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Geometric Inequalities by Nicholas D. Kazarinoff

Posted by NTL at Wednesday, March 31, 2010 , 0 Comments

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Book Details :
  • Title : Geometric Inequalities (New Mathematical Library)
  • Author : Nicholas D. Kazarinoff
  • Paperback: 132 pages
  • Publisher: Mathematical Association of America (MAA); 1 edition (June 1975)
  • ISBN-10: 0883856042
  • ISBN-13: 978-0883856048
  • Size : 11.0 MB
  • Type : Pdf
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  • Book Description :

Anybody who liked his first geometry course will enjoy the simply stated geometric problems about maximum and minimum lenghs and areas in this book. Many of these already fascinated the greeks, for example the problem of of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathemaicians, others by high school students.

About the Author

Nicholas D. Kazarinoff received his Ph.D in mathematics in 1954 from the University of Wisconsin, and went on to Associate Professor of Mathematics at the University of Michigan.


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Variational Calculus With Elementary Convexity by John Troutman

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Book Details :
  • Title : Variational Calculus With Elementary Convexity (Undergraduate Texts in Mathematics)
  • Author : John Troutman
  • Hardcover: 364 pages
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K (December 31, 1983)
  • ISBN-10: 3540907718 / 0387907718
  • ISBN-13: 978-3540907718 / 978-0387907710
  • Size : 3.0 MB
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This book is intended as an introduction to the use of variational methods in the formulation and solution of optimization problems of both mathematical and physical interest. It is an outgrowth of lectures presented in the Mathematics Department of Syracuse University during the past several years. In preliminary form, the material from Chapters 0-6 comprised a standard one-semester course of three hours per week given to upper-level students in mathematics, physics, computer science, and engineering, and that from the remainder of the book was offered on request during a succeeding semester.
When pursued systematically, it is designed to carry those who have completed a standard course in multidimensional calculus-with some exposure to differential equations-through the rudiments of rigorous analysis in (normed) linear spaces. For it is in the presence of the linear spaces of continuously differentiable functions that a theory for the integral inequalities which generated the calculus of variations can first be clarified.
In this setting, the fundamentals of the subject are explored, including the natural role of the differential equations of Euler-Lagrange in relating the behavior of integral inequalities to the physical principles of stationarity.


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Linear Algebra Through Geometry by Thomas Banchoff

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Book Details :
  • Title : Linear Algebra Through Geometry (Undergraduate texts in mathematics)
  • Author : M. Waldschmidt, P. Moussa, J. M. Luck
  • Hardcover: 257 pages / Hardcover: 324 pages
  • Publisher: Springer-Verlag (1983) / Springer; 2nd edition (November 25, 1991)
  • ISBN-10: 0387907874 / 0387975861
  • ISBN-13: 978-0387907871 / 978-0387975863
  • Size : 1.7 MB
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Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.


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From Number Theory to Physics by M. Waldschmidt, P. Moussa, J. M. Luck

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Book Details :
  • Title : From Number Theory to Physics
  • Author : M. Waldschmidt, P. Moussa, J. M. Luck
  • Hardcover: 690 pages
  • Publisher: Springer (April 1992) / Springer; Corrected edition (December 14, 1992)
  • ISBN-10: 0387533427 / 3540533427
  • ISBN-13: 978-0387533421 / 978-3540533429
  • Size : 84.6 MB
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Various developments in physics have involved many questions related to number theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, field theories, and dynamical systems and chaos. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint.


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The Elements of Statistical Learning by T. Hastie, R. Tibshirani, J. H. Friedman

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Book Details :
  • Title : The Elements of Statistical Learning
  • Author : T. Hastie, R. Tibshirani, J. H. Friedman
  • Hardcover: 552 pages
  • Publisher: Springer; Corrected edition (July 30, 2003)
  • ISBN-10: 0387952845
  • ISBN-13: 978-0387952840
  • Size : 11.3 MB
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  • Book Description :

During the past decade there has been an explosion in computation and information technology. With it has come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics.

Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry.

The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting--the first comprehensive treatment of this topic in any book.

Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie wrote much of the statistical modeling software in S-PLUS and invented principal curves and surfaces. Tibshirani proposed the Lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, and projection pursuit.

FROM THE REVIEWS:

TECHNOMETRICS "[This] is a vast and complex book. Generally, it concentrates on explaining why and how the methods work, rather than how to use them. Examples and especially the visualizations are principle features...As a source for the methods of statistical learning...it will probably be a long time before there is a competitor to this book."


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Research Trends in Combinatorial Optimization: Bonn 2008 by William J. Cook, László Lovász, Jens Vygen

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Book Details :
  • Title : Research Trends in Combinatorial Optimization: Bonn 2008
  • Editor : William J. Cook, László Lovász, Jens Vygen
  • Hardcover: 562 pages
  • Publisher: Springer; 1 edition (December 12, 2008)
  • ISBN-10: 3540767959
  • ISBN-13: 978-3540767954
  • Size : 4.5 MB
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This book, written by leading experts in combinatorial optimization, features in-depth surveys of current research areas in combinatorial optimization in the broad sense, ranging from applied graph theory to mathematical programming. It also contains numerous new results and shows many interesting current research directions. This book will be indispensible for any researcher in combinatorial optimization.


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Dimension and Recurrence in Hyperbolic Dynamics by Luis Barreira

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Book Details :
  • Title : Dimension and Recurrence in Hyperbolic Dynamics (Progress in Mathematics)
  • Author : Luis Barreira
  • Hardcover: 300 pages
  • Publisher: Birkhäuser Basel; 1 edition (August 27, 2008)
  • ISBN-10: 3764388811
  • ISBN-13: 978-3764388812
  • Size : 6.7 MB
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The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained.


