Book Description
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.
The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.
* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon
NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems
Customer Reviews:
A new version of a classic book.......2007-02-21
I bought a copy of this new book and I have its old version with Hirsch and Smale as its only authors. Main differences between these books are some new chapters covering chaos and the exercises. Old version has better chapters dealing with linear algebra. I find this new version hard to read and it leaves many details to be filled by the reader. I would say that the new version is still a good choice for a second course in ODE or supplementary text for a graduate course. I gave it four stars.
Excellent Book.......2006-05-05
This is a great introduction to the next stage of differential equations after a first course. Devaney is a master of presenation, and makes everything seem easy. It is not as encyclopedic as some other books on this material, such as Arnold and Perko, but it is easier to read and still covers the most important advanced material.
good, not ideal.......2005-12-08
the two books by hirsch smale, one with devaney, seem like good books, but I am not crazy about either, at least from the few pages one can search online here.
the latter book with devaney just seems a dumbed down version of the earlier book by the two more famous authors. i expected that earlier book to be far better, but found to my regret that the two books actually share almost the same first page, and the main difference noticeable in the early going is that the 2 author work is poorly written, and the 3 author one is not written much better.
it is clearer but seems to be talking down to the reader in an annoying way. so neither is the absolute pleasure to read that the wonderfully written text of arnol'd is, or the classic of hurewicz. i would skip these books and get arnold and hurewicz instead.
New Edition.......2004-02-26
You should be aware that there are two similar books with similar titles by the same authors. The old edition is a hardcover all green book by Hirsch and Smale called:
"Differential Equations, Dynamical Systems and Linear Algebra"
The second with the lorenz attractors in yellow on the cover is by Hirsch, Smale and Devaney and is called:
"Differential Equations, Dynamical Systems and an Introduction to Chaos"
Now, that may be obvious to you, but it is important to note that because those are VERY different books (which I have both of right here). The 'old' one is a more theoretical text that mainly addresses linear systems and is organized more like a math monograph than a contemporary (i.e. with pictures and examples) textbook. It is difficult for most people. The newer version is COMPLETELY different and is written for a more diverse audience. It starts with linear systems but then goes into nonlinear systems and discrete systems. It is somewhat similar in character to Strogatz's Nonlinear Dynamics and Chaos. If you do not have a very strong abstract theoretical type of math background I would not recommend you start learning about differential equations from the "old" edition. You will find it very difficult. If you are used to a general abstract presentation of results you should be fine. For the NEW edition the level is very different. I would guess that courses in multi-variable calc, elementary diff eq, and linear algebra (if you understood them) would be sufficient preparation. Both books are excellent, just be clear on what you are looking for.
Book Description
This book gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets.
This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.
· Presentation of many new results in one place for the first time.
· First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals.
· Fredholm determinants and Painlevé equations.
· The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.
· Fredholm determinants and inverse scattering theory.
· Probability densities of random determinants.
Customer Reviews:
The canonical book of random matrices.......2000-04-14
Mehta's book is the book that gets refered to in every article that deals with random matrices. It covers classical theory of random matrices well, but omits many important developments such as chiral random matrices. 'Random matrices' is somewhat pricey but it is nevertheless the best book there is on theory of random matrices. Unfortunately.
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Linear Algebra over Commutative Rings (Pure and Applied Mathematics)
Mcdonald
Manufacturer: CRC
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Interpolation of Operators, Volume 129 (Pure and Applied Mathematics)
Colin Bennett , and
Robert C. Sharpley
Manufacturer: Academic Press
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ASIN: 0120887304 |
Book Description
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.
The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Book Description
An introduction to one of the most celebrated theories of mathematics
Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as:
- The contributions of Lagrange, Galois, and Kronecker
- How to compute Galois groups
- Galois’s results about irreducible polynomials of prime or prime-squared degree
- Abel’s theorem about geometric constructions on the lemniscate
Customer Reviews:
Decent textbook with some good extras.......2006-03-20
Part 1 (pp. 1-70) deals with some classical algebra (the cubic equation, symmetric polynomials, the fundamental theorem of algebra). It is nice to see the classical roots emphasised, but I think this could have been done in a much more structured and efficient manner. The chapter on the cubic is 20 pages long and involve 28 exercises. One is impatient already---where's the freakin' Galois theory? Actually, there is still another hundred pages until the definition of the Galois group.
