Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

Table of Contents

1 Linear Algebra

2 Real Analysis

3 Calculus for Vector-Valued Functions

4 Point Set Topology

5 Classical Stokes’ Theorems

6 Differential Forms and Stokes’ Theorem

7 Curvature for Curves and Surfaces

8 Geometry

9 Countability and the Axiom of Choice

10 Elementary Number Theory

11 Algebra

12 Algebraic Number Theory

13 Complex Analysis

14 Analytic Number Theory

15 Lebesgue Integration

16 Fourier Analysis

17 Differential Equations

18 Combinatorics and Probability Theory

19 Algorithms

20 Category Theory

Review

‘Reading Garrity is like talking with your favorite uncle - he tells you the essential stories, in a clear and colorful way, and you get just what you need to explore further. The topics are well chosen (and there are more in this new edition). His points of view enrich the reader - not only do you learn what to know, but how to know it. I wish I had had this book when I started graduate school.’ John McCleary, Vassar College

‘I admired one of the intentions behind the first edition of Garrity’s All the Math You Missed: to give students the tools to appreciate the applications of mathematics without painting a simplistic picture of ‘Applied Mathematics’. In this second edition, he takes this idea to the next level by introducing four additional chapters, dealing primarily with number theory and category theory.’ Robert Kotiuga, Boston University

‘I felt like I was terribly underprepared for graduate school, and Garrity’s book helped me fill in some of those gaps. But far more importantly, the welcoming tone made me see that I wasn’t alone in feeling anxious, and it made grad school feel less intimidating.’ Daniel Erman, University of Wisconsin, Madison

‘Incoming graduate students would find the book most useful … this book is designed to provide some useful guidance … The writing is clear and easy to read.’ Bill Satzer, MAA Reviews

Book Description

Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

About the Author

Thomas A. Garrity is the Webster Atwell Class of 1921 Professor of Mathematics at Williams College, Massachusetts, where he was the director of the Williams College Project for Effective Teaching for many years. Among his awards are Rice University's Nicolas Salgo Outstanding Teaching award and the Haimo award of the MAA. His other books include Algebraic Geometry: A Problem Solving Approach (2013, co-authored) and Electricity and Magnetism for Mathematicians (2015).