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Thomas' Calculus including Second-order Differential Equations by Maurice D. Weir, Joel Hass, Frank R. Giordano

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Book Details :
  • Title : Thomas' Calculus including Second-order Differential Equations
  • Author : Maurice D. Weir, Joel Hass, Frank R. Giordano
  • Hardcover: 1228 pages
  • Publisher: Addison Wesley; 11 edition (August 27, 2006)
  • ISBN-10: 032149069X
  • ISBN-13: 978-0321490698
  • Size : 20.8 MB
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KEY Message: Thomas' Calculus including Second-order Differential Equations responds to the needs of today's readers by developing their conceptual understanding while strengthening their skills in algebra and trigonometry,two areas of knowledge vital to the mastery of calculus. This book offers a full range of exercises, a precise and conceptual presentation, and a new media package designed specifically to meet the needs of today's readers. The exercises gradually increase in difficulty, helping readers learn to generalize and apply the concepts. The refined table of contents introduces the exponential, logarithmic, and trigonometric functions in Chapter 7 of the text.

KEY TOPICS: Limits and Derivatives, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, Further Applications of Integration, Conic Sections and Polar Coordinates, Infinite Sequences and Series, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integration in Vector Fields, Second-order Differential Equations.

MARKET: For all readers interested in Calculus.


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What Is Calculus About ? by W. W. Sawyer

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Book Details :
  • Title : What Is Calculus About? (New Mathematical Library)
  • Author : W. W. Sawyer
  • Paperback: 118 pages
  • Publisher: Mathematical Association of America; Volume 2 edition (1962)
  • ISBN-10: 0883856026
  • ISBN-13: 978-0883856024
  • Size : 10.8 MB
  • Type : Pdf
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Reviews :

*"Whenever I teach calculus, my emphasis is always on the fact that the basic ideas of calculus can be understood by almost anyone. While I am not always successful in proving this to the students, Sawyer certainly would be. His explanations of the basics of a derivative are the clearest, most understandable that I have ever seen. There are many diagrams, and each one has a specific purpose and they are well integrated into the textual explanations.
This is not a book that you could use to teach a college calculus course. The mandatory epsilons and deltas that form the backbone of basic calculus are mentioned only as an incidental. Sawyer sets out to explain the foundation ideas of calculus in terms of everyday occurrences and for that reason it is better suited to someone who is curious about calculus. However, it could be used as a supplemental text in the foundations of science, as calculus is used in all areas of change, which describes almost all of nature.
While the notation of mathematics is concise, abstract and often appears esoteric, many of the ideas expressed in that notation are quite easy to follow. In this book, Sawyer explains what calculus is all about in terms that anyone who understands motion can follow. There needs to be more people like him writing books like this."
* "Sawyer's text introduces the concept of the derivative to students who are preparing to take a calculus course. Since Sawyer assumes only a solid foundation in algebra and some experience with graphing functions, the text is accessible to the lay reader. He takes an inutitive approach; formal definitions and proofs are not provided.

Sawyer begins his study of the derivative by looking at velocity. He describes the difference between average and instanteous velocity. He shows that instanteous velocity, the derivative of the position function, can be obtained as the limit of the average velocities as the time interval approaches zero. Sawyer then defines the derivative as the slope of the tangent line to a curve at a point, provided it exists. He shows that this definition is equivalent to the first. To keep things simple, he confines his attention to polynomial functions and reciprocal powers of the variable.

Sawyer uses his results to show how the derivative can be used to describe acceleration, curvature, and the behavior of graphs. The final chapters describe, without going into detail, how (integral) calculus can be used to compute areas and volumes and how calculus can lead to nonintuitve results.

Sawyer employs many diagrams and well-chosen examples to show why the formulas that he derives are reasonable. However, I think that formal definitions and proofs would have made his arguments far more convincing. Sawyer stresses conceptual understanding of the derivative, but the exercises, for which answers are provided in the back of the text, consist mostly of repetitive applications of the formulas he derives in his exposition.

The material in this text is covered in good calculus texts, making this text superfluous for students taking calculus. It is best suited to students who want to understand the basic concepts of calculus without having to deal with the formal machinery of calculus."


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Numbers: Rational and Irrational by Ivan Morton Niven

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Book Details :
  • Title : Numbers: Rational and Irrational (New Mathematical Library)
  • Author : Ivan Morton Niven
  • Paperback: 140 pages
  • Publisher: Mathematical Assn of America (June 1961)
  • ISBN-10: 0883856018
  • ISBN-13: 978-0883856017
  • Size : 11.0 MB
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Series: Anneli Lax New Mathematical Library

A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis.

This book deals with the number system, one of the basic structures in mathematics. It is concerned especially with ways of classifying numbers into various categories; for example, it provides some criteria for deciding if a given number is rational (i.e., representable as a common fraction) or irrational, if it is algebraic or transcendental. In the course of the later chapters, the reader is introduced to some of the more recent developments in mathematics. Professor Niven’s book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics. Most readers will find the early chapters well within their grasp while ambitious readers will profit by the more advanced material to be found in later chapters.

About the Author

Ivan Niven attended the University of British Columbia and the University of Chicago. He taught at the University of Illinois and Purdue and has lectured for two summers at Stanford.

Review :

A fine job of presenting the materials at a level which is attainable for the intended reading public. -- The Mathematics Teacher.


