Florida Atlantic University • Fall 2019 • Markus Schmidmeier

# Mathematical Problem Solving

Welcome to my course Mathematical Problem Solving (MAT 4937, 3 credits)! We meet Wednesdays and Fridays 11:00 - 12:20 noon in Fleming Hall 423. 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, 3rd edition, Wiley 2016, ISBN-13: 978-1-119-23990-1. 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. 2-3 weeks 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. 4-5 weeks 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. 3-4 weeks 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!) as available

Credit

Homework Problems & Quizzes: Every week, I'll assign some problems as homework. They are posted here:

Homework Problems

There will be a quiz on Friday, related to the homework and/ or what we covered in class. Together, the 12 best quizzes will count for 40% of the grade.

Presentations: Two presentations of at most 10 minutes, one before February 15, both before April 5, each solving a problem related to the topics covered in class, together count for 20% of the grade.

Final Exam: The final exam is on Wednesday, May 1, 10:30 - 13:00 noon. It will count for 40% of the grade.

Further Information

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.

Contact Me

 Office hours: Wednesdays and Fridays, 15:30 - 17:00 p.m. in SE 272, or by appointment. Telephone: 561-297-0275 E-mail: markus@math.fau.edu