Mathematics with Applications (9th Edition) [Hardcover]

Mathematics is the basic science that is very important in the development of science. Here is the important book on mathematics. 

Product Description
This edition of Mathematics with Applications continues to be an excellent learning tool for applied mathematics students. As always, the text includes the popular margin exercises as well as comprehensive review of algebraic topics, but with this revision comes the fresh insight of a new co-author. Also, at our customers' request, this textbook has additional calculus content, allowing the book to be all that you need and more.

The Language of Mathematics: Making the Invisible Visible

Keith Devlin is trying to be the Carl Sagan of mathematics, and he is succeeding. He writes: "Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be seen only with the eyes of the mind." All of his books are attempts to get around this problem, to "try to communicate to others some sense of what it is we experience--some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value."

Life by the Numbers, Devlin's companion book to the PBS series of the same name, is heavily illustrated and soothingly low on equations. But as he says, wanting mathematics without abstract notation "is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language."

The Language of Mathematics is Devlin's second iteration of the approach he used in Mathematics: The Science of Patterns. It covers all the same ground (and uses many of the same words) as the latter, but with fewer glossy pictures, sidebars, and references. Devlin has also added chapters on statistics and on mathematical patterns in nature. --Mary Ellen Curtin --This text refers to the Hardcover edition.

What Is Mathematics? An Elementary Approach to Ideas and Methods

Review: By By twit
This book genuinely has more mathematical content, for around $15-$25, than most, maybe all, "bridge" texts for college math majors, costing 5 or 10 times as much.

This book was written by a master, for an intelligent person knowing only 1950's style high school mathematics (some trig, algebra, and geometry).

When I fiorst tried to read it as a youngster however I was not used to books that required actually thinking about each statement, before proceeding to the next. Hence I could not read it at the pace I thought normal.

So this is not a breezy read, but is an outstanding one. It has literally no competitor to my knowledge at the present time, in quantity of material, quality of material, and quality of exposition.

Even experts may learn something here about the most familiar topics. E.g. in presenting the proof of the well known fact that all integers greater than one have unique prime factorizations, the authors show how a clever use of induction avoids developing the characterization of a gcd, which usually precedes this theorem. I had never seen that before.

If you are looking for a miracle book that treats the reader like a baby, and still covers calculus, this is not it. But if you have the prerequisites of a good high school course of elementary math, and are willing to spend time on the arguments, there is no better book for beginners and intelligent laypersons.

The Princeton Companion to Mathematics (Hardcover)

Review
The Princeton Companion to Mathematics makes a heroic attempt to keep [abstract concepts] to a minimum . . . and conveys the breadth, depth and diversity of mathematics. It is impressive and well written and it's good value for [the] money.
(Ian Stewart The Times )

This is a panoramic view of modern mathematics. It is tough going in some places, but much of it is surprisingly accessible. A must for budding number-crunchers.
(The Economist )

Although the editors' original goal of text that could be understood by anyone with a good background in high school mathematics provided short-lived, this wide-ranging account should reward undergraduate and graduate students and anyone curious about math as well as help research mathematicians understand the work of their colleagues in other specialties. The editors note some advantages a carefully organized printed reference may enjoy over a collection of Web pages, and this impressive volume supports their claim.
(Science )

Accessible, technically precise and thorough account of all math's major aspects. Students of math will find this book a helpful reference for understanding their classes; students of everything else will find helpful guides to understanding how math describes it all.
(Tom Siegfried Science News )

Massive . . . endlessly fascinating.
(Gregory McNamee The Bloomsbury Review )

The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics and some perspectives. Its presentations are selective, satisfying, and complete within themselves but not overbearingly comprehensive. Any reader from a curious high school student to an experienced mathematician seeking information on a particular mathematical subject outside his or her field will find this book useful. The writing is clear and the examples and illustrations beneficial.
(Frank Swetz Convergence )

Edited by Gowers, a recipient of the Fields Medal, this volume contains almost 200 entries, commissioned especially for this book from the world's leading mathematicians. It introduces basic mathematical tools and vocabulary, traces the development of modern mathematics, defines essential terms and concepts, and puts them in context. . . . Packed with information presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
(Library Journal )

Once in a while a book comes along that should be on every mathematician's bookshelf. This is such a book. Described as a 'companion', this 1000-page tome is an authoritative and informative reference work that is also highly pleasurable to dip into. Much of it can be read with benefit by undergraduate mathematicians, while there is a great deal to engage professional mathematicians of all persuasions.
(Robin Wilson London Mathematical Society )

This volume is an enormous, far-reaching effort to survey the current landscape of (pure) mathematics. Chief editor Gowers and associate editors Barrow-Green and Leader have enlisted scores of leading mathematicians worldwide to produce a gorgeous volume of longer essays and short, specific articles that convey some of the dense fabric of ideas and techniques of modern mathematics. . . . This volume should be on the shelf of every university and public library, and of every mathematician--professional and amateur alike.
(S.J. Colley Choice )

The book I'm talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this book. You don't have to click on the link with my referral if you don't want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight. . . . The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it's a monumental piece of work. I have never seen a book like this before. . . . [T]he bible of mathematics. . . . I believe this is the kind of book that will still be in use a hundred years from now.
(Antonio Cangiano Math-Blog.com )

I'm completely charmed. This is one of those books that makes you wish you had a desert island to be marooned on.
(Brian Hayes bit-player.org )

Review
This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is interested in mathematics must have a copy of their own.
(Simon A. Levin, Princeton University )