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Mathematical Puzzling by A. Gardiner

Posted by NTL at Tuesday, March 30, 2010 , 0 Comments

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Book Details :
  • Title : Mathematical Puzzling
  • Author : A. Gardiner
  • Paperback: 160 pages
  • Publisher: Dover Publications (December 30, 1999)
  • ISBN-10: 0486409201
  • ISBN-13: 978-0486409207
  • Size : 12.6 MB
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Challenging and stimulating collection of diverting brain-teasers helps high school students integrate simple techniques and complex problem-solving strategies in an enjoyable way. Problems involving squares and cubes, polyhedra, prime numbers, chess pieces, and other subjects are grouped into 29 sections, with easier problems appearing at the beginning of each. A valuable tool for teachers, this absorbing book will also appeal to individuals working alone who want to develop problem-solving techniques. Solutions included. 1987 ed.


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Calculus by Sarah Channon

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Book Details :
  • Title : Calculus
  • Author : Sarah Channon
  • Hardcover: 282 pages
  • Publisher: Global Media (2009)
  • ISBN-10: N/A
  • ISBN-13: 978-9380168111
  • Size : 2.9 MB
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No Description.


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Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life by Robin Wilson

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Book Details :
  • Title : Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life
  • Author : Robin Wilson
  • Hardcover: 208 pages
  • Publisher: W. W. Norton & Company; First Edition edition (November 17, 2008)
  • ISBN-10: 0393060276
  • ISBN-13: 978-0393060270
  • Size : 5.8 MB
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A penetrating work that explores the amazing imagination and mathematical genius of the man who wrote Alice's Adventures in Wonderland. Just when we thought we knew everything about Lewis Carroll, here comes a highly original biography that will appeal to Alice fans everywhere. Fascinated by the inner life of Charles Lutwidge Dodson, Robin Wilson, a Carroll scholar and a noted mathematics professor, has produced this revelatory book—filled with more than one hundred striking and often playful illustrations—that examines the many inspirations and sources for Carroll's fantastical writings, mathematical and otherwise. As Wilson demonstrates, Carroll—who published serious, if occasionally eccentric, works in the fields of geometry, logic, and algebra—made significant contributions to subjects as varied as voting patterns and the design of tennis tournaments, in the process creating imaginative recreational puzzles based on mathematical ideas. In the tradition of Sylvia Nasar's A Beautiful Mind and Andrew Hodges's Alan Turing, this is an engaging look at the incredible genius of one of mathematics' and literature's most enigmatic minds. 100 illustrations.

From Publishers Weekly

British mathematician Wilson (Four Colors Suffice) paints a charming picture of Charles Dodgson, aka Lewis Carroll, in this slender biography. Skipping over the most chronicled aspects of Dodgson's life with only a sharp side note deriding rumors of his pedophilia as bad history and bad psychology, Wilson focuses on Dodgson's mathematical and educational accomplishments: pamphlets and books on Euclid, an efficient way of calculating determinants, astute analysis of election methods, and systems of mnemonics and ciphers. Wilson also includes puzzles (some with unsatisfying solutions); a number of Dodgson's photographs, for which Wilson labels him one of the most important photographers of the nineteenth century; and humorous and satirical letters suggesting political postulates such as, Let it be granted, that a speaker may digress from any one point to any other point. Though Dodgson was apparently not always a brilliant teacher or writer in his field, Wilson chooses some of his best work for the examples, and any fan of Victorian mind-benders or mid-level mathematics will enjoy the Dodo's witty and eager explanations of logical puzzles and games. 100 illus. (Nov.)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

From Booklist

For readers amused by the antics of the Mad Hatter and the riddles of the Cheshire Cat, the story of their creator’s life delivers paradoxes as delightful as those embedded in his immortal fiction. Wilson explores that life in a narrative laced with the fantasy and puzzles that lovers of Through the Looking Glass expect. But rigorous formulas figured prominently in the workaday life of a university professor of mathematics. Wilson’s narrative indeed details Charles Dodgson’s skillful use of his mathematical skills in defending euclidean geometry and in developing a new system of proportional representation for Parliament. However, many readers will find their primary interest in the way the academic mathematics of Charles Dodgson metamorphosed into the literary gems of his alter ego, Lewis Carroll. Readers will find rare magic, for instance, in Carroll’s conversion of Dodgson’s professional analysis of terrestrial rotation into a whimsical Wonderland exchange between Alice and the Duchess on the nature of time. A biography as full of twists as the capering of the Jabberwocky! --Bryce Christensen.
About the Author

Robin Wilson is the author and editor of more than thirty books, including Four Colors Suffice and Lewis Carroll in Wonderland. He is a professor of pure mathematics at the Open University, and a Fellow of Keble College, Oxford University. He lives in London.


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Excessive Measures by R.K. Getoor

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Book Details :
  • Title : Excessive Measures (Probability and its Applications)
  • Author : R.K. Getoor
  • Hardcover: 189 pages
  • Publisher: Birkhauser Verlag AG (December 1990) / Birkhäuser Boston; 1 edition (May 1, 1990)
  • ISBN-10: 3764334924 / 0817634924
  • ISBN-13: 978-3764334925 / 978-0817634926
  • Size : 1.4 MB
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This little book is a nice complement to the classic treatise on Markov processes and potential theory by Dellacherie and Meyer, and gives probabilistic constructions for many analytic concepts.


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Introduction to Real Analysis, 3rd Edition, by Robert G. Bartle, Donald R. Sherbert

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Book Details :
  • Title : Introduction to Real Analysis, 3rd Edition
  • Author : Robert G. Bartle, Donald R. Sherbert
  • Hardcover: 388 pages
  • Publisher: Wiley; 3 edition (September 21, 1999)
  • ISBN-10: 0471321486
  • ISBN-13: 978-0471321484
  • Size : 17.0 MB
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In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.


