Florida Atlantic University
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Fall 2020
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Markus Schmidmeier


Mathematical Problem Solving

Welcome to my course Mathematical Problem Solving (MAT 4937, 3 credits)! We meet Tuesdays and Thursdays, 12:30 - 1:50 p.m. Pre-requisite for this course is Discrete Mathematics (MAD 2104).
This course will be taught Online-Live, we will be meeting on Zoom. Access to a computer with webcam and zoom is needed.



Textbook

We use the textbook by Paul Zeitz, The Art and Craft of Problem Solving, 3rd edition, Wiley 2016, ISBN-13: 978-1119424994. (In my opinion, the earlier editions are also fine textbooks.) 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 course objectives are to:



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. 3-4 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 and practise some of the following crossover techniques, the use of graphs, complex numbers and generating functions. 2-3 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: Every week, I'll assign some problems as homework. They are posted here:

Homework Problems

Please try to have nice solutions to several of the problems, then send me your work via e-mail, for example by scanning in handwritten work. Submit a single pdf-file, the file name should indicate your name. Together, the 11 best homework sets will count for 40% of the grade.

Presentations: Two presentations (enrollment permitting) of at most 10 minutes, one before October 1, both before November 19. In each, a problem from our textbook is to be solved which relates to one of the topics covered in class. The presentation in online, live on Zoom. Each presentation counts for 10% of the grade.

Final Exam: The final exam is on Thursday, December 10, 10:30 a.m. - 1 p.m. It will count for 40% of the grade. The first part consists of solutions to three new problems from our textbook of your choice (although one problem may be a previous homework problem, and another problem may be, say, a newspaper problem or a problem from MoMath). There is credit for picking interesting or substantial problems. No homework assignments, examples discussed in class, or problems presented before, please. The solutions need to be submitted by Tuesday, November 24 (Tuesday, December 1 at the latest), together with a scanned copy of a picture ID. I'll pick one of the problems for your talk. The second part is a presentation on Zoom during the time of the final exam. At the beginning of your talk please introduce yourself and turn the webcam on.



Math Learning Center

There is free math tutoring at the Math Learning Center.
Online tutoring is available through zoom. Click here for available times.
In-person tutoring is appointment based. Click here to search for availablitites.

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: TR 3-5 p.m. online via zoom :Meeting ID: 395 037 9152, Password: Markus3to5, from the waiting room please call me by telephone; or by appointment.
Telephone:561-459-1975 (home)
E-mail: markus@math.fau.edu

Last modified:  by Markus Schmidmeier