PMU 199H1F-L0291  Aha! Mathematical Discovery and Creative Problem Solving
   Sept. 15, 2011        http://www.math.toronto.edu/mccann/199

Prof. Robert J McCann   www.math.toronto.edu/mccann   BA 6124  (416) 978-4658
       Lectures:          Thursday 15h10-17h00   BF 215 
       Office hours:      Tuesday  15h10-16h00  BA 6124 
                    
Text:  Burger & Starbird  "The Heart of Mathematics. 3rd Ed." Wiley 2010
       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 (Sept 29, Oct 20, Nov 3, Nov 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 
prof; 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 Oct. 14  (5%)
                    Turn in a complete, full length rough draft Nov. 10 (15%)
                                        Revised final draft due Dec.  1 (80%)

    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 Oct. 14 
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