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Periodic Systems: Filtering and Control by Sergio Bittanti, Patrizio Colaneri

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Book Details :
  • Title : Periodic Systems: Filtering and Control (Communications and Control Engineering)
  • Author : Sergio Bittanti, Patrizio Colaneri
  • Hardcover: 424 pages
  • Publisher: Springer; 1 edition (November 17, 2008)
  • ISBN-10: 1848009100
  • ISBN-13: 978-1848009103
  • Size : 3.4 MB
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The advantages of periodic control have been known since humanity learned to cultivate crops in rotation to increase production. In more recent times, it has been recognized that some industrial and technological systems also work or function better in a periodic fashion. Moreover, with periodic control laws it has been possible to solve problems for which no time-invariant solution exists. Periodic models are also able to describe the intrinsic periodicity in many natural phenomena and time series.

Periodic Systems gives a comprehensive treatment of the theory of time-varying dynamical systems with periodic coefficients, including the problems of filtering and control.

Topics covered include: basic issues, including Floquet theory, controllability and observability, canonical decomposition, system norms and Lyapunov and robust stability;the problem of state estimation in its various forms, filtering, prediction and smoothing;control design methods, particularly optimal and robust control.

The text focuses on discrete-time signals and systems; however, an overview of the entire field, including the continuous-time case, is provided in the first chapter. The authors presentation of the theory and results is mathematically rigorous while maintaining a readable style, avoiding excessive formalism. This makes the book accessible to graduate students and researchers from the fields of engineering, physics, economics and mathematics.


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Ergodic Theory and Harmonic Analysis: Proceedings of the 1993 Alexandria Conference by Karl E. Petersen, Ibrahim Salama

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Book Details :
  • Title : Ergodic Theory and Harmonic Analysis: Proceedings of the 1993 Alexandria Conference (London Mathematical Society Lecture Note Series)
  • Editor : Karl E. Petersen, Ibrahim Salama
  • Paperback: 448 pages
  • Publisher: Cambridge University Press (January 27, 1995)
  • ISBN-10: 0521459990
  • ISBN-13: 978-0521459990
  • Size : 3.5 MB
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This volume contains articles that describe the connections between ergodic theory and convergence, rigidity theory, and the theory of joinings. These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. In the aggregate, they will provide a perfect introduction for anyone beginning research in one of these areas.


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An Introduction to Maximum Principles and Symmetry in Elliptic Problems by L. E. Fraenkel

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Book Details :
  • Title : An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics)
  • Author : L. E. Fraenkel
  • Hardcover: 352 pages
  • Publisher: Cambridge University Press (April 13, 2000)
  • ISBN-10: 0521461952
  • ISBN-13: 978-0521461955
  • Size : 2.6 MB
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This book presents the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of nonlinear elliptic equations. Gidas, Ni and Nirenberg, building on the work of Alexandrov and Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. These recent and important results are presented with minimal prerequisites, in a style suited to graduate students. Two long appendices give a leisurely account of basic facts about the Laplace and Poisson equations, and there is an abundance of exercises, with detailed hints, some of which contain new results.

Review :

"The originality of this book mainly consists in new proofs and new extensions of quite well known results concerning maximum principles and symmetry properties related to semilinear elliptic equations." Mathematical Reviews


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Computational Fluid Dynamics 2006: Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD4, Ghent, Belgium, 10-14 July 2006 by Herman Deconinck, E. Dick

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Book Details :
  • Title : Computational Fluid Dynamics 2006: Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD4, Ghent, Belgium, 10-14 July 2006
  • Editor : Herman Deconinck, E. Dick
  • Hardcover: 893 pages
  • Publisher: Springer; 1 edition (July 14, 2009)
  • ISBN-10: 3540927786
  • ISBN-13: 978-3540927785
  • Size : 67.7 MB
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The International Conference on Computational Fluid Dynamics (ICCFD) is the merger of the International Conference on Numerical Methods in Fluid Dynamics, ICNMFD (since 1969) and International Symposium on Computational Fluid Dynamics, ISCFD (since 1985). It is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid dynamics. The proceedings of the 2006 conference (ICCFD4) held in Gent, Belgium, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid mechanics.


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The Technique of Pseudodifferential Operators by H. O. Cordes

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Book Details :
  • Title : The Technique of Pseudodifferential Operators (London Mathematical Society Lecture Note Series)
  • Author : H. O. Cordes
  • Paperback: 396 pages
  • Publisher: Cambridge University Press; First edition. edition (February 24, 1995)
  • ISBN-10: 0521378648
  • ISBN-13: 978-0521378642
  • Size : 2.9 MB
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This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses "Leibniz' formulas" with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals.

Review :

"...interesting and appropriate as a text for an introductory graduate course...it reflects the author's originality and experience in graduate teaching." Alexander Dynin, Bulletin of the American Mathematical Society


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Quantum: The Quantum Theory of Particles, Fields and Cosmology by Edgard Elbaz

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Book Details :
  • Title : Quantum: The Quantum Theory of Particles, Fields and Cosmology (Theoretical and Mathematical Physics)
  • Author : Edgard Elbaz
  • Hardcover: 602 pages
  • Publisher: Springer; 1 edition (December 4, 1997)
  • ISBN-10: 3540620931
  • ISBN-13: 978-3540620938
  • Size : 15.8 MB
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This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.


