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All the Mathematics You Missed: But Need to Know for Graduate School Paperback – November 12, 2001

ISBN-13: 978-0521797078 ISBN-10: 0521797071 Edition: 1st

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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: 8.9 x 6.1 x 0.9 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #104,928 in Books (See Top 100 in Books)

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.

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Customer Reviews

3.6 out of 5 stars
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Most Helpful Customer Reviews

56 of 57 people found the following review helpful By Jason on January 19, 2003
Format: Paperback
There's no doubt about it -- this book designed for people who want to learn some real math. It doesn't take, as the title and description might lead you to believe, a "Math for Engineers" approach.
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.
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41 of 42 people found the following review helpful By Paul on January 27, 2004
Format: 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.
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36 of 37 people found the following review helpful By A Customer on November 8, 2002
Format: 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.
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31 of 34 people found the following review helpful By Stan Vernooy on January 16, 2006
Format: 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.
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18 of 19 people found the following review helpful By Kent S. Kapitan on January 19, 2005
Format: Paperback
I found this book to be very helpful as a guide to self-study in mathematics. I did not rely on the chapters for understanding, but rather used them as a topic list for a several year course of study. I used the bibliography to find the best books for study and then later used the chapters as an essential review. When I finished, I felt I had a completely satisfactory undergraduate education in mathematics at a fraction of the usual cost. I now have an excellent library as well.
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