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Matrix Editions is a small publisher committed to "serious mathematics, written with the reader in mind". Our goal is to publish rigorous books that go beyond correct statements to show why statements are correct and why they are interesting. We intend to produce the best possible books at a fair price to readers and with a fair return to authors.

Barbara Burke Hubbard
Matrix Editions
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If you are interested in outstanding mathematics books, you've come to the right place. Read reviews, reader comments, and sample pages to see which book is right for you.

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The 5th edition of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach,   with the corresponding student solution manual.

818 pages, hardcover, smythe-sewn binding, 8 x 10 inches $87. Sept. 2015
ISBN 9780971576681

This 5th edition contains all the things that made the earlier editions different from other textbooks.  Among others:

  • Integrating linear algebra and multivariable calculus
  • Using effective algorithms to prove the main theorems (Newton's method and the implicit function theorem, for instance)
  • A new approach to both Riemann integration and Lebesgue integration
  • Manifolds and a serious introduction to differential geometry
  • A new way of introducing differential forms and the exterior derivative.

There is also new material, in response to requests from computer science colleagues:

  • More big matrices!  We included the Perron-Frobenius theorem, and its application to Google's PageRank algorithm
  • More singular values!  We included a detailed proof of the singular value decomposition, and show how it applies to facial recognition: "how does Facebook apply names to pictures?"

Other changes are more cosmetic: unsuccessful exercises were removed, about 40 new exercises added, new examples added, some shaky proofs improved, and more.

For more information: Vector Calculus 5th edition

"...a text for a very particular type of student, one who accepts that reading and learning mathematics will no longer a a plug-and-chug activity, one who is intrigued by connections of mathematical ideas with one another, and more specifically, one who is looking forward to learning a vast amount of mathematics"  MAA Review of 3rd edition  Read entire review

Praise from readers

book cover
Featured Future Book: Dynamics: Introductory Lectures  by John Milnor Tentative table of contents

Complete list of future books

Functional Analysis Volume I: A Gentle Introduction 

by Dzung Minh Ha

Named an Outstanding Academic Title of 2007 by Choice Magazine (Current Reviews for Academic Libraries). 

640 pages, Hardcover, smythe-sewn binding. ISBN 9780971576612.   $73

"The author has set himself a monumental task: writing a functional analysis book that can be read by any well-motivated student, even one with only a modest background in analysis. He carried out this task with great patience and care and he did a remarkable job."    — from SIAM Review, June 2010, Vol 52, No. 2.

"A thorough ... presentation of all the standard topics any introductory functional analysis course might wish to cover ... highly accessible, self-contained ... Highly recommended."    — from the March 2007 issue of  Choice   See complete review  

  • Student-friendly but rigorous
  • Many examples and counterexamples.
  • Includes solutions to all odd-numbered exercises
  • Thorough index
More on this book (including links to table of contents, reviews, sample pages, etc.)

More on "outstanding academic titles"

Outstanding Academic Title seal


Teichmüller Theory and Applications to Geometry, Topology, and Dynamics  Volume I: Teichmüller Theory

by John H. Hubbard, with forewords by Clifford Earle and William Thurston

459 pages, Hardcover (with Smythe-sewn binding), ISBN 9780971576629  $77

"... beautiful treatments of classical theorems .... [and] of   more specialized topics that one can hardly find (and, for some of them, cannot find at all)  in other textbooks on Teichmüller theory....an invaluable book. It treats  a wonderful subject, and it is written by a great mathematician. It is now an essential reference for every student and every researcher in the field."  — Zentralblatt Math   

"As a motto, Matrix Editions has chosen "Serious mathematics, written with the reader in mind."  The volume under review ... beautifully exemplifies the motto... [Fields medalist William] Thurston writes that "John Hubbard approaches mathematics with his whole mind," and indeed he does.  Definitions, theorems, proofs, and remarks are embedded in a coherent narrative. Geometry is made visual whenever possible... — MAA Reviews   Read more

More information on Teichmuller Volume 1

Solving Linear Systems: An Analysis of Matrix Prefactorization Iterative Methods,  by Zbigniew Ignacy Woźnicki

554 pages, 8 x 10 inches, hardcover, smythe-sewn binding, ISBN 9780971576667 $89
June, 2009

Matrix Editions has scored a coup with this title  SciTech Book News (see complete review)

"This book contains a detailed treatment of linear algebra, and how it can be applied to the iterative solution of elliptic boundary-value problems.  In Chapter 5 the author  attacks the interesting and difficult problem of comparing the numerical work required to solve large elliptic problems by his  SOR-like AGA  method, with the numerical work required using newer computational methods, such as Krylov subspace methods and GMRES.
His conclusions here are quite unexpected!  Indeed, for some problems, he found that the  SOR-like methods were superior to Krylov subspace methods by several orders of  magnitude.
— From the foreword by Richard Varga, Emeritus University Professor of Mathematics, Kent State University

More information on Solving Linear Systems


(covers designed by Leila Joiner)

book cover, Solving Linear Systems

To order:  United States    To order: other countries

Future Books

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics Volume 2: Four Theorems by William Thurston
by John H. Hubbard
Teichmüller Theory Vol 2

Dynamics in One Complex Variable by Xavier Buff and John H. Hubbard

Complex Dynamics
Functional Analysis Volume 2: The spectral theorem for normal compact operators by Dzung Minh Ha
Functional Analysis Vol 2

Advanced Topics in Calculus (sequel to Vector Calclulus, Linear Algebra, and Differential Forms: A Unified Approach) by John H. Hubbard and Barbara Burke Hubbard
Advanced Topics in Calculus

Scientific Computing: Theory and Practice  by John H. Hubbard and Florence Hubert

War and Peace in America, 1853-1868 (no, this one's not math)

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Math in Literature

What author compared a woman 
to a table of logarithms?

Find out at Math in literature

Useful stuff

Article on the forced damped pendulum, in pdf. (This appeared in the American Mathematical Monthly, 106, Number 8 October 1999). This is a big file, and may take a while to open.

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