PMU 199H1S-L0291 Aha! Mathematical Discovery and Creative Problem Solving
Jan. 5, 2017 http://www.math.toronto.edu/mccann/199
Prof. Robert J McCann www.math.toronto.edu/mccann BA 6124 (416) 978-4658
Lectures: Thursday 14h10-16h00 RW 141
Office hours: Tuesday 14h00-14h50 BA 6124 *
* = except Jan 10 and 31; will hold 14h00 Friday Jan 6 and 27 instead
TA Yuan Yuan Zheng yuanyuan.zheng -at- mail -dot- utoronto -dot- ca
Office hours: TBD ? Wed ? 14h00-14h45 ? BA 6283 or BA 6191 ?
Text: Burger & Starbird "The Heart of Mathematics. 4th Ed." Wiley 2013
Handouts from "In process" by Peter D Taylor (Queen's University)
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This course is an exploration into the creative process and use of imagination
as they arise in the context of mathematical problem solving. The problems,
which are all at a pre-calculus level, are chosen primarily by the criterion
of aesthetic appeal, and emphasize reasoning rather than technique. Still, many
of them are quite challenging, and substantial independent thinking will be
required. The course is therefore appropriate for students from a variety of
backgrounds and disciplines. Its goal will be to hone each participant's
creativity and mathematical problem-solving skills while guiding them towards
the `Aha!' experience which accompanies independent discovery.
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Grading Scheme: Attendance and participation 10 %
Electronic Journals (Jan 20, Feb 10, Mar 3, Mar 24) 10 %
Assignments and quizzes 40 %
Final Project 40 %
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Late submissions of assigned work will be graded only at the pleasure of the
professor; if graded they'll be penalized 5% per day late, except in case of
documented medical justification.
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INDEPENDENT PROJECT: Settle on a topic in consultation with me Feb. 7 (10%)
Turn in a complete, full length rough draft Mar. 9 (30%)
Revised final draft due Mar. 30 (60%)
This project is intended to encourage you to begin to explore mathematics
independently, and pursue some topic of interest to you within the framework
of the course. Your challenge will be to address the question "What is
mathematics?" and to illustrate by investigating and discussing in depth a
particular mathematical topic of your choice, explaining how it supports your
answer. Books listed among the accompanying references, such as "The Heart
of Mathematics" or "The Princeton Companion to Mathematics" provide one set of
possible sources for students in search of topics.
Summarize your findings in a 6-8 page typed essay in logically organized
and clearly written, well-constructed sentences, paragraphs and sections.
Your report should include references to several research articles or books
that you studied while preparing it. You should have identified at
least two of these and communicated them to me by the time of our Feb. 6
consultation (which can be by email but is more usefully carried out in
person). I will provide you with feedback on your rough draft. You may
also benefit from getting feedback on both of your drafts from the writing
centers linked to the course webpage (and described in supplementary documents
posted there) before you hand them in. Schedule appointments early, as the
writing centers tend to book up far in advance.
RESOURCES FOR WRITING ASSISTANCE linked at www.math.toronto.edu/mccann/199