Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions)

The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.

Robert Young received his PhD from the University of Michigan in 1971. He currently teaches at Oberlin College where he holds the James F. Clark Chair in Mathematics. His main mathematical interest is nonharmonic Fourier series. He has published over 25 research articles in mathematics and is the author of An Introduction to Nonharmonic Fourier Series.