$\def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}}$
 © | Dror Bar-Natan: Classes: 2014-15: Math 475 - Problem Solving Seminar: (1) Next: Blackboards for Tuesday January 6 Previous: Class Home

Agenda: Solve! Solve! Write!

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu (for administrative matters only; math on email is slow and prone to misunderstandings, so I generally avoid it). Office: Bahen 6178, 416-946-5438. Office hours: here.

Classes: Tuesdays 3-4 and Thursdays 2-4 at MP 134.

Textbook. Loren C. Larson's Problem Solving Through Problems, Springer (1983), ISBN 978-0387961712.

Disclaimer. This will be my first time to teach this class. I've certainly solved some math problems myself, yet I'm not sure I know how to teach "problem solving". It will be a learning experience for me too, and it may well be that I will make mistakes.

Course Description. We'll get more competent at solving math problems and writing their solutions by solving many math problems and writing their solutions. In the first two thirds of the class or so, we will center the class around a half-hour (or so) quiz that will be given at the start of every Thursday class (usually). The Tuesday classes will usually introduce the material for the quiz, and the rest of each Thursday class will usually be devoted to analyzing the quiz and giving further examples. Sometime between the one-third point and the two-third point we may move on to the (internal) publication of the internally-refereed $5\cdot 5\cdot 619$ Journal of Mathematics, whose description will be provided later. (Or we may not). There will be a relatively "light" final exam at the end of the class.

Study Groups. Most of most of the quizzes will be questions from the relevant chapters of the book or minor variations thereof. I strongly encourage you to form study groups and spend a few hours every week on solving these problems. This is what may be the real heart of the course - everything else are just the means to encourage this to happen.

The Final Grade. I will compute a final numerical score using weights as follows. First, the score for each individual assignment will be renormalized via a power-law transform (a raw score $0\leq r\leq 100$ goes to a renormalized score $s=100(r/100)^\gamma$, for some $\gamma>0$) so that the median score on that assignment will be 75. Then:

• Assuming we stay with the quiz system throughout,
• Quizzes: 60%, though the worst 3 quizzes for each student will not be counted.
• Final Exam: 40%.
• Assuming we switch to the "Journal" option at some point between week 5 and 8,
• Quizzes + Journal score: 70%. The worst 2 quizzes for each student will not be counted, and the rules for the Journal score will be provided later. The percentage subdivision between the quizzes and the Journal score will be proportional to the length of time spent on each mode.
• Final Exam: 30%.
This done, I will then apply an appropriate increasing monotone transformation to the final numerical score determine the reported final grades. Thus the reported final grades may be different from the final numerical scores.

The reason for dropping the worst 2-3 quiz marks is to allow each student to miss 2-3 quizzes for whatever reasons, medical, family, personal, anything, with no penalty. Except in extremely unusual circumstances, no other accommodations will be made for students missing quizzes.

Class Photo. To help us learn each other's names, I will take a class photo on Tuesday of the third week of classes. I will post the picture on the class' web site and you will be required to identify yourself in the picture. With your individual consent, I will also post your names on the picture page.

Finally, here's our entry at the official UofT Calendar:

MAT475H1    Problem Solving Seminar[TBA]

This course addresses the question: How do you attack a problem the likes of which you have never seen before? Students will apply Polya's principles of mathematical problem solving, draw upon their previous mathematical knowledge, and explore the creative side of mathematics in solving a variety of interesting problems and explaining those solutions to others.

Prerequisite: MAT224H1/MAT247H1, MAT235Y1/MAT237Y1/MAT257Y1, and at least 1.0 FCE at the 300+ level in APM/MAT
Distribution Requirement Status: This is a Science course
Breadth Requirement: The Physical and Mathematical Universes (5)