# Math 402/502, Logic and Set Theory, Spring 2017, Class Announcements Page

## Welcome

Welcome to the class. You should expect to find homework assignments and other important class announcements and links to class resources on this page. You should be in the habit of checking this page regularly; I will not necessarily say much about homework assignments in class -- this is the official place to find out about them!

I will generally add new material near the top (a few items will stay at the top).

## Office Hours and other schedule information

My office hours are stated on my office door card (which is also attached to my office door), which also includes the times of my classes and seminars. I am thinking of typically coming in late on Mondays and leaving early Wednesdays and Fridays: at times when I am working at home, e-mail will reach me.

## The Text

This is your textbook. It may mutate as we go through the semester!

## The Marcel theorem prover

Here is the link where source and documentation for the Marcel theorem prover are found. We will be using the Python version.

Here is the lab manual.

## April 25th (and last) homework

This is due at the final exam period. It does include stuff which you can't approach until after I give the last lecture Thursday.

The 5.2 exercises, 1,2,4; exercises 5.3.1, 1,2,4; 5.4.1.1 optional (as many parts as you can manage); 5.6.1.1 (optional; I'll be impressed if you can make the essential point here; this requires the Thursday lecture).

Do note that I offer a lecture on the incompleteness theorems during the final exam period (as a piece of performance art) if you want to show up.

## April 19 Homework

Our lecture on the 18th can be supported by reading sections 3.16 (the first proof of Zorn's Lemma given is basically the one given in class) and sections 4.1, 4.3, 4.5, and 4.6. Your homework, which may be quite challenging [feel absolutely free to ask about it in class: I may give away whole problems]: 4.1.1 problem 1, 4.1.1 problem 2, 4.5.1 problem 1 (remember that I described the finite ranks V0, V1, V2, V3... and their sizes in the lecture), 4.5.1 problem 2. This is due on the last day of class. There will be one more assignment, due at the final exam time (though we are not having a final). It is possible that I will come up with one or two additional problems for this assignment, no later than Monday morning (easier ones, not harder ones!)

## April 7 Homework

Finished lecturing section 3.13 on Thursday the 6th. Your homework due Thursday the 13th is 3.12.1a (show which properties stated for the real number system are true of the positive rationals (prove them using the representation of fractions I give) and which are false (give counterexamples).), and 3.13.1 problems 1,2,3,4 (fun with infinite ordinals). Also do 3.13.1 problem 5, as I mentioned on Tuesday.

## Week 10

• Tuesday March 14 (writing in the morning on the 15th): covered section 3.10 and section 3.11 up to the discussion of addition. Homework (including stuff from 3.11 which I will review and/or newly cover on Thursday): problems 4 and 5 in 3.9.1 (newly added, update if you don't see them), problem 1 in 3.10.1, problems 1,2,4 (I did this in class, but do it: this is a good test question (hint, hint), 5,6 in 3.11.1.

This problem set is officially due the class session after the exam, but if you turn it in on Tuesday the 4th I will have it graded before the exam.

## Week 8

• Thursday March 2: currently in the middle of section 3.9. Homework due March 9: in section 3.9.1, problems 1-3. Notice that in problem 3 you need only do two parts, but you are encouraged to do more and will benefit. I will do a demonstration re problem 1 if you remind me.

## Week 7

• Thursday Feb 23 (actually posting on the 24th): We have just finished section 3.6 on (mostly familiar) definitions re relations and functions: you should review these.

Homework, due March 2: in section 3.5.2, do problems 1,2 (if you prove the result of exercise 3 I believe that can be used to do exercise 2), 4 (I did this in class: but write out your own proof, with care), 5 (5 is just an induction proof in arithmetic, no specific mention of set theory: but there is something funny about it), 8, 10. In addition, do section 3.6.1 exercise 2. You may optionally do question 6 in section 3.5.2 (compute a Quine pair and projections of a Quine pair) and the first part of question 7 in 3.5.2 (the first definition ever given of the ordered pair as a set). Some of these problems have solutions in the text, but there is real value in attempting them on your own first. In addition there is a Marcel lab, due March 9: here.

## Test I...

will be on Thursday February 16th. More news as it develops.

## Week Five

• Thursday, February 9. Today I lectured part of section 3.5 (up to the proof that Peano axiom 4 follows from the axiom of infinity); I strongly suggest reading section 3.5, which I will continue to lecture on Tuesday.

I am not posting paper homework today, though I am likely to post a Marcel lab for quantifier logic (with a longish due date) quite shortly. Your test will cover up to the end of section 3.4 (logic and simple set theory concepts: section 3.5 is on the next exam. I will try to get some review material for the test up by Sunday.

## Week Four

• Thursday Feb 2 (well, I'm actually posting this on the morning of the third; and sorry about the typoed month): lab is due (remember there is a paper proof in it too). The third homework assignment: exercises 2.14 4b, 5, 9 and the 3.4.1 exercises 1-4. In addition there will be a lab exercise or two in Marcel which I will post today (I'll try to give a little time to work on lab exercises in class so I can see what you are doing). The paper homework at least is due Thursday the 9th.

## Week Three

• Thursday Jan 26: First logic lab. You should show up with your laptop with Python installed, but I will work on this in class as time permits. The Marcel lab manual appears at the top of this page. The Lab I exercises are on page 55 of the lab manual. This file contains some commands for the lab set up for you (some of them you are supposed to set up yourself).

• Tuesday Jan 24: more logic lecture, up to introduction of quantifiers and their rules.

## Week Two

• Thursday, 19 January: Proved more theorems of propositional logic in chapter 2. Demonstration of the Marcel proof checker given. Please notice that on the morning of the 20th I posted an update of the text with more detailed proofs of the contrapositive theorem and the theorem motivating alternative elimination and disjunctive syllogism. I left the more informal English proofs in place for comparison.

I suggest installing Python 3 (the latest version seems to be Python 3.6) on your laptops for pending computer labs. You can get the Python version of Marcel here and the manual here.

• Tuesday, 17 January: Reviewed Thursday's lecture and continued up through the proof of the contrapositives theorem.

Homework I, due Thursday, January 26th: section 2.14 in the notes (Exercises for chapter 2) exercises 2,3,6,7,8,10. Examples of work in chapter 9 (the manual of logical style at the end) are a better model for your work than the current text of examples in section 2: I am more explicit about line numbers and indented structure in the chapter 9 examples.

## Week One

• Thursday, January 12th: I discussed basic sentence structure and the logic of implication, conjunction, and a touch of the biconditional (sections 2.1, 2.2, 2.4 and a touch of 2.5). I'll continue the proof example we were working on at the end of class on Tuesday. The first homework will appear on Tuesday or maybe even on Thursday.

• Tuesday, January 10th: This was a snow day!

## Test II

Test II will occur on Thursday, March 30th (the Thursday after the break; sorry about writing April 6th earlier!). Test III (which will not be cumulative but will contain makeup opportunities) will occur during the final examination period. Test II will cover all material covered before Spring Break. I will provide review material making it clear what sorts of things I intend to ask about either late this week or during the break.

Here is a review sheet for the test, to give you an idea what content in the text to study. I may expand on it in the next couple of days, or may not, depending on time...

Test II will be a hybrid take-home exam. You will receive two copies of the test, one of which you can complete in class for full credit, and the other of which you can complete at home and return on Tuesday for 60 to 90 percent credit (this percentage will be set for each question based on class performance and my opinion of the question). On the take home part, you may consult no person but me, and if I detect you copying a complete solution to a problem from another source it will be bad (this doesn't mean you can't consult whatever sources you have available to you, but you should use them to write your own answers).