Math 1090 A Course Information

Math 1090 A Course Information

Announcements, Lecture Notes, Outlines

(Feb 26) To obtain your grade on the Final Examination and unofficial grade for the course click here.

  • (Feb 13) The seating plan for tonight's final examination is available if you click here.

  • (Jan 9) I will meet the class on Friday, January 12, at the usual time and place to discuss the process of remediation. Details are also available on the web.

  • (Dec 7) Grades for the December exam and course grades will be available only after the drop date for the course (likely late January or early February). Arrangements for making up missed work will be established once the CUPE strike is over.
  • (Dec 1) The December exam will be given in the Student Fieldhouse. Click for directions on how to find the room and seating information.
  • (Nov 30) Assignment 5 will be collected Monday, December 4 at noon. Solutions will be posted later that day.
  • (Nov 30) Another old exam has been given to Club Infinity. Copies can be purchased today, Friday and early next week.
  • (Nov 30) For the notes for December 1, click here.
  • (Nov 25) For a continuation of my notes on existential quantification, click here.
  • (Nov 25) There will be a FINAL EXAMINATION for this course given on the originally scheduled date and at the originally scheduled time. (The room may change -- you should be able to check the registrar's web pages for details later in the week.) Old exams are available from Club Infinity, Ross N537. Students who do not write this exam will have the opportunity to write an exam after the makeup period planned to follow the end of the CUPE strike.
    Please note that it is not permitted to rewrite Final Exams. This means that once you have written the exam in December you will not be permitted to write a second time at a later date.
    There will be provisions for making up work missed due to the strike for all students, whether or not they write the exam in December.

  • (Nov 23) For corrected notes for the lecture planned for November 24, click here.
  • (Nov 21) For notes for the lecture planned for November 22, click here.
  • (Nov 20) We started working seriously through the theorems in Chapter 9. Click for some proofs.
  • (Nov 15) The Professor Ganong has updated his Leibniz notes and the previous link and the one below each point to the updated version. In class we finished our treatment of Chapter 8 and looked at the Trading Axioms (9.2) - (9.4) and Axiom (9.5). (9.5) is used to move expressions (where the condition on no free occurrences is met) in and out of universal quantifications.
  • (Nov 14) The midterm has been revised and sent for printing . It has four questions though the first now has two parts.
    1. (10 pts.) Proof of propostional result using the Deduction Theorem and proof of the same result using Chapter 3 methods.
    2. (6 pts.) Showing given predicate expression is NOT a theorem.
    3. (7 pts.) Fill in the blanks in the vein of HW 4, problem 4.
    4. (7 pts.) Proof in predicate logic. First step uses (8.18).
  • (Nov 13) Thanks to everyone who pointed out the error in my solution to problem 4 on the old midterm. A corrected version has been posted below. The lecture covered (8.14) (for details see the Nov 10 notes), (8.15) and the range split axioms (8.16) - (8.18).
  • (Nov 10) Click for a version of last year's second midterm exam and corrected solutions in pdf format. Please note that there will be no questions based on Chapter 9 on the midterm Friday. Once your test is drafted I will post an outline.
  • (Nov 9) The homework assignment due tomorrow will be picked up Monday noon instead. For my notes for the lecture I will give on November 10, click here.
  • (Nov 6) The typographical errors in assignment 4, problem 4 have been corrected. Please print a new version.
  • (Nov 3) For a definition and brief explanation of bound and free occurrences of variables click here

  • (Nov 1) Last Fall Professor Ganong posted notes supplementing the text's treatment of CONtextual substitution and the extended Leibniz rules.
    Click for his CONtextual substitution supplement and his Leibniz supplement. The treatment in class will closely follow these notes.

  • (Oct. 30) This is a list of the grades received on Test 1. The maximum possible grade was 30.
        1.5    3.0    4.5    5.0    5.5    6.0    6.0    7.0    7.0    7.5    7.5 
        7.5    8.0    8.0    8.0    8.0    8.0    8.5    8.5    8.5    8.5    9.0 
        9.0    9.5   10.0   10.0   10.0   10.0   10.0   11.5   11.5   11.6   12.0 
       12.0   12.0   12.0   12.5   12.5   13.0   13.5   14.0   14.5   14.5   14.5 
       14.5   14.5   15.0   15.0   15.0   15.0   15.5   15.5   15.5   16.0   16.5 
       17.0   17.0   17.5   17.5   17.5   18.0   18.0   18.0   18.5   19.0   19.0 
       19.0   19.0   19.5   19.5   19.5   20.0   20.0   20.5   21.0   21.0   21.0 
       21.0   21.0   21.5   21.5   22.0   22.0   22.0   22.5   22.5   23.0   23.0 
       23.0   23.0   23.5   23.5   23.5   23.5   24.0   24.0   24.5   25.0   25.0 
       25.0   25.0   25.0   25.0   25.5   25.5   25.5   26.0   26.0   26.5   26.5 
       26.5   26.5   26.5   27.0   27.0   27.0   27.5   27.5   27.5   27.5   28.0 
       28.5   28.5   28.5   28.5   28.5   28.5   29.0   29.5   29.5   29.5   29.5 
                     N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
                   132   18.171   19.000   18.331    7.454    0.649
                   MIN      MAX       Q1       Q3
                 1.500   29.500   12.000   25.000
    Grades to date are available if you click here.
    To find yours search under the last five digits of your student number.

