All the Mathematics You Missed: But Need to Know for Graduate School

Each chapter covers, in the span of 10 or 15 pages, what would normally be an entire semester's worth of material, and as a result, is quite dense -- there are alot of ideas crammed onto each page. But unlike traditional advanced math books (which are notoriously dense) the focus is more on developing intuitions than on long strings of equations.

An important strength is that every chapter ends with suggestions on textbooks in that chapter's subject. This turns out to be quite helpful, since one can't reasonably expect to learn everything important about any of these subjects from a brief chapter in any book.

I can envision three main ways in which this book might be useful: First, in combination with one or more of the books in listed in the bibliography for learning a new subject. Second, on its own for review of topics you've seen before. Third, as a reference for "basic" definitions and theorems, as in: "What's a Hilbert space again?"

Overall, this will be a good book to have around, but not a substitute for real study.


Uniquely Informative   November 8, 2002
19 out of 19 found this review helpful

I used this book for an opposite purpose to the one the author intended. For me it served to review all the math I *had* learned long ago in school (both undergraduate and graduate), but was starting to forget. The author's informal style and rapid-fire delivery were just right for these topics. The subjects I had truly missed, mainly the more abstract parts of algebra and geometry, I found difficult to follow, though I did come away with some feeling for them. This is not a perfect book. The informal style extends to numerous typos in equations, and modern computer-oriented approaches get short shrift. Nevertheless, I found it a unique resource and a pleasure to read.


I Wish I Had Done It   January 17, 2006
Stan Vernooy (Henderson, NV)
17 out of 19 found this review helpful

When I was in graduate school, it seemed that my professors were constantly making reference to a theorem or definition that I had never heard of, or that I had forgotten. The professors would usually acknowledge the possibility that their students were unfamiliar with the cited material, but they would say something like, "Oh, you can pick that up anywhere." Determining the "anywhere" was often a frustrating and time-consuming experience. I often thought that "someone" should write a book condensing all that material that I could "pick up anywhere" into one book. And I just discovered that someone has indeed done exactly that.

One can quibble about the choice of topics in this book. Three of the sixteen chapters in the book are devoted to vector calculus leading up to Stokes' Theorem. Five others concentrate on various forms of analysis and differential equations. Personally I think that perhaps some basic results in Number Theory might have been helpful; others may object to the omission of Algebraic Topology, although I don't think there is much material in early graduate school that depends on a knowledge of results or definitions in Algebraic Topology.

I agree with the previous reviewer who suggests that the book would be improved by the inclusion of answers to the exercises, but that omission doesn't upset me as much as it did her/him.

My biggest criticism of the book is that there is a disappointingly large number of typos. Even though this is a first edition, it should have been more carefully proofread. If a second edition is ever issued, I hope that problem will be corrected.