Since the first abstract mathematical thought arose in a human brain, experimental mathematics has been a fundamental component of the advance in mathematical knowledge. Computations have been the leading indicator of most mathematical proofs; someone does a few, sees that a pattern emerges and then is able to generalize the pattern into a formal proof.

The difference in the modern world is the incredible power of symbolic mathematical software packages such as *Maple* and *Mathematica*. Using a few lines of code, a researcher can potentially run millions of tests in order to verify a hypothesis or identify and prove a perceived pattern.

This book contains articles about some very advanced examples of experimental mathematics in action. The topics cover a wide spectrum of topics, from finding differential equations of the Calabi-Yau form to generating functions of several forms to algorithms for finding the digits of π. Many of the articles contain statements of open conjectures, which is always the goal of mathematics. Namely, prove something and pose a further question. Experimental mathematics can give a strong hint, but it is the formal reasoning of a proof that completes the task.

Outside of the common thread of being examined using experimental tactics, there is no common thread to the topics in this book. Therefore, few people will be interested in all the articles, but most will be interested in a few.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing *The Journal of Recreational Mathematics*. In his spare time, he reads about these things and helps his daughter in her lawn care business.