The Math You Need A Comprehensive Survey of Undergraduate Mathematics

A comprehensive survey of undergraduate mathematics, compressing four years of study into one robust overview.

In The Math You Need, Thomas Mack provides a singular, comprehensive survey of undergraduate mathematics, compressing four years of math curricula into one volume. Without sacrificing rigor, this book provides a go-to resource for the essentials that any academic or professional needs. Each chapter is followed by numerous exercises to provide the reader an opportunity to practice what they learned. The Math You Need is distinguished in its use of the Bourbaki style—the gold standard for concision and an approach that mathematicians will find of particular interest. As ambitious as it is compact, this text embraces mathematical abstraction throughout, avoiding ad hoc computations in favor of general results.

Covering eight areas—group theory, commutative algebra, linear algebra, topology, real analysis, complex analysis, number theory, and probability and statistics—this thorough and highly effective overview of the undergraduate curriculum will prove to be invaluable to students and instructors alike.

Thomas Mack is a mathematician, who earned his PhD in the field of combinatorial group theory and hyperbolic groups from the California Institute of Technology. He has worked for more than fifteen years as a researcher in the areas of defense, robotics, and finance.