Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica. The accompanying CD contains Mathematica Notebooks for illustrating most of the topics in the text and for solving problems in mathematical physics. Although it is primarily designed for use with the author's "Mathematical Methods: For Students of Physics and Related Fields," the discussions in the book sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering.