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All the Mathematics You Missed: But Need to Know for Graduate School, by Thomas A. Garrity
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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.
- Sales Rank: #305151 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2001-11-12
- Released on: 2002-01-17
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .83" w x 5.98" l, 1.30 pounds
- Binding: Paperback
- 376 pages
- Used Book in Good Condition
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
About the Author
Thomas A. Garrity is the William R. Kenan, Jr Professor of Mathematics at Williams College, where he was the director of the Williams College Project for Effective Teaching for many years. He has written a number of research papers and has authored or coauthored two other books, All the Mathematics You Missed (But Need to Know for Graduate School) and Algebraic Geometry: A Problem Solving Approach. Among his awards and honors is the MAA Deborah and Franklin Tepper Haimo Award for outstanding college or university teaching.
Most helpful customer reviews
40 of 41 people found the following review helpful.
Uniquely Informative
By A Customer
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.
38 of 41 people found the following review helpful.
I Wish I Had Done It
By Stan Vernooy
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.
8 of 9 people found the following review helpful.
Bird's-eye view of the big picture
By Joshua Loftus
A previous reviewer pointed out that this book is meant to organize ones knowledge about math- not supplement for lack of knowledge. I agree. It gives recaps of the main ideas, and helps one to see the big picture about various subfields of math. Of course, NO ONE BOOK could POSSIBLY teach all of those subfields with a significant level of detail. So one should not attempt to use it for that purpose.
I'm a math undergrad, starting my senior year soon. I've been using this book to preview areas of math before taking a class in that area. It's been tremendously helpful to me to have an idea about the big picture and the context before grinding into specifics. I would highly recommend this book for that purpose. I don't know about other purposes, but for that it has been great for me.
The author gives many insights that nobody bothers to tell you in textbooks or in any specific class. For example, in the preface he explains that mathematics on the whole is about sets of certain types of objects and certain types of functions between those objects. This is a major simplification- but that's the point! I applaud Garrity for having the guts to say this, though he makes himself a target for ridicule by making such a gross simplification. Students like me need to hear it. The rest of the book begins each chapter by telling the reader what types of objects are studied in that field of math, and what the functions are that map between said objects.
It's a blurry, bird's-eye view of the big picture. But it motivates me. I have an idea about what to look forward to in a given class. I love this book. I had it out from my university's library for almost an entire year, and then realized I wanted my own copy so I could keep it.
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