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

Thomas A. Garrity (Author), Lori Pedersen (Illustrator)

Book Description

ISBN-10: 0521797071 | ISBN-13: 978-0521797078 | Publication Date: November 12, 2001 | Edition: 1

Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author 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 topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

Editorial Reviews

Review

"This book will fill an interesting niche in a library collection...it should be used by browsing students interested in making sure that they are prepared for success in their graduate programs." Choice

"All the Mathematics You Missed...is a help for students going on to graduate school..Since many students beginning graduate school do not have the mathematical knowledge needed, All the Mathematics You Missed aims to fill in the gaps." Berkshire Eagle, Pittsfield, MA

"From the preface: 'The goal of this book is to give people at least a rough idea of many topics that beginning graduate students at the best graduate schools are assumed to know." Mathematical Reviews

"The writing is lucid mathematical exposition, at a level quite appropriate to beginning graduate students." The American Statistician

"Before classes began, I jump started my graduate career with the help of this book. Even though I didn't believe that I could have missed much math, it became clear that my belief was wrong during the first week of class. While proving a theorem, my professor asked if anyone remembered a previous result from calculus. While I did not remember it from my days as an undergraduate, I had read about the theorem and had even seen a sketch of the proof in Garrity's book...This will be one of the books that I keep with me as I continue as a graduate student. It has certainly helped me understand concepts that I have missed."
Elizabeth D. Russell, Math Horizons

"Point set topology, complex analysis, differential forms, the curvature of surfaces, the axiom of choice, Lebesgue integration, Fourier analysis, algorithms, and differential equations.... I found these sections to be the high points of the book. They were a sound introduction to material that some but not all graduate students will need."
Charles Ashbacher, School Science and Mathematics

Book Description

Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge. This book will help readers to fill in the gaps in their preparation by presenting the basic points and a few key results of the most important undergraduate topics in mathematics: linear algebra, vector calculus, geometry, real analysis, algorithms, probability, set theory, and more. By emphasizing the intuitions behind the subject, the book makes it easy for students to quickly get a feel for the topics that they have missed and to prepare for more advanced courses.

Product Details

• Paperback: 376 pages
• Publisher: Cambridge University Press; 1 edition (November 12, 2001)
• Language: English
• ISBN-10: 0521797071
• ISBN-13: 978-0521797078
• Product Dimensions: 8.8 x 6.2 x 0.9 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.4 out of 5 stars  See all reviews (16 customer reviews)
• Amazon Best Sellers Rank: #629,998 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

29 of 29 people found the following review helpful:

4.0 out of 5 stars Uniquely Informative, November 8, 2002

By A Customer

This review is from: All the Mathematics You Missed: But Need to Know for Graduate School (Paperback)

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.

28 of 29 people found the following review helpful:

3.0 out of 5 stars Good for a recap, bad for anything more, January 27, 2004

By 

Paul "kras" - See all my reviews
(REAL NAME)   

This review is from: All the Mathematics You Missed: But Need to Know for Graduate School (Paperback)

This book has a very particular purpose: to recap some basic concepts from undergraduate mathematics so that you get the "big picture". In other words, for every math course you took as an undergrad, this book provides a good outline of the major ideas and how they fit together. But, it is only an outline; nothing more. If you actually missed out on some topic, or your knowledge of a subject is shaky, then this book won't help much. It will only help by providing a bibliography of some other references for that subject.

This book is meant to organize your undergraduate math knowledge, not to supplement it.

With that said, I'll mention a few words about the content of the book. It is quite well written and definitely extracts the essential ideas for your quick consumption. There are a few topics that I personally feel are missing, such as Gram-Schmidt and Jordan Canonical Forms for Linear Algebra, and UFDs and PIDs from Algebra. In general, it seemed like the book leaned a little more towards analysis than algebra, but the vast majority of important topics were indeed encapsulated in their synopsis.

Good for a very specific audience, but otherwise not wonderfully useful.

23 of 25 people found the following review helpful:

4.0 out of 5 stars I Wish I Had Done It, January 16, 2006

By 

Stan Vernooy (Henderson, NV) - See all my reviews
(REAL NAME)   

This review is from: All the Mathematics You Missed: But Need to Know for Graduate School (Paperback)

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.