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Boundary Integral and Singularity Methods for Linearized Viscous Flow by C. Pozrikidis

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Book Details :
  • Title : Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge Texts in Applied Mathematics)
  • Author : C. Pozrikidis
  • Hardcover: 271 pages
  • Publisher: Cambridge University Press (February 28, 1992)
  • ISBN-10: 0521405025 / 0521406935
  • ISBN-13: 978-0521405027 / 978-0521406932
  • Size : 1.9 MB
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The aim of this book is to bring together classical and recent developments in the particular field of Newtonian flow at low Reynolds numbers. The methods are developed from first principles, alternative formulations are compared, a variety of configurations are addressed, the proper mathematical framework is discussed in the context of functional analysis and integral-equation-theory, and procedures of numerical solution in the context of the boundary element method are introduced. The text contains a fair amount of original material pertaining, in particular, to the properties and explicit form of the Green's functions, and the theory of the integral equations that arise from boundary integral representations.

Review :

"...well written. The author is to be congratulated for the excellent presentation of rather difficult and involved methodologies." S. Bhaduri, Applied Mechanics Reviews

"...a very readable and attractive book, packed with basic information and with a modern outlook on linear viscous fluid flow and it is written with authority." Frank Rizzo, SIAM Review


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Moduli of Curves by Joe Harris, Ian Morrison

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Book Details :
  • Title : Moduli of Curves (Graduate Texts in Mathematics)
  • Author : Joe Harris, Ian Morrison
  • Hardcover: 388 pages
  • Publisher: Springer; 1 edition (July 1, 1998)
  • ISBN-10: 0387984380
  • ISBN-13: 978-0387984384
  • Size : 10.8 MB
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This book provides a guide to a rich and fascinating subject: algebraic curves and how they vary in families. The aim has been to provide a broad but compact overview of the field, which will be accessible to readers with a modest background in algebraic geometry. Many techniques including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory are developed, with a focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, to illustrate typical applications with the proofs of the Brill-Noether and Gieseker -Petri theorems via limit linear series, and to survey the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results! and open problems about important topics which are not covered in detail.


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P-adic numbers, p-adic analysis, and zeta-functions by Neal Koblitz

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Book Details :
  • Title : P-adic numbers, p-adic analysis, and zeta-functions (Graduate texts in mathematics)
  • Author : Neal Koblitz
  • Hardcover: 122 pages
  • Publisher: Springer-Verlag (1977)
  • ISBN-10: 0387902740
  • ISBN-13: 978-0387902746
  • Size : 1.4 MB
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These lecture notes are intended as an introduction to p -adic analysis on the elementary level. For this reason they presuppose as little background as possible. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topological spaces.


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Random Effect and Latent Variable Model Selection by David Dunson

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Book Details :
  • Title : Random Effect and Latent Variable Model Selection (Lecture Notes in Statistics)
  • Editor : David Dunson
  • Paperback: 174 pages
  • Publisher: Springer; 1 edition (August 12, 2008)
  • ISBN-10: 0387767207
  • ISBN-13: 978-0387767208
  • Size : 2.3 MB
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Random effects and latent variable models are broadly used in analyses of multivariate data. These models can accommodate high dimensional data having a variety of measurement scales. Methods for model selection and comparison are needed in conducting hypothesis tests and in building sparse predictive models. However, classical methods for model comparison are not well justified in such settings.

This book presents state of the art methods for accommodating model uncertainty in random effects and latent variable models. It will appeal to students, applied data analysts, and experienced researchers. The chapters are based on the contributors’ research, with mathematical details minimized using applications-motivated descriptions.

The first part of the book focuses on frequentist likelihood ratio and score tests for zero variance components. Contributors include Xihong Lin, Daowen Zhang and Ciprian Crainiceanu.

The second part focuses on Bayesian methods for random effects selection in linear mixed effects and generalized linear mixed models. Contributors include David Dunson and collaborators Bo Cai and Saki Kinney.

The final part focuses on structural equation models, with Peter Bentler and Jiajuan Liang presenting a frequentist approach, Sik-Yum Lee and Xin-Yuan Song presenting a Bayesian approach based on path sampling, and Joyee Ghosh and David Dunson proposing a method for default prior specification and efficient posterior computation.


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Algebra 2, Student Edition by McGraw-Hill

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Book Details :
  • Title : Algebra 2, Student Edition
  • Author : Berchie Holliday, Gilbert J. Cuevas, Beatrice Luchin, Ruth M. Casey, Linda M. Hayek, John A. Carter, Daniel Marks, Roger Day
  • Contributor: Carol E. Mallory, Viken Hovseplan
  • Hardcover: 956 pages
  • Publisher: Glencoe/McGraw-Hill; 1 edition (December 27, 2006)
  • ISBN-10: 007873830X
  • ISBN-13: 978-0078738302
  • Size : 77.1 MB
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THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT!

Glencoe Algebra 2 is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today’s high-stakes assessments.

About the Author
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide.

Contents :

Unit 1 First-Degree Equations and Inequalities

1 Equations and Inequalities

2 Linear Relations and Functions
3 Systems of Equations and Inequalities
4 Matrices

Unit 2 Quadratic, Polynomial, and Radical Equations and Inequalities

5 Quadratic Functions and Inequalities
6 Polynomial Functions
7 Radical Equations and Inequalities

Unit 3 Advanced Functions and Relations

8 Rational Expressions and Equations
9 Exponential and Logarithmic Relations
10 Conic Sections

Unit 4 Discrete Mathematics

11 Sequences and Series
12 Probability and Statistics

Unit 5 Trigonometry

13 Trigonometric Functions
14 Trigonometric Graphs and Identities

About the Author

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide.


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Algebra 1, Student Edition by Berchie Holliday, Gilbert J. Cuevas,..

