Book Description
Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY retains these features. The problems have been consistently praised for being at just the right level for precalculus students like you. The book also provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics. ... Read more

Book Description
The study of two-dimensional analytic geometry has gone in and out of fashion several times over the past century, however this classic field of mathematics has once again become popular due to the growing power of personal computers and the availability of powerful mathematical software systems, such as Mathematica, that can provide an
interactive environment for studying the field. By combining the power of Mathematica with an analytic geometry software system called Descarta2D, the author has succeeded in meshing an ancient field of study with modern computational tools, the result being a simple, yet powerful, approach to studying analytic geometry. Students, engineers and mathematicians alike who are interested in analytic geometry can use this book and software for the study, research or just plain enjoyment of analytic geometry.

Mathematica provides an attractive environment for studying analytic geometry. Mathematica supports both numeric and symbolic computations meaning that geometry problems can be solved for special cases using numbers, as well as general cases producing formulas. Mathematica also has good facilities for producing graphical plots which are useful for visualizing the graphs of two-dimensional geometry.

* A classic study in analytic geometry, complete with in-line Mathematica dialogs illustrating every concept as it is introduced
* Excellent theoretical presentation
*Fully explained examples of all key concepts
*Interactive Mathematica notebooks for the entire book
* Provides a complete computer-based environment for study of analytic geometry
* All chapters and reference material are provided on CD-ROM in addition to being printed in the book
* Complete software system: Descarta2D
* A software system, including source code, for the underlying computer implementation, called Descarta2D is provided
* Part VII of the book is a listing of the (30) Mathematica files supporting Descarta2D; the source code is also supplied on CD-ROM
* Explorations
* More than 120 challenging problems in analytic geometry are posed;Complete solutions are provided both as interactive Mathematica notebooks on CD-ROM and as printed material in the book
* Mathematica and Descarta2D Hints expand the reader's knowledge and understanding of Descarta2D and Mathematica
* Sortware developed with Mathematica 3.0 and is compatible with Mathematica 4.0
* Detailed reference manual
* Complete documentation for Descarta2D
* Fully integrated into the Mathematica Help Browser ... Read more

Book Description
Check your work-and your understanding-with this manual, which provides solutions for all of the odd-numbered exercises in the text. You will also find strategies for solving additional exercises and many helpful hints and warnings. ... Read more

Book Description
Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann. ... Read more

Customer Reviews (1)

A fine book.
This book is a good reference for anyone who wants to know about the development of riemannian geometry. It covers many active topics in modern differential geometry for every graduated students who can choose some interested fields for the thesis. ... Read more

Book Description
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest. ... Read more

Customer Reviews (6)

The Best Introduction to General Relativity
If you want to engage in a serious study of general relativity, then you must master the mathematical language of semi-Riemannian manifolds in which it is cast. Sadly, the development of classical Riemannian geometry as studied by pure mathematicians only parallels the development of semi-Riemannian geometry in the early stages;eventually, the two subjects diverge rather drastically.For example, the famous Hopf-Rinow Theorem, one of the cornerstones of modern Riemannian geometry, simply has no Lorentzian analogue at all;every single equivalence in the theorem fails in Lorentzian geometry.Thus, one could master all five volumes of Spivak's definitive treatment of Riemannian geometry and still be unprepared to deal with light cones, timelike, null and spacelike geodesics, and the multitude of other uniquely semi-Riemannian constructs that appear in general relativity.O'Neill's wonderful book, which first appeared in 1983, provides the well-prepared reader with a mathematically rigorous, thorough introduction to both Riemannian and semi-Riemannian geometry, showing how they are similar and pointing out clearly where they differ.After developing the mathematical machinery in the early chapters, the last part of the book turns to general relativity by offering lucid introductions to the Robertson-Walker cosmological models (Big Bang singularities), the Schwarzschild model for a single non-rotating star (including black holes), and a brief introduction to Penrose-Hawking causality theory.If you would like to study a pure Riemannian text in parallel with this one, I would recommend the text by Boothby, written at a comparable level of difficulty, which remains one of the clearest and most accessible Riemannian geometry texts on the market.For the serious reader who wishes to continue on with a study of the Kerr solution to Einstein's equations, modeling the exterior spacetime of a rotating star, O'Neill wrote an entire book on the subject in 1995, now difficult to find but well worth tracking down.This 1995 text contains one of the clearest, most accessible
introductions available to the difficult subjects of the algebraic classification of the Weyl curvature tensor and the corresponding Petrov classification of spacetimes.I studied from O'Neill's 1983 text when it first came out and I have continued to use it as the primary text for an advanced undergraduate course I have taught over the past 20 years.It is not an "easy" text to read, but then, I have never found the "easy" introduction to differential geometry and general relativity.The reviewer who says this is not a suitable first text is simply in error;there is no better first text on the subject.If you have studied linear algebra, advanced calculus, and a little topology, then with dedication and hard work, you can learn more from O'Neill's text than from many of the far more popular recent texts, written by physicists, which attempt to circumvent the mathematics insofar as is possible while introducing general relativity.This is a perilous course for which the serious student will pay dearly later on, when she/he wants to study any of the many areas of modern physics in which differential geometry (differential forms, bundle theory, connections on a principle fiber bundle, gauge theory, etc.) plays an essential role.