Part 2 (pp. 71-188) develops the Galois theory. Modern Galos theory is couched in the language of field extensions (chapters 4-5); more precisely, the Galois group of a field extension is the group of automorphisms that keeps the base field fixed (chapter 6), and the key to the theory is the "Galois correspondence" between the structure of this group and structure of the field extension (chapter 7).
Part 3 (pp. 189-309) deals with applications. The standard applications are here of course (solvability by radicals; straightedge-and-compass constructions; finite fields and their polynomials) but there are also some more novel ones: automorphisms in geometry (finite subgroups of linear fractional transformations); the "casus irreducibilis" (it is not always possible to express real roots by real radicals); Gauss's work on roots of unity (Gauss showed the solvability by radicals of x^p-1=0 by constructing radical expressions for primitive roots of the intermediate field extensions); "origami" (constructions using straightedge, compass and paper folding).
Part 4 (pp. 310-508), "Further Topics", is what sets this book apart from the usual books. In chapter 12 we study some early works on Galois theory. Lagrange's work on solvability by radicals was the obituary for purely classical methods, but as so often before the grave site soil proved fertile and from here Galois sprang forth with his brilliant little paper containing virtually all the ideas we have seen so far. But Galois's insights into solvability by radicals go beyond the insolvability of the quintic, as we see in chapter 14. In fact, his paper culminates with the theorem that if f is of degree p and f=0 is solvable by radicals then, for any two roots a,b of f, Q(a,b) is the splitting field of f. Going further calls for more sophisticated group theory--we study the case when f is of degree p^2, alluded to by Galois, which is about understanding the solvable primitive subgroups of S_(p^2). Chapter 13 treats methods for computing Galois groups. Finally, Cox has saved the best for last: chapter 15 is on Abel's suggestive work on the division of the lemniscate by ruler and compass (n-division is possible when n is a product of a power of 2 by distinct Fermat primes, just as in the case of the circle). Abel had the idea to employ an analog of the sine function, which is given as the inverse of an arc length integral. This function is not only periodic like the sine but doubly periodic in the complex plane, and it has not only addition formulas but formulas for complex multiplication, which we use in our proof of Abel's theorem. Throughout the book one has grown sick and tired of Cox's abusive use of exercises -- arguments are often shortened by statements like "in exercise x you will show so-and-so; therefore ...". Cox has made sure to end on a high note in this respect: after much preparation the proof of Abel's theorem is just over two pages, but it contains no less than eight references to exercises.
Very nice book.......2005-12-06
This is a wonderful book.
One of the things about abstract algebra is that for the non initiate you tent to loose sight of the problems that motivated an original concept. This book goes an explains the history behind every step. Even some of the demonstrations contain references like (this step here is following a demonstration given by Gauss or Lagrange etc) it is very interesting reading.
Similar to Galois Theory, Third Edition by Ian Stewart but this book containts a lot more detail.
there is a lot of reference to classic works by Galois,Gauss,Cauchy
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Post-Modern Algebra (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Jonathan D. H. Smith , and
Anna B. Romanowska
Manufacturer: Wiley-Interscience
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Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
ASIN: 0471127388 |
Book Description
Advanced algebra in the service of contemporary mathematical researchâ a unique introduction.
This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebraâa book that has dominated the field for nearly seventy years. Post-Modern Algebra offers a truly up-to-date alternative to the standard approach, explaining topics from an applications-based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras. The text features:
- A clear and concise treatment at an introductory level, tested in university courses.
- A wealth of exercises illustrating concepts and their practical application.
- Effective techniques for solving research problems in the real world.
- Flexibility of presentation, making it easy to tailor material to specific needs.
- Help with elementary proofs and algebraic notations for students of varying abilities.
