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**SLU Inquiry Seminar**

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**Infinity, the Fourth Dimension, Chaos and Prime
Numbers**

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**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.

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**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.