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)

Topics

• Art
  • Mosaic Knots -- beautiful and practical
  • The Golden Rectangle
• Religion
  • The Fourth Dimension -- The Mathematics of Angels, Aliens, and Miracles
• Philosophy
  • The Platonic Solids
• 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
    • Fractal Music
• Society
  • Primitive Counting, and a related card trick based on counting
  • Egyptian Mathematics
  • Surveying embarrassing questions
    • one-coin-toss sampling technique
    • two-coin-toss sampling technique
• 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
    • The Birthday Problem
• Pure mathematics
  • Number Theory and Secret Codes
  • Geometry
    • Mobius Bands
    • The Platonic Solids
  • Infinity
    • Hotel Infinity
  • The Logic of Lewis Carroll
    • From "Lewis Carroll in Numberland"
• Fun and Games:
  • Mathemagics -- Magic tricks that involve mathematics
  • Mathemaction -- Exposing the world to mathematics!
    • Vi Hart does mathemactions
  • 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.

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Resources

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

• Andy Long's course at Northern Kentucky University
  • Andy's Topic Matrix
• 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