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Book Details :
  • Title : Algebra 1, Student Edition
  • Author : Berchie Holliday, Gilbert J. Cuevas, Beatrice Luchin, Ruth M. Casey, Linda M. Hayek, John A. Carter, Daniel Marks, Roger Day
  • Contributor: Carol E. Mallory, Viken Hovseplan
  • Hardcover: 773 pages
  • Publisher: Glencoe/McGraw-Hill; 1 edition (2008)
  • ISBN-10: 0078738229
  • ISBN-13: 978-0078738227
  • Size : 56.1 MB
  • Type : Pdf
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THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT!
Glencoe Algebra 1 is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today’s high-stakes assessments.

About the Author

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide.

Contents :

Unit 1 Foundations for Functions
1 The Language and Tools of Algebra
2 Solving Linear Equations

Unit 2 Linear Functions
3 Functions and Patterns
4 Analyzing Linear Equations
5 Solving Systems of Linear Equations
6 Solving Linear Inequalities

Unit 3 Polynomials and Nonlinear Functions
7 Polynomials
8 Factoring
9 Quadratic and Exponential Functions

Unit 4 Advanced Expressions and Data Analysis
10 Radical Expressions and Triangles
11 Rational Expressions and Equations
12 Statistics and Probability

About the Author

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide.


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A Practical Guide to Scientific Data Analysis by David J. Livingstone

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Book Details :
  • Title : A Practical Guide to Scientific Data Analysis
  • Author : David J. Livingstone
  • Hardcover: 358 pages
  • Publisher: Wiley; 1 edition (January 26, 2010)
  • ISBN-10: 0470851538
  • ISBN-13: 978-0470851531
  • Size : 2.8 MB
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Inspired by the author's need for practical guidance in the processes of data analysis, A Practical Guide to Scientific Data Analysis has been written as a statistical companion for the working scientist. This handbook of data analysis with worked examples focuses on the application of mathematical and statistical techniques and the interpretation of their results.

Covering the most common statistical methods for examining and exploring relationships in data, the text includes extensive examples from a variety of scientific disciplines.

The chapters are organised logically, from planning an experiment, through examining and displaying the data, to constructing quantitative models. Each chapter is intended to stand alone so that casual users can refer to the section that is most appropriate to their problem.

Written by a highly qualified and internationally respected author this text:

* Presents statistics for the non-statistician
* Explains a variety of methods to extract information from data
* Describes the application of statistical methods to the design of “performance chemicals”
* Emphasises the application of statistical techniques and the interpretation of their results

Of practical use to chemists, biochemists, pharmacists, biologists and researchers from many other scientific disciplines in both industry and academia.


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Hypergeometric Orthogonal Polynomials and Their q-Analogues by Roelof Koekoek, Peter A. Lesky, René F. Swarttouw, Tom H. Koornwinder

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Book Details :
  • Title : Hypergeometric Orthogonal Polynomials and Their q-Analogues (Springer Monographs in Mathematics)
  • Author : Roelof Koekoek, Peter A. Lesky, René F. Swarttouw, Tom H. Koornwinder
  • Hardcover: 578 pages
  • Publisher: Springer; 1 edition (June 26, 2003)
  • ISBN-10: 3642050131
  • ISBN-13: 978-3642050138
  • Size : 3.7 MB
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The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function.

Replacing the differential equation by a second-order difference equation results in (discrete) orthogonal polynomial solutions with similar properties. Generalizations of these difference equations, in terms of Hahn's q-difference operator, lead to both continuous and discrete orthogonal polynomials with similar properties. For instance, they can be expressed in terms of (basic) hypergeometric functions.

Based on Favard's theorem, the authors first classify all families of orthogonal polynomials satisfying a second-order differential or difference equation with polynomial coefficients. Together with the concept of duality this leads to the families of hypergeometric orthogonal polynomials belonging to the Askey scheme. For each family they list the most important properties and they indicate the (limit) relations.

Furthermore the authors classify all q-orthogonal polynomials satisfying a second-order q-difference equation based on Hahn's q-operator. Together with the concept of duality this leads to the families of basic hypergeometric orthogonal polynomials which can be arranged in a q-analogue of the Askey scheme. Again, for each family they list the most important properties, the (limit) relations between the various families and the limit relations (for q --> 1) to the classical hypergeometric orthogonal polynomials belonging to the Askey scheme.

These (basic) hypergeometric orthogonal polynomials have several applications in various areas of mathematics and (quantum) physics such as approximation theory, asymptotics, birth and death processes, probability and statistics, coding theory and combinatorics.


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Fixed Point Theory by Andrzej Granas, James Dugundji

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Book Details :
  • Title : Fixed Point Theory
  • Author : Andrzej Granas, James Dugundji
  • Hardcover: 552 pages
  • Publisher: Springer; 1 edition (June 26, 2003)
  • ISBN-10: 0387001735
  • ISBN-13: 978-0387001739
  • Size : 17.6 MB
  • Type : Djvu
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This monograph gives a carefully worked out account of the most basic principles and applications of the theory of fixed points. Until now, a treatment of many of the discussed topics has been unavailable in book form. The presentation is self-contained and is accessible to a broad spectrum of readers, including mathematically oriented people interested in applications. The main text is complemented by numerous exercises, comments and a comprehenseive bibliography.

About the Author

Andrzej Granas studied in Warsaw and then Moscow, where he earned his doctorate in 1958 under Lazar Lusternik. Since 1958 he has held various research and teaching posts in Poland, Canada, and elsewhere. During the Spring of 1970 he occupied a special chair at the Collège de France. In the early nineties, Dr. Granas founded the journal Topological Methods of Nonlinear Analysis, and since 1992, he has served on the Editorial Board of the Zentralblatt. He is an honorary member of the Gdansk Scientific Society.

