SLU Inquiry Seminar

Math 1250 Mathematical Thinking in the Real World

Infinity, the Fourth Dimension, Chaos and Prime Numbers

Who should take this course? Mathematical Thinking in the Real World is approved for the Ways of Thinking: Quantitative Thinking University Core requirement. It is designed for students who do not need any further math classes and who are looking for an interesting way to satisfy a mathematics or core requirement. The prerequisite is EITHER Math 1200 with a grade of C- or higher OR Math Waiver per Advisor with a minimum score of 1200, or SLUMP with a minimum score of 1400.

What do you learn in this course? We study some of the great ideas of mathematics: infinity, the fourth dimension, prime numbers and chaos. We explore these topics in a variety of ways, sometimes using puzzles to motivate us, and sometimes solving puzzles using the mathematics we study. A variety of often surprising applications arise along the way. The course will develop critical thinking and problem-solving skills, and let you see some fun mathematics that is usually hidden from view in lower division courses.

What will you do? In this class you will explore the beauty and power of mathematics in a variety of ways. During class you will participate in group activities, class discussions, computer activities, and give short presentations. You will be asked to read the text and to come to class prepared to work with classmates, to think deeply, and to have fun with mathematics. You will write reflective paragraphs and short essays, produce creative works, and read short stories related to the course content.

Sample topics

Puzzles: We start the course with a week of puzzles, some of which relate to later topics in the course. Examples: How can we detect which is the underweight coin in a stack of nine gold coins if we have available only a balance scale that can only be used twice? How can we rescue someone trapped on the other side of a square moat if we have only two boards available that are not quite long enough to reach across the moat? How can three officers get three prisoners across a river using only a rowboat that can carry at most two people if the officers can never be outnumbered by prisoners on either side of the river or on the rowboat?

Infinity: Imagine you are the manager of a hotel with an infinite number of rooms, all of which can hold one guest. When the hotel is full, can you accommodate one additional guest? How? How about adding an infinite number of new guests?

Fourth Dimension: What does a four dimensional cube look like? How can we think about and picture a four-dimensional object in three (or two) dimensions? What would it be like to live in a four-dimensional house?

(Image from (archived site) “Shawn’s Mathematical Gallery”, http://web.archive.org/web/20011104195202/http://www.math.washington.edu/~cokus/Gallery.html)

Prime Numbers: How can we prove that there is an infinite number of prime numbers? How do public key codes (used for secure internet communication and for financial transactions) work? Why is it easy to use these codes but (almost) impossible to break them?

Chaos: What is a fractal? How can you create fractal images? How can small differences in starting conditions result in huge differences in future behavior? What does this have to do with the weather?

Is this course a prerequisite for other math courses? No. If your program requires that you take calculus eventually, then you should take the course appropriate to your background to prepare for calculus.

What if the course fills up for the Fall? Talk with your advisor about arranging your schedule to take this course in the Spring. Since the topics in this course don’t much depend on your high school math courses, but mainly require careful logical thinking, you won’t be adversely affected by waiting a semester.