Post-Modern Algebra is an excellent primary or supplementary text for graduate-level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.
Book Description
Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject—effectively holding your interest and creating a more seamless method of instruction. Filled with in-depth insights and over six hundred exercises of varying difficulty, this invaluable text can help anyone appreciate and understand this subject.
Download Description
As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing with extensive use in computing science, physics, chemistry, and data communications as well as in new areas of mathematics such as combinatorics. This book contains the essentials of abstract (or modern) algebra together with a wide variety of applications.
Customer Reviews:
The best modern algebra text I have seen.......2006-07-22
It has been some time since I taught a course in modern algebra, but if I were to teach it again, I would use this book. The first chapter covers the basics of binary operations and algebraic structures. Seven pages in length, it is a basic overview of what the students should already know. Chapter two covers what is arguably the simplest abstract algebra, Boolean algebra. Propositional logic, switching circuits, posets and lattices are the examples used. I am in strong agreement with the introduction of switching circuits this early in a course. It is an application of abstract algebra that students can easily understand and relate to. Switching circuits also immediately demonstrates that the inclusion of "with applications" in the title is not a misnomer.
Basic group theory is the topic of chapter three, quotient and symmetry groups are covered in chapters four and five. The Polya-Burnside method of enumeration is the topic of chapter five, monoids and machines the focus of chapter seven, rings, fields, polynomial, Euclidean and quotient rings are examined in chapters eight, nine and ten. Field extensions are covered in chapter eleven, Latin squares in chapter twelve, geometrical constructions in chapter thirteen and error-correcting codes in chapter fourteen.
The exposition is excellent, it is one of the more readable texts in advanced mathematics that you will find. There are many examples of the applications of modern algebra to the real world and a large number of exercises are included at the end of the chapters. Solutions to the odd numbered exercises are found in an appendix.
Modern algebra is a difficult topic due to the abstract nature of the material. It is easy for students to get confused and lost when they are studying the book on their own. The risk of that is minimized if they are reading this book.
important computer applications.......2005-01-01
This book is pitched at the level of a third or fourth undergraduate year in maths, or at a graduate level course. Gilbert assumes a solid background in maths, especially linear algebra. He expounds on groups and rings.
You can certainly treat this book as a pure maths text on algebra. But there is a twist to it, for some of you. He discusses applications in engineering. Notably Boolean algebra. Boolean logic forms the conceptual and practical basis of computer hardware and software. Gilbert shows how to represent a Boolean expression in a normal form and how to simplify it. Very practical and vital to circuit design.
Later on in the book, he gives a good but all too brief discussion of finite state machines. These can be used in control systems and even in the construction of computer languages like Java. Where the Java bytecode can be validated precisely because Java is a finite state machine.
Finally, error correcting codes take up an entire chapter. Important in communications theory, and even in such common items as storing information on computer media like DVDs.
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Incidence Algebras (Pure and Applied Mathematics)
Eugene Spiegel , and
Christopher O'Donnell
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover
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ASIN: 0824700368 |
Book Description
This work covers the maximal and prime ideals of the incidence algebra, derivations and isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions include a study of the Mobius function, reduced incidence subalgebras, and the coalgebra approach to incidence algebras.;College or university bookstores may order five or more copies for a special student price, which is available on request from Marcel Dekker.
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Introduction to Lie Groups and Lie Algebra, 51 (Pure and Applied Mathematics (Academic Pr))
Arthur A. Sagle , and
R. Walde
Manufacturer: Academic Press
ProductGroup: Book
Binding: Paperback
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ASIN: 0126145512 |
Books:
- Discovering Statistics Using SPSS (Introducing Statistical Methods S.) (2nd Edition)
- Distribution System Modeling and Analysis, Second Edition (Electric Power Engineering Series)
- Dynamic Modeling (Modeling Dynamic Systems)
- Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring and Optimal Control (Advances in Industrial Control)
- Elementary Numerical Analysis
- Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications)
- Fast Fourier Transform and Its Applications
- Finite Difference Schemes and Partial Differential Equations
- Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition)
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