The number systems --
Factorials and binomial coefficients --
The Fibonacci numbers --
Polynomials --
Binomial sums --
Catalan numbers --
The Stirling numbers of the second kind --
Rational functions --
Wallis' formula --
Farey fractions --
The exponential function --
Trigonometric functions --
Bernoulli polynomials --
A sample of classical polynomials: Legendre, Chebyshev, and Hermite --
Landen transformations --
Three special functions

New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the