An accessible introduction to mathematical infinity for the endlessly curiousInfinity has traditionally been a topic for philosophers, physicists, and artists, and it can be large, scary, or highly metaphorical. For mathematicians, however, infinity is not frightening or hopelessly abstract (though it is certainly big) but rather is a normal part of their work. In this guide, award-winning professor and author Edward R. Scheinerman offers an exploration of infinity...

A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. T...

Designed for those wishing to study mathematics beyond linear algebra but unready for abstract material, this "invitation" to the excitement of dynamical systems appeals to readers from a wide range of backgrounds. Rather than taking a theorem-proof-corollary-remark approach, it stresses geometry and intuition. Topics include both the classical theory of linear systems and the modern theory of nonlinear and chaotic systems as well as bifurcation, symbolic dynamics, fractals, and complex sy...