Please note that this section of the course is ONLY for those of you that have not passed Math 1090 in Fall 98/99. If you

FINAL FILE

- Assignments 4&5 (due 5th April)
- Assignment 3 (due 5th March)
- Assignment 2 (due 10th February)
- Assignment 1 (due 29th January)

The grades are up outside my door. Remember there is no point in mailing/trying to visit me as I am *no longer around* (by the time you read this). If you have concerns about your grade you must see Rick Ganong. Thanks to all of you that told me how much you enjoyed my section, I enjoyed teaching you too!

So it is all over. The grades will be up outside my door by Monday unless there is some unforseen problem. If you have any problems after that you must contact Prof RICK GANONG, as I will have moved to another country. (No, the course wasn't that bad...)

For news flashes on the final, check the final file, above.

The last assignment, and (hopefully) the last test will be available for collection from my office DURING OFFICE HOURS on Monday. After that they will be available from outside my office.

The solutions to today's tests are here, Test 2A part 2, Test 2B part 2. For Q1 I decided a 1 place predicate was nicer to look at in the solutions, although your 2 place ones involving cars and wheels were also correct.

The test tomorrow will go ahead as planned, 8-30am-9am CLH C. For more details on York's policy in the event of a strike click here.

NEWSFLASH EXTRA TUTORIALS!!!

**All tutorials are to be in S203 Ross:
**

**
Thurs 22 April 1-3pm
Fri 23 April 11am-2.30pm (half hour break at 12.30pm)
Mon 26 April 11am-2.30pm (half hour break at 12.30pm)**

About the impending TTC strike, Senate are making a descision (concerning the whole university), which will be known tomorrow, so watch this space for more details! Also note that Q 9.28 has a typing error, it should say ` \not occurs ('x', 'Q')', and Metatheorem 9.16 DOES NOT say 'For all boolean expression P, P==(forall x |:P) is a theorem'...

The solutions to assignment 4/5 are here.

NOTE: from April 9th onwards office hours will be 10.30am-12.30pm MONDAY ONLY upto and including April 26th.

I am stating here once and for all that those people who miss tests and do not give me a reason backed up by a witness, and do not sign a contract will get 0 for the test. Notice that you have to do ALL of these things, and BY MONDAY 29th unless you have a fantastic reason, or you will get 0.

The solutions to the partial test just gone is here: Test 2A pt 1, Test 2B pt 1.

Here is a file on the test for April 9th.
**30. (Mar 25th 4.10pm)**

Good practice for predicate logic are those Theorems and questions in Ch 9 which we haven't done in class. However do not focus too much on english to predicate logic.

**29. (Mar 22nd 11.37am)**

Note that the next test will be on April 9th, office hours Monday 29th March will run until 1.30pm, due to no office hours on Wednesday 31st, and there is an exam sale on until April 5th in Ross N537.

**28. (Mar 16th 2.22pm)**

Here are the solutions to Assignment 3.

**27. (Mar 15th 2.18pm)**

FOR TEST 2 Part 1: Here are some nice nested deduction theorems to look at from Profesor Dow (using the Deduction theorem more than once in a proof). Here is also a note on bullet proofs for chapter 4.

**26. (Mar 12th 2.01pm)**

Joint assignment 4&5 is now up.

**25. (Mar 11th 10.37am)**

NOTE the test 2 file has been updated!!!Don't forget to bring photo i.d. to the test. Also for test 1 everyone's score was raised by 3.5 marks.

**24. (Mar 8th 1.40pm)**

The solutions for Assignment 3 will go up once it has been graded, in the meantime here are a few notes on the next test.

**23. (Feb 26th 4.18pm)**

Apologies for the typo in Q4 c) -should say sound instead of complete.

**22. (Feb 26th 11.51am)**

Test 1 and assignment 2 are available outside my office.

**21. (Feb 22nd 1.00pm)**

The solutions to assignment 2, test 1A, test 1B.

**20. (Feb 22nd 12.45pm)**

Assignment 3 is now up and running. Sorry about the lateness. Later today the solutions for assignment 2 and the tests should go up.
**19. (Feb 5th 10.07 am) **

IMPORTANT! For ASSIGNMENT 2 use ONLY the methods of CHAPTER 3!!

**18. (Feb 3rd 4.15pm)**

The first assignment has been marked, and can be collected from outside my door. For the test: BRING I.D. WITH YOUR PHOTO AND SIGNATURE ON. The solution to Assignment 1 is here.

**17. (Feb 3rd 10.50 am)**

Note that the THURSDAY tutorial has been moved to 12.30pm, Ross N501.

**16. (Feb 1st 12.03pm)**

Thanks to the student who pointed out that in the model proof there is a symbol missing in the first reason - the substitution should read

p,q:= ~p, p(The first of those 2 substitutions is "not p").

Actually now there is an updated Assignment 2. Do the one now at the link.

"Something for the weekend" and the Divine Comedy once sang...Assignment 2 is out!

Ah yes, and anyone caught cheating on the test (or an assignment) will automatically get 0 for it.

My hearing is going. To the student who asked about a subtitution in class the reply is "No, you can only substitute into theorems". Thanks to the student who pointed out I had misheard where the substitution was taking place.

