SLU Inquiry Seminar
Infinity, the Fourth Dimension, Chaos and Prime Numbers
Who should take this course? Mathematical Thinking in the Real World is for students in the humanities and other disciplines that require one math course at or above a set level (usually College Algebra) to satisfy a core requirement. It is designed for students who already know the material of College Algebra and who are looking for a new and definitely more interesting way to satisfy the math requirement.
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 seminar 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 will give short presentations. You will be asked to read the text (which comes with an activity kit that includes 3-D glasses to use with 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.
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 “Shawn’s Mathematical Gallery”, http://www.math.washington.edu/~cokus/Gallery.html)
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?
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.