Markus Schmidmeier
Mathematical Sciences
Charles E. Schmidt College of Science

Mathematical Problem Solving

Fall 2012

Welcome to my course Mathematical Problem Solving (MAT 4937, 3 credits)! We meet Tuesdays and Thursdays 5:00 - 6:20 p.m. in BU 308. Pre-requisite for this course is Discrete Mathematics (MAD 2104).

Textbook

We use the textbook by Paul Zeitz, The Art and Craft of Problem Solving, Wiley 2006, ISBN-13: 978-0471789017. Highly recommended for extra reading (and inexpensive) is George Polya, How to solve it, Princeton University Press 2004, ISBN 0-691-11966-X

Course Description

This course will concentrate on understanding, exploring, and solving, or attempting to solve, problems of various contexts and complexity. Heuristics, strategies, and methods of problem solving are discussed and practised extensively in class and in student assignments. Communicating mathematics, reasoning and connections between topics in mathematics are emphasized.

Course Objectives

The student will be able to:

• recognize and understand precisely stated problems,
• explore various parts of a problem, introduce variables, draw pictures and look for related problems,
• learn a variety of problem solving techniques,
• apply logical reasoning and mathematical methods towards solving problems,
• practise efficient communication about problems and solutions, both orally and in writing.

Topics

 Strategies for Investigating Problems (Chapter 2) A good math problem, one that is interesting and worth solving, will not solve itself. You must expend effort to discover the combination of the right mathematical tactics with the proper strategies. Strategy is often non-mathematical. Some problem solving strategies will work on many kinds of problems, not just mathematical ones. Fundamental Tactics for Solving Problems (Chapter 3) Many fundamental problem-solving tactics involve the search for order. Often problems are hard because they seem chaotic or disorderly; there appear to be missing parts (facts, variables, patterns) or the parts do not seem to be connected. Finding and using order can quickly simplify such problems. Consequently we will begin by studying problem-solving tactics that help us find or impose order where there seemingly is none. The most dramatic form of order is symmetry. Three Important Crossover Tactics (Chapter 4) A crossover is an idea that connects two or more different branches of math, usually in a surprising way. In this chapter we will introduce perhaps the three most productive crossover topics: Graph Theory, Complex Numbers, and Generating Functions. Special Topics At the beginning of the course we will see which areas of mathematics interest us most, so please let me know! (Have a look at what our textbook has in store!)

Credit

Homework Problems: Some homework problems will be assigned every week.

Quizzes: There will be a quiz every other Thursday about some of the homework problems. Together, the quizzes will count for 20% of the grade.

Presentations: Be prepared to give two talks of at most 15 minutes each, for example about a problem from our textbook. Both presentations count for 30% of the grade.

Midterm Exam: The midterm exam takes place on Thursday, October 4. It will count for 10% of the grade.

Final Exam: The final exam on Thursday, November 29, 4:00 - 6:30 p.m. will count for 40% of the grade.

Contact Me

 Office hours: Tuesdays and Thursdays, 10 a.m. - noon in SE 230 or by appointment. Telephone: 561-297-0275 E-mail: markus@math.fau.edu

Generalities

For the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale and Financial Assistance Opportunities please see the Infos for all my courses.