Mathematics is a distinctly human activity that everyone engages in at some level ranging from the subconscious and intuitive to the extreme limits of rational intellectual activity. For thousands of years mathematics has demonstrated its power to enrich the minds of men and women and modify the human condition. Yet, few people have an accurate feeling for the history, nature, goals and accomplishments of mathematics. What exactly is mathematics, what do mathematicians do and why do people do mathematics? These are the fundamental questions addressed in this course.

Since it is difficult to understand a subject with knowing its history, we include a study of some of the people and times in the history of mathematics. We examine mathematical proofs, the foundations of mathematics. We start our study with the study of the natural numbers, the basic building block that began it all. This discussion leads to the concept of infinity. What does it mean to be infinite? Why would a mathematician care?

By the end of the course, we pull the pieces together and again address the question: What is mathematics?

The course is open to everyone and is especially suited to those with inquiring minds, regardless of their previous mathematical experience.

Course Topics:

• Figures from the history of mathematics
• An introduction to rigorous thought
• Numbers
  • Prime numbers
  • Modular Arithmetic
  • Bar codes
  • Irrational numbers
  • Real numbers and the real number line
• Infinitely
  • One-to-one correspondence
  • Sizes of Infinity
• Geometry
  • Fractal Geometry
  • The Pythagorean Theorem
  • Non-Euclidean Geometries
  • The Fourth Dimension