Math 47a - Introduction to Research

(From Problem-Solving to Research-Writing)

Information for students, Fall 2011

Class meets at: Goldsmith 226, MW 2 - 3:20 PM
Lecturer: Dmitry Kleinbock
Office: Goldsmith 207, phone 6-3059
Office Hours: Tu and Fr 4 - 5 PM, or by appt.
E-mail address:
Teaching assistant: Matthew Moynihan, office hours: Tue 2 - 3 PM and Fr 1 - 2 PM, Goldsmith 111.

Course materials:


TeX links:

The goal of this writing-intensive course is to give students an idea of what it's like to do mathematical research. The only prerequisites are calculus, basic linear algebra, and some familiarity with proofs.

In the first half of the course basic mathematical problem-solving skills and strategies will be surveyed and then applied to a wide variety of situations. Many of the problems will be essentially background-free, that is, the key to a solution will lie in a creative idea rather than in use of "heavy machinery" of higher mathematics. There exist numerous examples of fun (Olympiad-style) problems which require only elementary school background but lead to some serious mathematics. There will be weekly problem assignments preceded by instructor's explanations, in some cases reviewing the background needed for problems, and discussion sessions where students will present and discuss their solutions (after one or two weeks of work). Possible topics include: games and algorithms, combinatorics and counting principles, induction, invariants, divisibility, elementary algebra, geometry and analysis.

In the second half of the course, selected problems mentioned in the first part will be gradually transformed into research projects, which will involve generating data, making conjectures and eventually writing a mathematical paper in LaTeX (we plan to spend part of the class time in a computer lab learning basic typesetting skills). As the course satisfies the writing-intensive requirement, there will be several writing assignments, including a mid-term project and the final paper. Each will need to be revised. Students will also give oral presentations on their projects.

Reading materials will be distributed in class whenever relevant; in the beginning of the course we will closely follow the book Problem-Solving Strategies by A. Engel, which is placed on reserve at the library. Many useful links related to LaTeX can be found at the web site of this course as taught in Spring 2003 by Ira Gessel.

Have a great semester!