Problem Solving - Spring 2021

Florida Atlantic University • Spring 2021 • Markus Schmidmeier

Mathematical Problem Solving
Welcome to my course Mathematical Problem Solving (MAT 4937, 3 credits)! We meet Wednesdays and Fridays, 2:00 - 3:20 p.m. Pre-requisite for this course is Discrete Mathematics (MAD 2104).
This course will be taught hybrid, either person-to-person in GS 116 on the Boca Raton campus, or online-live via zoom. Access to a computer with webcam and zoom is needed, I will send you meeting number and password by e-mail.
In this course, there will be no recordings to encourage active live participation.

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:
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. 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 one or two of the following crossover techniques, the use of graphs, complex numbers and generating functions. one week, perhaps two

Special Topic During the course we will see which area of mathematics interests us most, so please let me know! (Have a look at what our textbook has in store!) Then we can cover some sections about this topic. 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 February 19, both before April 2. In each, a problem from our textbook is to be solved which relates to one of the topics covered in class. The presentation is either in person on the white board or online-live on Zoom. Each presentation counts for 10% of the grade.

Final Exam: The final exam is on Wednesday, April 28, 1:15 - 3:45 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). I'll give details later. The second part is a presentation on zoom of one of the problems during the time of the final exam.

Update regarding the Final Exam (2021-03-19):

For the first part, please send me three problems by Friday, April 2. The problems should not be former homework problems or topics of previous presentations. One problem needs to be from Chapter 9, the second from our textbook, the third may be a newspaper problem or a mindbender. Please include a copy of a picture id (drivers licence or Owl Card).

The second part on Wednesday, April 28, is a presentation about one of the three problems (I'll pick it for you). As part of the presentation, please introduce yourself. The web cam needs to be kept on.

Tutoring
There is free math tutoring available in the Math Learning Center. Online tutoring is available through zoom. For in-person tutoring, click here for appointments. For more details, please e-mail mlc@sci.fau.edu or see the Assistant Director in GS 211E.

Further Information

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

Contact Me

Office hours: WF 10:00 - 11:30 a.m. online via zoom (Meeting ID: 395 037 9152, Passcode: Markus3to5, from the waiting room please call me by telephone); or in person in my office SE 230; or by appointment.

Telephone: 561-459-1975 (home), 561-297-0275 (office)

E-mail: markus@math.fau.edu

Last modified: by Markus Schmidmeier

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.	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 one or two of the following crossover techniques, the use of graphs, complex numbers and generating functions.	one week, perhaps two
Special Topic	During the course we will see which area of mathematics interests us most, so please let me know! (Have a look at what our textbook has in store!) Then we can cover some sections about this topic.	as available

Office hours:	WF 10:00 - 11:30 a.m. online via zoom (Meeting ID: 395 037 9152, Passcode: Markus3to5, from the waiting room please call me by telephone); or in person in my office SE 230; or by appointment.
Telephone:	561-459-1975 (home), 561-297-0275 (office)
E-mail:	markus@math.fau.edu