Contact information:
Mike Zabrocki
My last name ``at`` mathstat.yorku.ca
Office: DB (TEL) 2026
office hours: Monday 1-2 (online), Wednesday 3-4 in N Ross 501 (and online)
Course description:
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. Prerequisite: 12U Advanced Functions (MHF4U) or Advanced
Functions and Introductory Calculus (MCB4U). NCR note: Not open to any
student who is taking or has passed a MATH course at the 3000 level or higher.
Most High School mathematics problems are solved using algorithmic methods or
via reference to model solutions. One purpose of this course is to enable
students to develop the confidence and ability to attack richer and more
demanding problems. The attempt to check work and to explain one’s discoveries
to others leads naturally to the need for explanation. Learning how to present
convincing reasoning — or proof — is one of the course outcomes.
With an emphasis on communication/convincing argument, there is a critical
contribution to be made by: group work, reading a proposed 'proof' including
other student's work, presenting and discussing as a whole class. There is also
value in working through several different approaches to solve a problem, and
taking the time to understand an alternative approach offered by a peer in the
class. Doing mathematics well includes talking and listening to mathematics
and there will be assignments that require collaborative work with another
student in the class, as well as support for forming study groups.
The main goal of this course is to develop skills that lead to understanding
and communicating a convincing argument. Support will be given for proof
presentation, especially for the kinds of proofs that students are expected
to produce in their second year and higher level courses. This includes
induction, and arguments with counting and with inequalities. Formal proof
writing exercises will be introduced in the second half of the course, once
problem solving and informal justification skills reach an acceptable level.
Course references:
The course textbook is available free online
Mathematical Reasoning: Writing and Proof Version 3 by Ted Sundstrom.
Other useful references are
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.
Announcements:
(September 1, 2021) Welcome. Tutorials for this class will meet for the first
time on in the week of September 13. Please see e-class for class material
and information about this course, but the schedule of topics and important dates
will be recorded here.