Reviews :

"Granas-Dugundji’s book is an encyclopedic survey of the classical fixed point theory of continuous maps (the work of Poincaré, Brouwer, Lefschetz-Hopf, Leray-Schauder) and all its various modern extensions. This is certainly the most learned book ever likely to be published on this subject."-Felix Browder, Rutgers University

"The theory of Fixed Points is one of the most powerful tools of modern mathematics. Not only is it used on a daily basis in pure and applied mathematics, but it also serves as a bridge between Analysis and Topology, and provides a very fruitful area of interaction between the two. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications"-Haim Brézis, Rutgers University

"This is the most comprehensive, well-written and complete book on fixed point theory to date. The book studies just about every aspect of fixed point theory … . The book carries an extensive literature on the subject and many examples. Many of the interesting results, given as exercises, constitute an extension of the theory established in the main text. … I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." (A.G. Kartsatos, Mathematical Reviews, 2004d)

"Thousands of papers have been published in fixed point theory and its applications … . The book of Granas and Dugundji is a new and major contribution to this purpose. … The main text is self-contained, the necessary background material being collected in an appendix … . I can assert this monograph represents an exceptional event and I am sure it will become a reference work in the field. … this book will be extremely valuable to anyone involved in fixed point theory … ." (R. Precup, ZAA-Zeitschrift für Analysis und ihre Anwendungen, Vol. 23 (2), 2004)

"The new edition of Granas and Dugundji’s book is, in my opinion, the most important and complete survey in the last years on fixed point theory … . The main text is self-contained … . New and interesting results and applications can be found all over the book. The style is alert and pleasant. The technical presentation of the book is exceptional. … it will be a very useful work for anyone … involved in fixed point theory in particular and nonlinear analysis in general." (Adrian Petrusel, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLIX (1), 2004)

"This monograph gives a carefully worked-out account of the most basic principles and applications of the theory of fixed points. Until now, a treatment of many of the discussed topics has been unavailable in book form. The presentation is self-contained and is accessible to a broad spectrum of readers." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003)

"Really, this book is an up-to-date and carefully worked out unified account of (not only) classical results in fixed point theory … . The presentation is self-contained and is accessible to a broad spectrum of readers. The main text is complemented by numerous exercises, detailed comments, and a comprehensive bibliography. … The rich bibliography comprises almost 50 pages. The book is useful to all mathematicians who deal with fixed points. It will become an obligatory volume for every serious mathematical library." (Peter Zabreiko, Zentralblatt MATH, Vol. 1025, 2003)

"This monograph provides an immense text … on classical topics in fixed point theory that lie on the borderline of topology and nonlinear functional analysis. … The book is well understandable and requires only a basic knowledge of topology and functional analysis … . It can be warmly recommended to a broad spectrum of readers – to graduate students, experts and everybody who wishes to become acquainted with the basic elements and deeper properties of this part of functional analysis." (EMS Newsletter, March, 2005).


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Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm Al-Din Al-Misri by Francois Charette, Muhammad Ibn Muhammad Misri

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Book Details :
  • Title : Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm Al-Din Al-Misri (Islamic Philosophy, Theology, and Science)
  • Author : Francois Charette, Muhammad Ibn Muhammad Misri
  • Library Binding: 582 pages
  • Publisher: Brill Academic Publishers (July 1, 2003)
  • ISBN-10: 9004130152
  • ISBN-13: 978-9004130159
  • Size : 11.2 MB
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  • Book Description :

This volume contains the critical edition with English translation of a richly-illustrated Arabic treatise on the construction of over 100 various astronomical instruments, many of which are otherwise unknown to specialists. It was composed by Najm al-Din al-Misri, a rather shadowy figure, in Cairo, c.1330. The edition is accompanied by a detailed technical and historical commentary, which is framed as a self-standing essay on Islamic mathematical instrumentation. While this essay/commentary is mainly based on Najm al-Din's treatise, it also benefits from the consultation of a large number of previously unstudied manuscripts, and includes a discussion of all relevant sources from the period 800-1500.


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Infinitary Logic: In Memoriam Carol Karp by D. W. Kueker

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Book Details :
  • Title : Infinitary Logic: In Memoriam Carol Karp (Lecture Notes in Mathematics)
  • Editor : D. W. Kueker
  • Paperback: 220 pages
  • Publisher: Springer; 1 edition (December 18, 1975)
  • ISBN-10: 3540074198
  • ISBN-13: 978-3540074199
  • Size : 10.8 MB
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Carol Karp died on August 20, 1972 after a brave battle against cancer which had lasted for three long years (I) To her, teaching had always been more than a duty, and even during her illness she taught all her classes in addition to carrying out her administrative tasks. Her research, tod, was pushed forward with her usual determination, but unfortunately the planned new monograph on infinitary languages remained unfinished. Her early work was collected in her one published book, but she realized that it very much needed to be brought up to date.


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Calculus: Concepts and Contexts by James Stewart

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Book Details :
  • Title : Calculus: Concepts and Contexts (Stewart's Calculus Series)
  • Author : James Stewart
  • Hardcover: 1152 pages
  • Publisher: World Scientific Publishing Company (August 7, 2009)
  • ISBN-10: 0495557420
  • ISBN-13: 978-0495557425
  • Size : 237.7 MB [2 part]
  • Type : Pdf
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  • Book Description :

Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

About the Author

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning—Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.


