Experimental Mathematics

This textbook is designed for an undergraduate course in computational or experimental mathematics. Many of the most interesting and important topics in theoretical mathematics are both motivated and illuminated by computation. By using a computer to explore and investigate mathematical phenomena, students are encouraged to conduct experiments and make their own discoveries. The explorations are motivated by rich and interesting mathematical examples drawn from diverse areas such as number theory, complex analysis, and probability. In this setting, students are exposed to key concepts from programming such as algorithms, recursion, and probabilistic sampling, allowing them to develop practical computational skills. Over 450 practice problems, exercises, and explorations are distributed regularly throughout the text, reinforcing the material and encouraging further investigations. A code repository, providing implementations of these examples, is available at the AMS webpage for the text. Thoroughly classroom tested and designed to show students how to combine mathematical and computational thinking, the book requires prior knowledge of only calculus and introductory linear algebra. Only minimal prior experience with computer programming is necessary, provided the reader has a computing environment, access to online documentation, and a willingness to experiment. Notably, the volume has been carefully prepared so that it may be used with almost any programming language.