Book Description
The study of small and local deformations of algebraic varieties originates in the classical work of Kodaira and Spencer and its formalization by Grothendieck in the late 1950's. It has become increasingly important in algebraic geometry in every context where variational phenomena come into play, and in classification theory. Today deformation theory is highly formalized and has ramified widely. This self-contained account of deformation theory in classical algebraic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with relatively little known proofs, yet of everyday relevance to algebraic geometers. It also includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. The exposition, amenable at graduate student level, includes many examples.
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- A masterpiece in wavelets
- Distinguished link between math and computer science
- A fresh look at wavelets
- an intriguing new wavelet book
- An Intriguiging New Book
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Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)
Ola Bratteli , and
Palle Jorgensen
Manufacturer: Birkhäuser Boston
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Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics)
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ASIN: 0817642803 |
Book Description
This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.
Customer Reviews:
A masterpiece in wavelets.......2003-03-14
This is a very well written book on the theory of wavelets and its applications. The presentation is self-contained and may serve as an introduction for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts. This book gives a general presentation of some recent developments in wavelet theory with an emphasis on techniques that have a geometric and spectral-theoretic flavor. It can be certainly used as a textbook for graduate students as well as as a reference book for the specialists and researchers. A very nice feature of the book are the tutorials at the beginning of each chapter and some sections, which serve as summaries of main ideas and guides through the background ideas and motivation. At the end of every chapter there are plenty of excercises of various level of difficulty. Overall, this is a great book and I recommend it highly to a motivated reader.
Distinguished link between math and computer science.......2003-03-11
This is an important mathematical reference written in excellent style. Wavelets have found applications in many areas of engineering and CS. The authors provide a detailed, rich and entertaining tour through this relatively young but important field for both math and CS/Eng. Connections are, e.g., made between advanced CS virtual-reality applications such as audio-systems processing, future applications such as quantum computing, and advanced math in functional analysis and operator theory.
A fresh look at wavelets.......2002-10-08
The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particular
1- The book covers the theory of wavelets from the point of view of operators and functional analysis and will appeal to a growing number of pure as well as applied mathematicians interested in the subject.
2- The writing of the book is very appealing: every chapter starts by a tutorial that gives motivation as well as intuition. It is then followed by a very clean mathematical development of the subject, together with many examples, figures, and applications from physics and engineering. A set of nice problems is provided at the end of each chapter. Thus this book can be used as a graduate textbook or for mathematical seminars in mathematics departments.
3- This book can even be used by experts in wavelet theory for learning about recent developments and new perspectives from operator theory and functional analysis.
I highly recommend this book.
an intriguing new wavelet book.......2002-09-09
This is a book about an important topic in applied mathematics by two authors with excellent credentials in both pure and applied areas. The reader will find many intriguing threads connecting wavelets to other parts of mathematics, including a wavelet index theorem, quantum computing, the ubiquitous C*-algebras O_n and, of course, spectral theory. The graphics are meticulously done.
I look forward to learning a lot from it.
An Intriguiging New Book.......2002-08-30
This is a book about an important topic in applied mathematics by two authors with excellent
credentials in both pure and applied areas.
The reader will find many intriguing threads connecting wavelets to other parts of mathematics, including a wavelet "index theorem", quantum computing, the ubiquitous Cuntz C*-algebras and, of course, spectral theory. The graphics are excellent. I look forward to learning a lot from it.
Book Description
From the reviews:
"The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. ... The author has sought to make his treatment complete and he has succeeded. The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. ... This book is, all in all, a very admirable work and a valuable addition to the literature...
(S.Y. Husseini in Mathematical Reviews, 1976)
Customer Reviews:
This might take a while..........2002-06-09
The earlier chapters are quite good; however, some of the advanced topics in this book are better approached (appreciated) after one has learned about them elsewhere, at a more leisurely pace. For instance, this isn't the best place to first read about characteristic classes and topological K theory (I would recommend, without much hesitation, the books by Atiyah and Milnor & Stasheff, instead). Much to my disappointment, the chapter on spectral sequences is quite convoluted. Parts of 'user's guide' by Mcleary would certainly come in handy here (which sets the stage rather nicely for applications).
So it turns out that supplemental reading (exluding Whitehead's massive treatise) is necessary to achieve a better understanding of algebraic topology at the level of this book. The homotopical view therein will be matched (possibly superseded) by Aguilar's book (forthcoming, to which I am very much looking forward).
Good luck!
Book Description
Since the beginning of the modern era of algebraic topology, simplicial
methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques.
Discussed here are the homotopy theory of simplicial sets, and other basic
topics such as simplicial groups, Postnikov towers, and bisimplicial sets.
The more advanced material includes homotopy limits and colimits,
localization with respect to a map and with respect to a homology theory,
cosimplicial spaces, and homotopy coherence. Interspersed throughout are
many results and ideas well-known to experts, but uncollected in the
literature.
Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Customer Reviews:
Excellent book!.......2001-06-19
Gives a well-written and concise treatment of developments in an area of topology that has seen considerable progress in the past 50 years. The only other general expository books in this area are more than 20 years old. This is particularly important because the book unifies many seemingly disparate results and approaches. Even classic constructions (like the Hurewicz homomorphism) are give modern (and very concise) interpretations. I strongly recommend this book to students and researchers in algebraic topology.
Book Description
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Book Description
The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to construct singular homology and cohomology, as well as K-theory. Throughout the text many other fundamental concepts are introduced, including the construction of the characteristic classes of vector bundles. Although functors appear constantly throughout the text, no knowledge about category theory is expected from the reader. This book is intended for advanced undergraduates and graduate students with a basic knowledge of point set topology as well as group theory and can be used in a two semester course. Marcelo Aguilar and Carlos Prieto are Professors at the Instituto de Matemticas, Universidad Nacional Autonoma de Mexico, and Samuel Gitler is a member of El Colegio Nacional and professor at the Centro de Investigacion y Estudios Avanzados del IPN.
Customer Reviews:
A bad book.......2007-07-05
Good for reference sometimes but has too much garbage/symbols and unnecessary details everywhere. Spends pages proving something which can be explained with a small picture and remarks. Not recommended.
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Algebraic Homotopy (Cambridge Studies in Advanced Mathematics)
Hans Joachim Baues
Manufacturer: Cambridge University Press
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ASIN: 0521333768 |
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The author describes new tools for the homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group of homotopy equivalences. Applications and examples of such computations are given.
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The Statistical Theory of Shape (Springer Series in Statistics)
Christopher G. Small
Manufacturer: Springer
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ASIN: 0387947299 |
Book Description
The shape of a data set can be defined as the total of all information under translations, rotations, and scale changes to the data. Over the last decade, shape analysis has emerged as a promising new field of statistics with applications to morphometrics, pattern recognition, archaeology, and other disciplines. This book provides a comprehensive coverage of the statistical theory of shape. Both the Kendall and the Bookstein schools of shape analysis are described. It is written for graduate students and researchers in statistics who have some knowledge of multivariate models. An understanding of the basic concepts of differential manifolds is also helpful.
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