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All the Mathematics You Missed

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

$44.99 (P)

  • Date Published: November 2001
  • availability: Available
  • format: Paperback
  • isbn: 9780521797078

$ 44.99 (P)
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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.

    • An overview of undergraduate mathematics
    • Intuitive reasons why each covered topic is important in mathematics
    • Also covers applied topics such as algorithms and probability
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    Reviews & endorsements

    "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

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    Product details

    • Date Published: November 2001
    • format: Paperback
    • isbn: 9780521797078
    • length: 376 pages
    • dimensions: 226 x 155 x 23 mm
    • weight: 0.52kg
    • contains: 177 b/w illus. 2 tables 94 exercises
    • availability: Available
  • Table of Contents

    Preface
    On the structure of mathematics
    Brief summaries of topics
    1. Linear algebra
    2. e and d 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. Complex analysis
    10. Countability and the axiom of choice
    11. Algebra
    12. Lebesgue integration
    13. Fourier analysis
    14. Differential equations
    15. Combinatorics and probability
    16. Algorithms
    A. Equivalence relations.

  • Author

    Thomas A. Garrity, Williams College, Massachusetts

    Illustrated by

    Lori Pedersen

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