187:**section 3523 was due

**Math 502:****Monday October 16 :****Math 187:**section 3624 due; 26.1, 26.2, 26.3, 26.4, 26.5, 26.12; 28.1,28.2,28.7,28.8.

**Math 502:**quantifier lab and a related file are on top level of my web page, posted Sunday afternoon. The propositional logic lab is due shall we say at the lab session Wednesday and the quantifier lab next Monday. Today we finish the lecture on the Completeness Theorem.

**Tuesday October 17 :****Math 187:**section 3625 due

**Math 502:****Wednesday October 18 :****Math 187:**section 3726 due;34.1, 34.2, 34.4.

**Math 502:**Today we meet in lab. I have decided that the Test will be 1 week from the coming Monday, and that the current lab is due next Wednesday.

**Friday October 20 :****Math 187:**section 4228 and 34 still accepted Monday; new assignment is 35.1,2,4 (experiment),10,11,13.

**Math 502:**Watch this space for notes on what I said today which may include or be accompanied by new homework. It might not go up until Sunday or even Monday morning.

**Monday October 23 :****Math 187:**section 45no new assignment given

**Math 502:**New homework assignment is at the end of expanded notes on the Completeness Theorem and its consequences. Exercises are due Wednesday after the test. They are quite hard: completing three of them will probably be quite adequate, but you should look at all of them in thinking about the test.

**Tuesday October 24 :****Math 187:**section 4536.1-4; 36.13; 36.14b (the idea in 36.14b will not be on the test but will be _important_ afterward).

**Math 502:****Wednesday October 25 :****Math 187:**section 4635 due; 37.1,3,6,7.

**Math 502:****Friday October 27 :**Test 3

**Math 187:**Test 3see the top level of my web page for review material. The pointers are to the summer Test III and the summer final but I'm not copying all my comments to here.

**Math 502:**Test 3 (not)**Monday October 30 :****Math 187:**section 4736 due

**Math 502:**Test 2 (for real)**Tuesday October 31 :****Math 187:**sections 48 and 49sorry about posting late: 38.1,2,9,12,13(hard),18,20(hard)

**Math 502:****Wednesday November 1 :****Math 187:**section 50 and hamiltonian cycles too37 due

**Math 502:****Friday November 3 :****Math 187:**section 50 and hamiltonian cycles too**Math 502:****Monday November 6 :****Math 187:**section 51there is no section 42 assignment; the section 45 assignment is 45.1-3. 45.4 is in principle suitable but the calculations would be appalling (you could do them in Maple if you know Maple; a TI89 can actually do all the math for 45.4, and I may discuss how in class). I think I'll put together a worksheet with problems appopriate for sections 42 and 45.

**Math 502:**p. 6: 1.3 abde,1.4 abc; these should be quite straightforward (but write them out carefully). P. 15: Exercise 2.9, for multiplication of positive reals only. Exercise 2.10. Exercise 2.11. The in-class exercise from the other day: using the definition of -r for a real r which I have given in class, prove that r + -r = 0. Bear in mind that when you have the goal of showing that two sets are equal, the strategy is to show that any element of the first belongs to the second and any element of the second belongs to the first (two directions!)

**Tuesday November 7 :****Math 187:**section 51Here is a worksheet on modular exponentiation and the RSA algorithm, due Friday. Your homework for section 46 is 46.1,2,3,5,12,13.

**Math 502:****Wednesday November 8 :****Math 187:**section 52In spite of the fact that we are behind my very optimistic projected schedule, we're doing fine for time (better than I did in the summer), so we have new homework not copied from the old schedule: 47.1abdegh, 47.3 (standard counting!), 47.4, 47.7a (I'd be interested if you could see how to do the other parts), 47.8.

**Math 502:****Friday November 10 :****Math 187:**section 5248:1,3,4,7 (I don’t know how hard this is),11ab (hint: for a, suppose that a graph G is disconnected (say into a part with a vertices and a part with b vertices) and has as many vertices as possible under this condition: show that it has fewer than "n-1 choose 2" vertices: this is really just algebra; b is easy).

**Math 502:****Monday November 13 :****Math 187:**section 29section 49: 49.1, 49.4, 49.7, 49.8 (if you keep your wits about you 49.8 should not be too hard).

**Math 502:**exercises 2.26 and 2.27 (2.27 may be rather difficult); exercise 4.13 (you need a counterexample); 4.20, 4.31, 4.33, 4.36.

**Tuesday November 14 :****Math 187:**section 3049 homework assigned -- see Monday. I'll post a worksheet on the other material I discuss.

**Math 502:****Wednesday November 15 :****Math 187:**section 30handout on basic graph theory definitions distributed (photocopies, not available on web -- see me if you don't have it).

**Math 502:****Friday November 17 :****Math 187:**section 31RSA examples handout (link on my main web page); planning to do 50 (and related extra stuff); section 48 due

**Math 502:****Monday November 20 :**break

**Math 187:**break**Math 502:****Tuesday November 21 :**break

**Math 187:**break**Math 502:****Wednesday November 22 :**break

**Math 187:**break**Math 502:****Friday November 24 :**break

**Math 187:**break**Math 502:****Monday November 27 :****Math 187:**section 31planning to do 51

**Math 502:****Tuesday November 28 :****Math 187:**sections 32 and 33planning to do 52

**Math 502:****Wednesday November 29 :****Math 187:**section 56 and sortingpaper worksheet of graph theory examples to be handed out in class; extra copies at my door, where solutions will be found Thursday eve or Friday morn. Homework section 51.1,4 (a variation of the proof of proposition 51.5 works),8,13.

**Math 502:**watch main page for notes; I'll try to write notes for the whole rest of the course by Sunday at the latest, and at least have notes for each day up before the lecture. Exercises will be found in the document with the notes.

**Friday December 1 :**Test 4

**Math 187:**Test 4Test will cover up to section 52

**Math 502:**Test 4 (not)**Monday December 4 :****Math 187:**section 56 and sorting**Math 502:**The set theory lecture notes document now contains lecture notes through at least part of Monday's lecture and contains exercises. Watch this document: any additional assignments will appear there.

**Tuesday December 5 :****Math 187:**review and overflow52.2,5,6 (5-regular means every vertex has degree 5),11

**Math 502:****Wednesday December 6 :****Math 187:**review and overflowworksheet on bubble sort and heap sort; final review sheet;student evaluations distributed at end of class.

**Math 502:****Friday December 8 :****Math 187:**reviewreview only; student evaluations collected at end of class.

**Math 502:**