# Mathematics for Liberal Arts

## Mathematics for and from All Areas of the Human Experience

### Themes

Some of the themes we want to hit in this course are

- Recursion - Just do it, then do it again, do it again, etc. This occurs, for example, in
- Prime factorization
- Egyptian math
- Fractals
- Fibonacci decomposition
- Fibonacci spirals
- Golden rectangles

- The importance of binary numbers
- Counting by partition
- Egyptian Math
- Computer representation of numbers
- Binary Finger Dancing

- One-to-one correspondence
- Any time we have a unique representation
- Counting by partition
- Infinity

- Duality
- Platonic solids
- Graphs

- We emphasize the use of
- trees:
- Probability
- Prime and Fibonacci factorization
- Fractals
- binary trees
- What is a Fractal? (Thanks Cory!)

- sets:
- Pascal's triangle (all subsets)
- Infinity (the power set)
- Probability (universal set)

- trees:

### Topics

- Art
- Religion
- Philosophy
- Science
- Chaos
- Dynamics

- Nature
- The Fibonacci Numbers
- Fibonacci Spirals
- Fibonacci Nim - A counting game that will allow you to win big! (There's a fairly complicated winning strategy)
- A Fibonacci Puzzle

- Fractals

- The Fibonacci Numbers
- Society
- Business
- Economics
- Construction (e.g. pyramids, Pythagorean theorem)
- Personal finance
- Great Graphic Illustrations

- Practical "real life" problems
- Approximation, conversions and back-of-the-napkin computations
- Probability

- Pure mathematics
- Fun and Games:
- Mathemagics -- Magic tricks that involve mathematics
- Mathemaction -- Exposing the world to mathematics!
- The Birthday Problem

In the NKU Department of Mathematics we believe that the study of mathematics can make you a better thinker. One of our objectives is to provide mathematics that will help you to improve your life.

## Resources

Some Resources that might help those interested in teaching or studying mathematics for Liberal Arts:

- Andy Long's course at Northern Kentucky University
- Aimee Krug's Guide for MAT115 Instructors at NKU(for those using
*The Heart of Mathematics*) - Aimee's Guide for instructor's, Fall 2008 (for those using the Tanenbaum text)
- David Lippman's wonderful on-line text Math in Society