Great book, terrible print quality
This is a wonderful book, with a clear, concise and precise exposition of the fundamental idea in riemannian and semi-riemannian geometry.Although I would not recommend it as a first text, it will be the text that you continue to reference later, and turn to when you want the best mathematical treatment.

However, I do not recommend that you buy a new copy.The print quality is terrible; the binding is poor, but even worse, the text quality is absurd.I have been using a library copy with cloth binding and sharp, clear text.It is obvious that the new printing in the green cover is based on a photocopy of the original rather than a new typesetting.While this means that no errors have been introduced, I found it painful to read.I would suggest looking for a used copy.

So 5 stars for the book, but only 3 stars for this printing.

Very good contents but..
The only drawback, and it is a serious one, is the binding. For a such expensive book, one could expect a DECENT binding, but the outcome is a SHAME.

So 5 star for the contents an 0 for the binding

Addendum
This book is now available at Amazon.co.uk!

Its contents are: Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorentz Geometry. Special Relativity. Constructions.Symmetry and Constant Curvature. Isometries. Calculus of Variations.Homogeneous and Symmetric Spaces. General Relativity; Cosmology.Schwarzschild Geometry. Causality in Lorentz Manifolds.

Let's go buy it!

Excellent for beginner and experienced mathematicians
This is one of the best books on Differential Geometry I've ever read. It includes a clear exposition of all the basic results and then goes on to the most deep aspects of the subject, making it useful for undergraduateand graduate students, as well as experienced working mathematicians. It'sa pitty that it's no longer available. ... Read more

Book Description
SOLID ANALYTIC GEOMETRY SOLID ANALYTIC GEOMETRY By ADRIAN ALBERT Professor of Mathematics The University of Chicago FIRST EDITION McGRAW-HILL BOOK COMPANY, INC. NEW YORK TORONTO LONDON 1949 SOLID ANALYTIC GEOMETRY Copyright, 1949, by the McGraw-Hill Book Company, Inc. Printed in the United States of America. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. THE MAPLE PRESS COMPANY, YORK, PA. PREFACE In a recent text on college algebra the author gave a brief pre senlation of what seems to him to be the best basis for a modern course on plane analytic geometry, that is, the algebraic vector approach. The present text contains an extension of this approach, yielding an exposition in full for the three-dimensional case, and thereby ties up the study of space analytic geometry with the theory of vectors and matrices. Chapters 1 and 2 contain a treatment of the equations of lines and planes. After a preliminary study of the linear operations on n-dimensional vectors, rectangular coordinates are introduced, three-dimensional vectors and inner products are interpreted geometrically, and, from a consideration of scalar products and axis translations, the parametric equations of a line are obtained. The vector approach then yields a very simple derivation of the normal form of an equation of a plane, and the standard forms of plane and line equations are rather immediate consequences. Chapter 3 contains an exposition of classical elementary sur face and curve theory. Chapter 4 contains the usual treatment of spheres, and Chapter 5 gives the classical descriptions of quadric surfaces in standard position. The latter chapter ends with a rather novel classification of quadrics according to certain invariants. Chapter 6 is an exposition of that part of the theory of matrices which is needed for a complete development of the so-called principal axis transformation. A full account of the orthogonal reduction of a real quadratic form in n variables is given, and the theory is applied in Chapter 7 to the three-dimensional case of quadric surfaces. This latter chapter ends with a discussion of the symmetries of quadric surfaces. The first seven chapters of this text provide an exposition of the basic topics of solid analytic geometry, the material being adequate for a one-quarter course on the subject. The remain ing chapters contain additional material for longer courses or out side reading. Chapter 8, on spherical coordinates, contains a dis vi PREFACE cussion of some practical aspects of the theory of rotations and translations of axes in space. It is quite clear that rectangular coordinates are not as practical for actual measurements as are the coordinates of range, azimuth, and elevation, and in this chapter methods are developed for actual computation of the changes in these measurable coordinates after translations or rotations of axes. The chapter ends with a discussion of gno monic charts. Our final chapter contains a brief presentation of the elements of protective geometry. The effect on the theory of linear trans formations of the use of homogeneous coordinates is given, and the chapter contains a rigorous matrix proof of the invariance of the cross ratio under projective transformations. It is hoped that the use of modern algebraic techniques in this and in the earlier chapters of the present text will serve to make the subject of solid analytic geometry fit better in the teaching of modern mathematics than it has in the past. ADRIAN ALBERT CHICAGO, ILL. March, 1949 CONTENTS PREFACE v 1 COORDINATES AND LINES I 1. Vectors 1 2. Scalar multiplication 2 3. Inner products 3 4. The angle between two vectors 4 5. Directed lines 5 6. Orthogonal projections 6 7. Rectangular coordinates in ordinary space 7 8. The length of a vector in space 10 9. Lines through the origin 10 10. The angle between two vectors in space 12 11. Translation of axes 13 12... ... Read more

Book Description

Customer Reviews (3)

If you're devote to math, this book must be your bible !
Very few are the books that can take you from the beginning all the way to the end. This book haven't missed any step on its attempt to guide you to a succesful comprehension of mathematics.

