Math 1200 A Course Information


  • (Mar 29) Course evaluations can be accessed by clicking here. There will be a bonus of 2 or 3 points on the final examination given to those students who complete the evaluation.
  • (Mar 20) The handout for the tutorial (Mar 23 and Mar 30) is available here.
  • (Mar 14) A handout on Pascal's triangle is available here. A problem solving exercise to be handed in as part of the Problem Solving Journal is available here.
  • (Mar 5) Homework due March 18 is available here. The handout for the tutorial (Mar 9 and Mar 16) is available here.
  • (Feb 13) Homework due March 4 is available here. The handout for the tutorial (Feb 16 and Mar 2) is available here.
  • (Feb 7) Here is the arrangement for Wednesday's tutorials. The Tutorial 2 group is split. See below.
  • (Feb 2) All tutorial groups will meet on Wednesday, February 9.
  • (Jan 27) Homework due February 11 is available here. The handout for the tutorial (Feb 2 and Feb 9) is available here.
  • (Jan 27) The deadline for handing in Homework 7 has been changed to Monday, January 31 at 5:00 p.m..
  • (Jan 17) Homework due January 28 is available here. The handout for the tutorial (Jan 19 and Jan 26) is available here.
  • (Jan 11) The proof from Krantz together with some details it discussion in class in available here.
  • (Jan 3) The proof from Krantz which we will read together in class tomorrow is available here.
  • (Dec 29) Homework due January 14 is available here. The handout for the tutorial (Jan 5 and Jan 12) is available here.
  • (Nov 29) The handout for the tutorial (Dec 1 and Dec 8) is available here. There is no additional homework this term. Please use the time you would normally allocate to it to work on the Problem Solving Journal assignment.
  • (Nov 12)Homework due November 26 is available here. The handout for the tutorial (Nov 17 and Nov 24) is available here.
  • (Nov 1) Homework due November 12 is available here. The handout for the tutorial (Nov 3 and Nov 10) is available here.
  • (Oct 26) New due date for Homework 3 is Monday, November 1, at Noon.
  • (Oct 18) Homework due October 29 is available here. It will be handed out in class tomorrow. The handout for the tutorial (Oct 20 and Oct 27) is available here.
  • (Sep 27) Homework due October 8 is available here. It will be handed out in class tomorrow. The handout for the tutorial (Sep 29 and Oct 6) is available here.
  • (Sep 21) Everyone attends tutorial tomorrow.
    Please check your current registration as to which tutorial you are currently in. There have been some changes made by the Registrar. We will return to three separate tutorial meetings beginning next week.

  • (Sep 20) An excerpt from Rosen, Discrete Mathematics and Its Applications on Mathematical Induction is available here.
  • (Sep 20) The handout for Tutorial 1 is available here.
  • (Sep 14) There will be no tutorial during the first week of class. All tutorial groups will meet on Wednesday, September 22.
  • (Sep 14) For an excerpt on pictorial proofs from the book Street-Fighting Mathematics click here. We will initially concentrate on Section 4.1.
  • (Sep 14) Homework due September 24 is available here. The excerpt from Krantz, Techniques of Problem Solving is available here.

    Instructor: Eli Brettler
    Office: South 508 Ross
    Telephone: 736-2100 Extension 66321
    Normal Office hours: By appointment. I am normally on campus every day but Thursday.

    Schedule of Classes and Tutorials (with Quiz dates shown):

    FULL CLASS MEETINGS, Tuesdays 10:00 - 11:30, PSE 321
    FALL: Sep 14, 21, 28, Oct 5 (Quiz 1), 19, 26, Nov 2 , 9 (Quiz 2), 16, 23 , 30 (Quiz 3), Dec 7,
    WINTER: Jan 4, 11, 18, 25 (Quiz 4), Feb 1, 8, 15 , Mar 1 (Quiz 5) , 8, 15, 22 (Quiz 6), 29.

    TUTORIAL 01, Wednesdays 10:30 - 11:30, CC 318
    Sep 22, 29, Oct 20, Nov 3, 17, Dec 1, Jan 12, 26, Feb 9, Mar 2, 16, 30.
    TUTORIAL 02, Wednesdays 10:30 - 11:30, SC 219
    Sep 22, Oct 6, 27, Nov 10, 24, Dec 8, Jan 5, 19, Feb 2, 16, Mar 9, 23.
    TUTORIAL 03, Wednesdays 10:30 - 11:30, CC 335
    Sep 22, Oct 6, 27, Nov 10, 24, Dec 8, Jan 5, 19, Feb 2, 16, Mar 9, 23.


    Text: 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.

    Statement of Purpose: This is a critical skills course. Here are some questions to consider.

