2012S PMU199H1S Mathematical Discovery

From TorontoMathWiki

Course Information (COURSE COMPLETED, see Fall 2012 version of course)

Course ID: PMU199H1S Mathematical Explorations

Instructor: Marco Gualtieri

Class schedule: Thursday 3pm-5pm in Bahen Centre, room 2179, starting Thursday 12th January, 2012.

Course Outline

This course is an exploration of great ideas in mathematics. The course will feature a variety of interesting mathematical topics accessible to the intelligent layperson. Topics will include infinity, paradox, dimension, Möbius strips, fractals, recursion, trees, space, and other topics. Students will write a non-technical paper, make a presentation on a mathematical topic, and keep a journal which summarizes their progress as well as their difficulties in understanding the topics of the course.

Textbook

Burger & Starbird "The Heart of Mathematics. 3rd Ed." Wiley 2010. Older versions are fine.

Assignments

The homework problems do not require mathematical training, but they are challenging and require deep thought and independent thinking. They emphasize reasoning rather than technique. Late assignments are not accepted. It is better to hand in something incomplete than nothing at all. Do not, under any circumstances, make it seem complete (by writing nonsense) if you know it is not.

Click on the assignments below, login to google docs, and make your own copy of the assignment and then share your assignment with me (allowing me to comment) on google docs. I don't want a printout.

Assignment 1: Due Jan 19

Assignment 2: Due Jan 26

Assignment 3: Due Feb 2

Assignment 4: Due Feb 9

Assignment 5: Due Feb 16

Assignment 6: Due Mar 1

Assignment 7: Due Mar 8

Assignment 8: Due Mar 15

Assignment 9: Due Mar 29

Question site

The question site for this course is located here. Please participate in the discussion by asking and answering questions on here.

Join the site, and enter your full name where it asks you to. I will be there regularly to answer questions, and your classmates will hopefully do the same.

Evaluation

1. Class participation: 10%
2. Assignments: 30%
3. Final project: 60%

Final project

The final project is an opportunity to explore independently a topic of your choosing in mathematics. You should aim for the style to be that of a popular science writer, such as these feature columns of the AMS, the columns of S. Strogatz in the NY Times, or the science writing of J. Bohannon. You would also benefit from the very interesting videos by Vi Hart. There are many fascinating topics in the textbook which we will not have time to cover, and you may use the book as a starting point for finding more resources.

The format is a 4000-5000 words document shared with me by google docs. The document will be developed in three stages:

1. (20%) Feb 16: Decide on a topic and submit a single page containing:
   • a (grammatically correct!) single paragraph topic description
   • a diagram of the possible structure of the paper including sections, subsections, and the purpose of each subsection (they could be examples, arguments, evidence, etc.)
   • a list of at least two references which will be used, besdies the textbook.
2. (40%) Mar 15: Submit a complete first draft on google docs. I will be marking with the following three criteria in mind:
   • Clarity of overall document structure: each part must have a clear purpose and must contribute to the whole paper.
   • Quality of the mathematical explanations: would this make sense to the average non-math student? Is the reasoning correct?
   • Quality of the language: Are the sentences carefully constructed? Are there spelling/grammar errors? Is it written in an engaging style?
3. (40%) March 29: Submit the final draft. I will comment on your first draft, and so will another student in the class. These issues must be addressed, and you must make your own improvements as well. The overall quality of the paper will be assessed using the same criteria as above.

Some ideas for final project topics: Projective geometry and the Renaissance, Special relativity and Minkowski space, Polytopes and the work of H. S. M. Coxeter, Sorting algorithms, Colour space, Voronoi diagrams and clustering, the Quaternions, Tessellations of the plane, The projective plane, the Dirac belt trick, the complex numbers and the Riemann sphere, combing the hair on a sphere...

Writing Assistance

Writing Centre

Writing workshops

How not to plagiarize

How to reference properly

Improving your English

Accessibility Needs

If you require accommodations for a disability, contact Accessibility Services: email webpage.