SLU Inquiry Seminar

Math 125 Mathematical Thinking in the Real World

Infinity, the Fourth Dimension, Chaos and PrimeNumbers

Who should take thiscourse? Mathematical Thinking in theReal World is for students in the humanities and other disciplines that requireone math course at or above a set level (usually College Algebra) to satisfy acore requirement. It is designedfor students who already know the material of College Algebra and who arelooking for a new and definitely more interesting way to satisfy the mathrequirement.

What do you learn in thiscourse? 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, sometimesusing puzzles to motivate us, and sometimes solving puzzles using themathematics we study. A variety of often surprising applications arise alongthe way. The course will developcritical thinking and problem-solving skills, and let you see some funmathematics that is usually hidden from view in lower division courses.

What will you do? In thisseminar you will explore the beauty and power of mathematics in a variety ofways. During class you willparticipate in group activities, class discussions, computer activities, andwill give short presentations. Youwill be asked to read the text (which comes with an activity kit that includes3-D glasses to use with the text) and to come to class prepared to work withclassmates, to think deeply, and to have fun with mathematics. You will writereflective paragraphs and short essays, produce creative works, and read shortstories related to the course content.

Sample topics

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

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

(Image from“Shawn’s Mathematical Gallery”,http://www.math.washington.edu/~cokus/Gallery.html)

Prime Numbers: How do public key codes (used for secure internet communication andfor 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 inhuge differences in future behavior?

Is this course aprerequisite 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 forcalculus.

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