  • Just what are the objects which you consider when you do mathematics?
    What is meant by the fraction one half? How does it represent a ratio? How does it represent a quantity? Are these conceptions different? Can you reconcile them?
    How would you describe a triangle to someone (for example a blind person) who has never seen one.
    How would you describe a circle?
    What conventional conceptions do you have which inform your own thinking about these and other mathematical objects?
  • What is meant by a proof?
    How you convince yourself, and how do you convince others that an answer is correct? What are the conventions for presenting concise mathematical proofs? How well does the presentation reflect the means by which a particular mathematical discovery was made? What does it mean for an ordinary language argument (mathematical or otherwise) to be valid? What is a counterexample? How does one make conjectures and how does one go about trying to assess whether they are correct?
    It is pretty easy to convince oneself or others of the correctness of answers which seem intuitively correct. What is much harder is to convince when answers while correct are counterintuitive. An example some of you may have seen is the "Monty Hall Problem".
  • Can you learn problem solving?
    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 to deal with problems which are genuinely novel?
    The text, "Thinking Mathematically" by John Mason has a rich selection of problems for consideration. Most require minimal technical background but almost all require hard thinking. Mason suggests a way of working strongly grounded in self awareness both in terms of what you are doing, and what you experience while doing it.
  • Are there techniques which extend your problem solving and proving capabilities?
    You will learn about combinatorial proofs which are arguments based on the analysis of situations rather the manipulation of formulas.
    You will learn about recursive methods and mathematical induction as a tool in calculations and in proofs.
    You will learn to use representations from other branches of mathematics (for example, geometric models to solve probability problems) to help obtain answers.
    You will learn to present proofs and explanations which are concise and logically correct.
  • What are expected outcomes of this course?
    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.

  • Evaluation:

    ParticipationSee below10%
    Individual Investigation and Writing AssignmentsOne assignment to be handed in every other week25%
    Problem Solving Journal See below20%
    Quizzes3 Fall, 3 Winter15%
    Final ExaminationWinter examination period30%

  • Participation: 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.

    Attendance at the weekly classes and at the tutorials is obligatory. You will lose 2 points from your course grade for each class or tutorial in excess of two which you miss each term. You are expected to actively participate in small group and whole group discussion.

  • Individual Investigation and Proof Assignments: Questions for investigation and solution will be assigned biweekly. Solutions are to be handed in. The following grading rubric will be used.

    Homework will be graded from 4 points. Grades will be assigned as follows:

    Note that to receive full credit (4 points from 4) you must go beyond simply solving the problem as posed. Learn to think of your solutions as a starting point.

    Do your own work. Don't look for a solution on the web or copy one from another student's work unless you already have found your own solution and intend to review another to make a comparison. Work that is not original will be graded accordingly. Presenting someone else's work as your own without proper citation is academic dishonesty. You must cite any internet sources which you have consulted. You will be required to take the York University Academic Integrity Tutorial.

    The lowest assignment grade each term will be dropped.

  • Problem Solving Journal: You are expected to continue working on the problems discussed in class and in the tutorials and to keep a running record of your experiences and discoveries. The journal will be submitted at the end of each term for grading. Due dates are December 10 for the Fall and April 4 for the Winter. More detail as to format and expectations will be given in class.

  • Quizzes: There will be 6 in class quizzes, 3 per term.

    Here are some sample quiz question types:

    1. Given a problem and a sketch of a solution, formulate a more complete solution and present it with justification.
    2. Given a proof of some result, find any errors and correct them.
    3. Given various conjectures, find counterexamples if false, proofs if true.
    4. Provide simple proofs including direct proofs, indirect proofs, proofs by mathematical induction.
    The grade will be obtained by taking the average of the best 2 quiz grades from each of the terms. There will be no makeups for missed quizzes.

  • Final Examination: This will be a conventional timed, closed book exam, scheduled during the University Final Examination period. Question types would be similar to those examples given for the quizzes. Click here to view last year's examination.

    Handouts and other resources:

  • Excerpt on pictorial proofs from the book Street-Fighting Mathematics. For the complete book, download from here.
  • Homework due September 24 and excerpt from Krantz, Techniques of Problem Solving.
  • Tutorial 1
  • Excerpt from Rosen, Discrete Mathematics and Its Applications on Mathematical Induction
  • Homework due October 8
  • Tutorial 2
  • Homework due October 29
  • Tutorial 3
  • Homework due November 12
  • Tutorial 4
  • Homework due November 26
  • Tutorial 5
  • Tutorial 6
  • Homework due January 14
  • Tutorial 7
  • Proof from Krantz
  • Discussion of Proof from Krantz
  • Tutorial 8
  • Homework due January 28
  • Tutorial 9
  • Homework due February 11
  • Tutorial 10
  • Homework due March 4
  • Tutorial 11
  • Homework due March 18
  • Pascal's triangle summary
  • Problem solving exercise for Journal
  • Tutorial 12

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

    Note: The last date to drop the course without academic penalty is Feb 11.

    Eli Brettler