  • (Oct. 28) Click for October 30 lecture notes.
  • (Oct. 26) Click for October 27 lecture notes.

    October 26, 2000

    Please take note:

    I am a member of the YUFA bargaining unit which is not on strike.

    My courses, MATH 1090 A, MATH 2320 A, ITEC 1011 A, BETHUNE 1800 A, will continue to meet. All tests and quizzes will be given as scheduled.

    Students should be aware that under Senate Guidelines they cannot be penalized if they choose not to cross picket lines to attend lectures, write tests or quizzes, submit assignments.

    Once the strike is over, arrangements will be made for makeup tests and quizzes and to submit assignments which were due during the period of the strike. I will post to the appropriate course web pages lecture information to help students who miss classes keep up with the course material covered.

    Some paternal advice:

    This strike may very well last three or more weeks. If you lose touch with your studies during this time interval it may be very difficult to adequately catch up afterwards. Make every attempt to do whatever reading is assigned, to work through whatever notes are made available, and to do (even when you might wait to submit them) any course assignments.

    During the last strike, students suffered loss of credits, loss of money (for courses they ended up dropping), and reduced GPAs because they misjudged their ability to catch up once the strike ended.

    Stay informed:

  • CUPE 3903
  • York University Administration
  • YUFA
  • Announcements:

  • (Oct. 15) I have prepared a draft version of the test for Friday. Here is the outline. I will assign point values once I have the questions in final form.
    1. Given two boolean formulas, P and Q, write their truth tables and answer questions related to validity, logical implication, local equivalence and (a syntactic question based on semantic information) theoremhood.
    2. Fill in complete reasons (in style of model proof) for a single proof step.
    3. Prove a Derived Inference Rule. The proof steps are given, you just need to fill in the reasons.
    4. Proof of a Chapter 3 result in style of text.
    5. Proof of a Chapter 3 result in style of text.
  • (Oct. 3) I have posted a version of the first midterm from the previous winter term. It has been slightly modified to conform to the current approach of the course. Click for a pdf version of the question paper and for a pdf version of the solutions.

    To view and print pdf you need the free Acrobat reader.

  • (Sept. 25) I have posted a Model Proof in the Logic E in (html) and (postscript) and (pdf). It is intended to indicate the greatest level of detail I would normally require in proving a theorem.
  • (Sept. 21) Homework 2 has been posted. The solutions to Homework 1 will be available once the papers have been collected.
  • Tutorial times and locations for the week of September 18 and for the rest of the term are available here.
  • I am no longer the course instructor for Section B of this course. For Section B information, consult Professor Ganong's 1090 HomePage.

    Lecturer: Eli Brettler
    Office: South 508 Ross
    Telephone: 736-2100 Extension 66321
    Normal Office hours: MW 11-12:30 and by appointment

    Lectures: MWF 9:30 - 10:30 CLH B

    Tutorials: Click here.

    Text: Gries and Schneider, A Logical Approach to Discrete Math. Make certain that you have the third or later printing.

    Syllabus: The core consists of the Kemeny, Snell, Thompson supplement and Chapters 2, 3, 4, 6.2, 8, 9 of the text.

    Professor Kemeny's 1983 Lectures are available in RealPlayer format.

    Homework: These homework problems will be collected for grading. Groupwork is permitted and (in most cases) encouraged. Group assignments may be handed in. Homework is to be placed in the appropriate assignment box, North 5th floor Ross. Late assignments will not be accepted for grading.

    To view and print pdf you need the free Acrobat reader.


    Graded Assignmentsvarious dates15%
    Class TestsOctober 20, November 1730%
    Final ExamExamination Period55%

    Alternate Grading Scheme: Assignments 15%, Class Tests 55%, Final Exam 30%.
    The scheme which gives the higher grade will be used in each case.

    Note: There will be no makeups for missed tests. If you miss a test and provide a certificate indicating clearly that you were unable to write the test for reasons beyond your personal control, the weight of the test will be transferred to the final exam. Otherwise, the mark for the missed test will be 0.

    The last date to drop the course without academic penalty is November 10. It is extremely important to realistically assess your course performance prior to this date.


  • Test 1 October 20:
  • Version 1 (white) solutions in postscript and pdf.
  • Version 2 (blue) solutions in postscript and pdf.
  • Test 2 November 17:
  • Version 1 solutions in postscript and pdf.
  • Version 2 solutions in postscript and pdf.
  • Resources:

  • A Model Proof in the Logic E in (html) and (postscript) and (pdf).

    We are not alone. Click for course information from other sections.

  • Sections B, C
  • Section D

    Eli Brettler
    Last modified: Mon Feb 26 10:58:02 EST 2001