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.

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

**Instructor:** Eli Brettler

**Office:** South 508 Ross

**Telephone:** 736-2100 Extension 66321

**E-mail:**
brettler@mathstat.yorku.ca

**WWW:** http://www.math.yorku.ca/Who/Faculty/Brettler/

**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.

**Tutor:** TBA

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

**Resources:**

** 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.

**Participation:**

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 Activities | Normally, one every two weeks | 25% |

Class Tests | Oct 20, Dec 1, Feb 2, Mar 16 | 30% |

Final Examination | Examination period (Apr 7 - 24) | 45% |

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.

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