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The Origin of Discrete Particles by T. Bastin, C. W. Kilmister

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Book Details :
  • Title : The Origin of Discrete Particles (Series on Knots and Everything)
  • Author : T. Bastin, C. W. Kilmister
  • Hardcover: 196 pages
  • Publisher: World Scientific Publishing Company (August 7, 2009)
  • ISBN-10: 981426167X
  • ISBN-13: 978-9814261678
  • Size : 1.0 MB
  • Type : Pdf
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  • Book Description :

This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (107).
  • Combinatorial Space
  • The Story of the Particle Concept
  • Dimensionality
  • The Simple Bit-String Picture
  • The Fine Structure Constant Calculated
  • Process and Iteration
  • Pre-Space: High-Energy Particles: Non-Locality
  • Space, Relativity and Classical Space
  • Perception
  • Current Quantum Physics, State/Observer Philosophy: Complementarity
  • Just Six Numbers
  • Quantum or Gravity?


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Nonlinear Optimization: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1-7, 2007 by Immanuel M. Bomze, Vladimir F. Demyanov, Roger Fletcher, Tamás Terlaky

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Book Details :
  • Title : Nonlinear Optimization: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1-7, 2007 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze)
  • Author : Immanuel M. Bomze, Vladimir F. Demyanov, Roger Fletcher, Tamás Terlaky
  • Editor : Gianni Di Pillo, Fabio Schoen
  • Paperback: 279 pages
  • Publisher: Springer; 1st Edition. edition (March 1, 2010)
  • ISBN-10: 3642113389
  • ISBN-13: 978-3642113383
  • Size : 2.0 MB
  • Type : Pdf
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  • Book Description :

This volume presents recent advances in continuous optimization; it is authored by four well-known experts in the field and presents classical as well as advanced material on currently active research areas, such as: the family of Sequential Quadratic Programming methods for local constrained optimization, the study of Global Optimization by means of (non-convex) standard quadratic problems, Nonsmooth Optimization, and recent advances in Interior Point Methods for nonlinear optimization. The book is intended as a reference work for advanced research in the field of optimization theory and methods.


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Perspectives in Mathematical Sciences II: Pure Mathematics by N. S. Narasimha Sastry

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Book Details :
  • Title : Perspectives in Mathematical Sciences II: Pure Mathematics (Statistical Science and Interdisciplinary Research)
  • Author : N. S. Narasimha Sastry
  • Editor : N S Narasimha Sastry, T S S R K Rao, Mohan Delampady, B Rajeev
  • Hardcover: 280 pages
  • Publisher: World Scientific Publishing Company (July 1, 2009)
  • ISBN-10: 9814273643
  • ISBN-13: 978-9814273640
  • Size : 1.7 MB
  • Type : Pdf
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  • Book Description :

This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics.

* Use of Resultants and Approximate Roots for Doing the Jacobian Problem (S S Abhyankar)
* Monodromy of Principal Bundles (I Biswas & A J Parameswaran)
* Oligomorphic Permutation Groups (P J Cameron)
* Descriptive Set Theory and the Geometry of Banach Spaces (G Godefroy)
* Multiplicity-Free Homogeneous Operators in the Cowen Douglas Class (A Korányi & G Misra)
* The Standard Conjectures on Algebraic Cycles (M S Narasimhan)
* On the Classification of Binary Shifts on the Hyperfinite II1 Factor (G L Price)
* Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs (S S Sane)
* Perturbation Determinant, Krein's Shift Function and Index Theorem (K B Sinha)
* Zero Cycles and Complete Intersection Points on Affine Varieties (V Srinivas)
* Root Numbers and Rational Points on Elliptic Curves (R Sujatha)
* von Neumann Algebras and Ergodic Theory (V S Sunder)
* Gutzmer's Formula and the Segal Bargmann Transform (S Thangavelu)
* Finite Translation Generalized Quadrangles (J A Thas)
* Super Geometry as the Basis for Super Symmetry (V S Varadarajan).


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A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact by George Gheverghese Joseph

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Book Details :
  • Title : A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact
  • Author : George Gheverghese Joseph
  • Hardcover: 236 pages
  • Publisher: Sage Publications Pvt. Ltd (December 8, 2009)
  • ISBN-10: 8132101685
  • ISBN-13: 978-8132101680
  • Size : 2.7 MB
  • Type : Pdf
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  • Book Description :

This book traces the first faltering steps taken in the mathematical theorization of infinity which marks the emergence of modern mathematics. It analyzes the part played by Indian mathematics through the Kerala conduit, which is an important but neglected part of the history of mathematics.


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Six Lectures on Commutative Algebra by J. Elias, J. M. Giral, Rosa M. Miró-Roig, Santiago Zarzuela

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Book Details :
  • Title : Six Lectures on Commutative Algebra (Modern Birkhäuser Classics)
  • Editor : J. Elias, J. M. Giral, Rosa M. Miró-Roig, Santiago Zarzuela
  • Paperback: 412 pages
  • Publisher: Birkhäuser Basel; 1st. ed 1998. 2nd printing edition (November 23, 2009)
  • ISBN-10: 3034603282
  • ISBN-13: 978-3034603287
  • Size : 3.0 MB
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Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it.

Reviews :

"All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum

Avramov lecture: "Although this text is not presented as a textbook, it contains all the major results in its area, it explains carefully all the different techniques that apply, it provides complete—albeit short— proofs (some new, some with a new twist) of most of the results and references for the rest, and it presents numerous relevant questions. This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews

Huneke lecture: The topic is tight closure, a theory developed by Melvin Hochster and the author which has in a short time proved to be a useful and powerful tool. This paper is intended to be an introduction to the theory, and it is also a good source of examples and insight into the more recent developments that can be of interest to the more experienced.(…) The paper is extremely well organized, written, and motivated. - Zentralblatt MATH

Schenzel lecture: "… this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH

"This interesting survey would be useful for both the novice and the expert." - Mathematical reviews

Valla lecture: "But since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory. (…) It will serve as a useful reference source for people interested in Hilbert functions." - Mathematical reviews

Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH.


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