Notes on the class test can be found here.**11. (Jan 27th 1.22pm)**

Thanks to the student who found an error in the proof of the Lemma we had in the proof of Theorem 3.43b). The problem lies in the VERY LAST application of Leibniz. That point should read

Leibniz with E being (p v p)==(p v q)==r gives |- ((p v p)==(p v q)==p v (p v q))==((p v p)==(p v q)==(p v p) v q). By transitivity we get |- ((p v (p==q)==p v (p v q))==((p v p)==(p v q)==(p v p) v q).

Note that

|-, ==stands for our turnstile, equivalence symbol respectively.

Remember, the first test will be in class on Friday Feb 12th. It will cover chapter 3. You will be given all the theorems/axioms you need, and the test will be in the style of Q2 on Assignment 1.

Here is a model proof for your assignments, and a correction to the step in the proof of theorem 3.32

Here are the places in the notes where I meant IE (thats the double bar "E" for equational logic) instead of E (for sentences). Sorry.

- before the definition of logic "search for theorems in E".
- "For E: Language".
- "For E: Sentences".
- "For E: Theorems".
- "For E: Inference Rules".
- "Some more about E...Soundness".
- "Important fact: E is both sound and complete".
- "Proof of soundness of E".
- "To prove soundness of E".

Due to York being closed on January 15th, there was no class. However, unless York is closed again tomorrow, there will be a class.

For those of you that missed class, or were late, don't worry, we didn't cover very much. We just finished the proof from last time, looked at some notation, and proved one theorem. We are still doing Chapter 3, and no homework/assignment was set.

The course outline (minus these notes) is available here. Tutorials will be Tuesday and Thursday 11.30am-12.20pm Ross N501 with Michael Hrusak.

Note the revisions to the general info (now renamed as the course outline), such as grading schemes, below.

Here are some suggested excercises if you want some practice. However at this stage it is MUCH more important that you understand all the notes so far.

**Chapter 3:**3.12, 3.17, 3.19, 3.23, 3.25, 3.27, 3.30, 3.31, 3.32, 3.37, 3.38. Try proving Theorem (3.49), 3.44, 3.45, 3.47, 3.48, 3.50, 3.52, 3.57, 3.60, 3.63, 3.67, 3.68, 3.71, 3.76, 3.78, 3.80, 3.82, 3.83.**Chapter 4:**4.2, 4.5, 4.8, 4.9, 4.10, 4.11, 4.12.

Don't forget to bring the sheets with the axioms of E from the back of the book to lectures, we'll use them alot.

One other thing to note, if you have a problem with the course, please come and see ME first. If you are still not happy, go to the course co-ordinator, Richard Ganong. After this the next in line is the Undergraduate Director Mort Abramson, and only if he cannot help you are you allowed to approach the Chair, Alan Dow.

Ok, so you wanted a web page, here it is, web page. For those of you who turned up late for the class here is some general information which you probably missed.

If you wish to transfer into/out of this section DO NOT come to me for a letter!!! For this course ONLY go directly to the Undergraduate Office Ross N503.

**Course:** 2090.03 N.
**Lectures:** MWF 8.30am-9.30 am, CLH C.
**Instructor:** Stephanie van Willigenburg.
**Email:** steph@mathstat.yorku.ca (please don't use unless necessary, thank you).
**Office hours:** MW 10.30am-12 pm, Ross S621.
**Tutorials:** TTh 11.30am-12.20pm, Ross N501 (Michael Hrusak).

**Course Text:*** "A logical approach to discrete math" *by David Gries, and Fred B. Schneider, Springer Verlag, 3rd, 4th or 5th printing.

**Syllabus:** The course will cover chapters 3,4,8,9 of the course text, *however*, the lectures will cover a lot more than this too.

**Evaluation:** There will be 5 assignments, 2 class tests, and 1 final exam. Failure to complete any of these requires a medical certificate, and for me to be contacted within 48 hrs of the deadline by either you/a friend/relative. Any other reasons come and see me.

**Marking Scheme:**

Note, invariably term marks are higher than Exam marks so try your best on those tests.

Undergraduate grades (i.e., marks) at York are always *letters*
(A+, A, ..., F). In this course, the letter grade will correspond to a
numerical grade *roughly* according to the following formulas:

90-100: A+ 80-89: A 75-79: B+ 70-74: B 65-69: C+ 60-64: C 55-59: D+ 50-54: D below 50: E or F (both fails)The homework assignments will be worth 15%. The remaining 85% is calculated as follows:

LetTbe the average of the test grades andFthe grade on the final exam. The remaining points are calculated with the formula, max{.20T+ .65F, .20F+ .65T}.

Suggested background reading for the course is Chapters 1 and 2 of the course text.

If you have a problem with the course, please come and see ME first. If you are still not happy, go to the course co-ordinator, Richard Ganong. After this the next in line is the Undergraduate Director Mort Abramson, and only if he cannot help you are you allowed to approach the Chair, Alan Dow.

**Courses in Computer Science, in which formal logic gets used**

- 1020, 1030, 2011 all feature boolean "expressions"
- 3111 (program verification; uses pred. logic)
- 3101 analysis of algorithms
- 3311 software design
- 3331 object-oriented programming
- 4352 real time systems
- the future stream in software engineering

Stephanie van Willigenburg