Math 2200 A (2016 - 17) Course Information


  • (Mar 25) The FINAL EXAM for this course is on Monday April 17 at 2:00 p.m. in DB 1004.

    The exam has seven questions. The first question has three parts and is worth 30 %. The remaining seven questions are each worth 10 %.
    Here is an indication as to what to expect.

    1. A single statement is given and is to be proved using each of three different (proof by cases, mathematical induction, direct proof) methods.
    2. A divisibility statement is given and is to be proved true or shown to be false.
    3. As above, a divisibility statement is given and is to be proved true or shown to be false.
    4. Proof of a basic divisibility fact with application to a question on common divisors.
    5. Proof using Strong Mathematical Induction.
    6. A geometry question using Pythagorean Theorem and the area formula for a triangle.
    7. Statement of the Fundamental Theorem of Arithmetic with an application.
    8. A coordinate geometry question whose solution uses high school algebra.
    For warmup questions for some the topics and methods, CLICK HERE.

  • (Mar 23) The tutorials on Mar 27 and Apr 3 are CANCELLED.
  • (Jan 23) The drop date for the course is February 10. The date on the course outline was wrong and has been corrected below.
  • (Nov 24) The date of Class Test II has been corrected on the review sheet.

    Instructor: Eli Brettler
    Office: South 508 Ross
    Telephone: 736-2100 Extension 66321

    Normal Office hours: By appointment. I am usually available Monday afternoon (2:00 - 4:00) and Thursday, early afternoon (1:00 - 3:00). To make an appointment, please send me an email.

    Classes: Thursdays, 4:00 - 5:30, VH 3006.

    The first Fall class is on Thursday, Sep 8 and the last Fall class is on Thursday, Dec 1. The first Winter class is on Thursday, Jan 5 and the last Winter class is on Thursday, Mar 30. There is no class on Thursday, Oct 27 (Reading Days) and on Thursday, Feb 23 (Reading Week).

    Tutorials: Mondays, 6:00 - 7:00, alternate weeks. Tutorial attendance and participation is an integral part of the course. New problems and exercises are considered in tutorial.

  • TUTORIAL 1 will meet Sep 19, Oct 3, Oct 31, Nov 14, Jan 23, Feb 13, Mar 6 and Mar 27 in VH 1152.
  • TUTORIAL 2 will meet Sep 26, Oct 17, Nov 7, Nov 21, Jan 30, Feb 27, Mar 13 and Apr 3 in VH 1016.

    Tutor: TBA

    Text: There is no assigned textbook. Supplementary notes and other study materials will be posted from this page.


  • Martin Liebeck, A Concise Introduction to Pure Mathematics, Third Edition.
  • John Mason, Leone Burton, Kaye Stacey, Thinking Mathematically, Second Edition. This book gives an approach to problem solving and the problem solving experience. It is also a source for rich and varied problems.
  • G. Polya, How to Solve It: A New Aspect of Mathematical Method.

    Online Resource: Steven Strogatz on the Elements of Math (New York Times, Opinionator Blog). For access to his posts click here. You can hear Strogatz on NPR (National Public Radio) by clicking here.

    And just for fun: Tom Lehrer singing, That's Mathematics.

    Statement of Purpose: Most of the problems you solved in high school were done mechanically or by mimicking solutions to similar problems in the textbook. What means are available and how do you develop the skills necessary to deal with problems which are genuinely novel? This course is intended to address this concern.

    You will learn to take risks as you engage with learning new mathematics and doing mathematical problem solving.
    You will learn to express mathematical ideas with precision and clarity.
    You will learn to ask questions whose consideration can lead to deeper understanding.
    You will discover for yourself that mathematics is as much about thinking as about doing. A polemic by Paul Lockhart on the current state of mathematics in schools is available here.

    Be brave. You will venture to places which are new.


    You are expected to attend the classes and tutorials and to participate actively. Participation is how you show your commitment to the course and to the other students taking the course with you. You are expected to share both of your mathematical knowledge and the feelings you have as you engage in doing mathematics.


    Homework and In Class Problem ActivitiesNormally, one every two weeks25%
    Class Tests Oct 20, Dec 1, Feb 2, Mar 1630%
    Final ExaminationExamination period (Apr 7 - 24)45%

  • Homework: Homework consists of one or more questions related to the material considered in class or in the tutorials. You may discuss the problems with other students and with the tutors but must write up solutions completely on your own. Do your own work. Presenting someone else's work as if it is your own (i.e., without proper citation) is academic dishonesty. You must cite any outside sources which you have used.

    You will be asked to complete the York University Academic Integrity Tutorial prior to handing in any homework. Work that shows evidence of having been copied will receive a grade of 0.

    Tentative homework due dates are Sep 15, Sep 29, Oct 13, Nov 10, Nov 24, Jan 19, Feb 9, Mar 2, Mar 23.

  • In Class Problem Activities: Your understanding of the homework and course material may also be tested through in class problem activities. More detail on these activities will be available later.

  • Class Tests: These are conventional timed, closed book tests. Each will be 75 minutes in length.

  • Final Examination: This will be a conventional timed, closed book, 180 minute exam, scheduled during the University Winter Examination Period. Do not make travel plans prior to the publication of the examination date.

    Handouts and other resources:

  • Homework 1 due Sep 15
  • Tutorial, Sep 19 and 26
  • Homework 2 due Sep 29
  • Class Exercises Sep 22
  • Tutorial, Oct 3 and Oct 17
  • Homework 3 due Oct 13
  • Homework 4 due Nov 10
  • Test 1 Coverage and Review
  • Class Exercises Oct 13
  • Tutorial, Oct 31 and Nov 7
  • Class Exercises Nov 10
  • Tutorial, Nov 14 and Nov 21
  • Homework 5 due Nov 24
  • Test 2 Coverage and Review (corrected)
  • Class Exercises Nov 24
  • Homework 6 due Jan 19
  • Tutorial, Jan 23 and Jan 30
  • Class Discussion Problems, Jan 2017
  • Homework 7 due Feb 9
  • Divisibility Problems, Jan 2017
  • Test 3 Coverage and Review
  • Homework 8 due Mar 2
  • Tutorial, Feb 13 and Feb 23 with reading from Polya.
  • Homework 9 due Mar 23
  • Tutorial, Mar 6 and Mar 13
  • Class Discussion Problems, Method of Euclid's Lemma
  • Test 4 Coverage and Review
  • Class Discussion, Fundamental Theorem of Arithmetic
  • Warmup Questions to practice for Final

    To read files in pdf format you can use the the free Acrobat reader.

    Note: The last date to drop this course and not receive a grade is Feb 10. If you drop the course by this date it will not appear on your transcript. If you drop this course between Feb 11 and Apr 5 it will appear on your transcript with a grade of "W". Withdrawal does not affect your GPA or count towards the credits required for your degree.

    It is extremely important that you realistically assess your course performance prior to these dates.

    Eli Brettler