Problems, Conjectures and Proofs
MATH 1200 3.00
Section B

Lecturer: Paul Szeptycki
Office: TEL 2031
Mondays 5:30-7:00 in SL107

Mondays 7:00-8:30 in either VH 1016 (tutorial 1) or VH 1018 (tutorial 2). You are enrolled in one of these.

Office hours Tuesday and Thursday 1:00-2:00

Course Description

From the undergraduate course calendar: Extended exploration of elementary problems leading to conjectures, partial solutions, revisions, and convincing reasoning, and hence to proofs. Emphasis on problem solving, reasoning, and proving. Regular participation is required.

Main Objectives: This course is designed for first year mathematics majors to develop basic skills essential for more advanced courses in mathematics. An emphasis will be placed on writing proofs. There are two main aspects to proofs that we will focus on, problem solving and exposition. One of the challenges in upper division mathematics courses is to come up with proofs to problems that are not familiar or similar to problems presented in lectures or in the textbook. This requires a variety of problems solving techniques and lots of practice to develop the confidence to attack a problem without yet knowing how to solve it. Once one has solved a problem, or come up with a proof, one must then clearly communicate that solution in a clear and concise manner. Learning how to present convincing reasoning (aka a proof) is the main objective of this course. We will be learning the language of mathematical exposition.

Of course, this means a lot of hard work on your part. You will not succeed in this course if you do not actively engage in solving problems, writing proofs, and working through examples each and every week. If you fall behind one week, it can be very difficult to get caught up. E.g., attend the tutorials and start work on the homework assignments early!!


12U Advanced Functions (MHF4U) or Advanced Functions and Introductory Calculus (MCB4U). Course credit exclusion 2200 3.00. NCR note: Not open to any student who is taking or has passed a MATH course at the 3000 level or higher. (or equivalent).


A Concise Introduction to Pure Mathematics by Martin Liebeck, CRC Press ISBN 978-1584881933
We will cover, time permitting, chapters 1-6, 8, 10, 11, 13, 17-19, 21, and 22 of the text.



Important dates

Academic dishonesty

Any form of academic dishonesty (e.g., cheating on a test, quiz or final exam etc...) will not be tolerated. If I suspect a student of cheating, I will deal with the case in accordance with the Senate Policy on Academic Honesty . Penalties for cheating on a test, quiz or final exam may range from failing the course, suspension from the university or even expulsion from the university. DO NOT CHEAT, it is not worth it.


Suggested homework

I will give a list of suggested homework problems from the end of each section and perhaps from other sources. Do as many of these as you can. They might appear on future tests so if you have trouble with any of them, bring your questions to class and your tutorial.