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: Science
Breadth Requirement: The Physical and Mathematical Universes (5)

The core part of the course work is a presentation. During the course each student should make a presentation (exactly one presentation). The length of the the presentation: 1.5--2 hours.

Each presentation consists of two parts (the second part usually immediately after the first part or a week later). Each presentation should be made either by a single student or by a group of 2 students, in which case each student should talk at least 45 minutes. Currently we have enrolment of 32, so teamwork is encouraged.

Presentation should based on the study of the literature. Each presentation should be self-contained and contain major proofs. The major content of the presentation should be made on-screen (12--18 frames). Like one of those

• Previous years talks
• Random_Walk_and_PDE
• Hydrogen Atom

Students select topics either on their own or from the list at least 6 weeks before presentation (8 weeks would be preferable).

Students should work on their presentations independently, meeting me several times (the first meeting to select the topic, the last meeting to present me with (almost) final version--one/two weeks before the presentation, and as many as necessary (at least one) in between.

During presentation by other students each student is supposed to write down lecture notes, ask questions and answer my questions. Also discussion could continue on the Forum--coming!

• Presentation: 70 pts (bonus of 5 pts for exceptionally good presentation). Each team member is evaluated separately.
• Other participation (discussion): 30 pts. During each discussion student activity is evaluated (0--2 pts, 1 bonus point is possible). Then the total number of discussion points is divided by the number of presentations and multiplied by 15.

• You did not take Real Analysis, Complex Analysis or PDE classes?
• You don't know LaTeX and beamer package? –