If you're devote to math, this book must be your bible !
Very few are the books that can take you from the beginning all the way to the end. This book haven't missed any step on its attempt to guide you to a succesful comprehension of mathematics.

If you're devote to math, this book must be your bible !
Very few are the books that can take you from the beginning all the way to the end. This book haven't missed any step on its attempt to guide you to a succesful comprehension of mathematics. ... Read more

Book Description

This book combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. Chapter topics cover functions, graphs, and models; prelude to calculus; the derivative; additional applications of the derivative; the integral; applications of the integral; calculus of transcendental functions; techniques of integration; differential equations; polar coordinates and parametric curves; infinite series; vectors, curves, and surfaces in space; partial differentiation; multiple integrals; and vector calculus. For individuals interested in the study of calculus.

Customer Reviews (2)

Top notch reference
I agree with the previous reviewer that this is not a book for people who are looking for a gentle introduction to calculus.But for those who are looking for a sturdy reference that will give the proofs for the most common theorems used in calculus, this is a great book.

It has rigorous proofs, an excellent set of appendices for reviewing trigonometry and common identities, and a well chosen problem set.

I run a blog that is focused on complete mathematical proofs (http://fermatslasttheorem.blogspot.com), whenever one of my blog topics touches on calculus, this is the book that I go to.

Buy another book for the gentle introduction but if you want to understand the proofs that make up calculus, buy this book.

One of the Worst Textbooks for Learning Calculus.
I would give this book zero stars if I could. This textbook should only be used as a review for those who have completed Calculus-not for those trying to learn it. From the very beginning of the book the notation is very complex and was clearly written by a mathematician who decided his notation was the most conducive to learning. After completing Calculus III everything makes a lot more sense, but this is only because I had a brilliant instructor. The most laborious part of the notation is used when explaining how a Riemann Sum goes from discrete to integral calculus. It is more like learning a different language along with calculus when you use this book. The examples, which should be straightforward in order to get the concepts across are of course just as complicated as everything else in the book. Because of this, the excercises are very difficult to follow without the use of a solutions manual. The solutions manual also has some glaring flaws, but I won't get into that. The only real redeeming quality of the book is that at most universities you will be able to use it for three semesters. So you get your money's worth. I hope that when they release a new edition that some of the problems will be addressed, because at its current new price the book has little value to most. If you plan to teach yourself Calculus, do not buy this book. It will be a waste of your time and money. ... Read more

Book Description
This book introduces the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader to understand and construct proofs and write clear mathematics. The authors achieve this by exploring set theory, combinatorics and number theory, which include many fundamental mathematical ideas. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all time great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas. ... Read more

Customer Reviews (2)

Excellent reading
Note: This is for the 'Alternate' edition.

This book takes the reader from the ground up, up to (nearly) "everything else". Theorems are proven and discussed clearly. The format of the book is consistently appropriate. This book could be considered a must-try, perhaps a must-have.

BRAVO!!!!
I HAVE USED SEVERAL OTHER TEXTS (ALGEBRA & TRIG AND PRECALCULUS)
WRITTEN BY MICHAEL SULLIVAN. WHEN I BEGAN CALCULUS I FOUND THIS
TEXT BY SULLIVAN AND MIZRAHI. mY COMMENTS APPLY TO ALL BOOK BY SULLIVAN. THEY ARE UNIFORMLY OUTSTANDING BECAUSE THE EXPLANATION ARE CLEAR AND WRITTEN FOR THE INTENDED AUDIENCE. SULLIVAN NEVER
FORGETS WHO HIS AUDIENCE IS. THERE ARE LOTS AND LOTS OF EXAMPLES
WORKED OUT STEP BY STEP WITH EACH STEP EXPLAINED. THE EXERCISES AND PROBLEMS START WITH MECHANICS OF INCREAING DIFFICULTY AND THEN WORD PROBLEMS AND THEN ONTO CHALLENGING THEORETICAL PROBLEMS. THE BOOKS ARE VERY READABLE BUT ARE STILL STIMULATING
AND CHALLENGING AT THE PROPER LEVEL FOR EACH BOOK. HE IS ONE OF THE VERY FEW MATHEMATICS AUTHORS I HOLD IN HIGH REGARD. i AM A
STUDENT AND TUTOR AND I LOOK AT A TEXT FROM BOTH POINTS OF VIEW.
YOU CAN BUY ANY TEXT BY MICHAEL SULLIVAN SIGHT UNSEEN. ... Read more