كتب رياضيات mathmatic

Sha Huang, Yu Ying Qiao, Guo Chun Wen, "Real and Complex Clifford Analysis"
Springer; 1 edition (November 16, 2005) | ISBN: 0387245359 | 251 pages | PDF | 1,3 Mb

Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors investigations, and this new monograph will be interesting for researchers studying the theory of functions.

Robert Kaplan, Ellen Kaplan, "Out of the Labyrinth: Setting Mathematics Free"
Oxford University Press, USA; 1 edition (December 19, 2006) | ISBN:0195147448 | 256 pages | PDF | 10,3 Mb


Review
"Out of the Labyrinth rejoices in the serious play of mathematics and explains how to think about math as a truly common pursuit... This beautiful book - full of fun and full of the wisdom of a lifetime of teaching - is so deftly done that by the time the Kaplans tell us that "math is our other native language," we believe them utterly." -- Barry Mazur, Gerhard Gade University Professor, Harvard University

"I found the book to be a provocative guide to the beauty and glory of mathematics with many excellent suggestions on how to communicate this to others, written by two masters of the art. I enjoyed the sections the most where I agreed with them the least. It challenged every prejudice I had developed about the subject." -- Benedict Gross, Leverett Professor of Mathematics and Dean of Harvard College

Book Description
Who hasn't feared the math Minotaur in its labyrinth of abstractions? Now, in Out of the Labyrinth, Robert and Ellen Kaplan--the founders of The Math Circle, the popular learning program begun at Harvard in 1994--reveal the secrets behind their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Written with the same wit and clarity that made Robert Kaplan's The Nothing That Is an international bestseller, Out of the Labyrinth offers an engaging and practical guide for parents and educators, and a delight for anyone interested in sharing the pleasures of mathematics. The Kaplans begin by describing the state of modern math education--the lockstep acquisition of "skills," "number facts," and "mad minute" calculations. Instead, they argue, math should be taught as the highest form of intellectual play, an endeavor to be explored and enjoyed by children (or adults) of any age. One by one, they dismantle the many barriers to appreciating mathematics, from the self-defeating belief that mathematical talent is inborn, to the off-putting language of mathematics, to the question of why anyone should care. They show, for instance, that mathematical ability is not a matter of inborn genius, but of doggedness and attention. Even Einstein admitted that "I know perfectly well that I myself have no special talents. It was curiosity, obsession, and sheer perseverance that brought me to my ideas." Enhanced throughout with puzzles, practical equations, and colorful anecdotes from their own classrooms, Out of the Labyrinth will delight readers with its engaging exploration of mathematics. It will allow students, parents, teachers, and others to wrestle with the accessible mysteries of math--and discover their inner math genius.

Multiple Testing Procedures with Applications to Genomics
Publisher: Springer | Language: English | ISBN:0387493166 | 590 pages | Data: 2007 | PDF | 4 Mb

Description: This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. The methods are applied to a range of testing problems in biomedical and genomic research, including the identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments, such as microarray experiments; tests of association between gene expression measures and biological annotation metadata (e.g., Gene Ontology); sequence analysis; and the genetic mapping of complex traits using single nucleotide polymorphisms. The book is aimed at both statisticians interested in multiple testing theory and applied scientists encountering high-dimensional testing problems in their subject matter area. Specifically, the book proposes resampling-based single-step and stepwise multiple testing procedures for controlling a broad class of Type I error rates, defined as tail probabilities and expected values for arbitrary functions of the numbers of Type I errors and rejected hypotheses (e.g., false discovery rate). Unlike existing approaches, the procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The multiple testing results are reported in terms of rejection regions, parameter confidence regions, and adjusted p-values.

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations
Publisher: Springer | 1999-12-31 | ISBN 1402008023 | Pages: 686 | DJVU | 7.4 MB

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

Topics in Functional Analysis (Lecture Notes in Mathematics vol 45)
Publisher: Springer | 1997-01-01 | ISBN 3540039163 | Pages: 112 | PDF | 2.5 MB

Topics in Functional Analysis (Lecture Notes in Mathematics)
By Albert Wilansky

Seminar on Periodic Maps (Lecture Notes in Mathematics Vol 46)
Publisher: Springer | 1997-01-01 | ISBN 3540039171 | Pages: 124 | PDF | 3.2 MB


Seminar on Periodic Maps (Lecture Notes in Mathematics)
By Pierre E. Conner

Rolf Berndt, " Representation of Linear Groups An Introduction Based on Examples from Physics and Number Theory"
Friedr Vieweg & Sohn Verlagsgesellschaft (January 2007) | ISBN: 3834803197 | 270 pages | PDF | 1,6 Mb

Representation of Linear Groups: An Introduction Based on Examples from Physics and Number Theory

Yuli B. Rudyak, "On Thom Spectra, Orientability, and Cobordism"
Springer; 1st ed. 1998. Corr. 2nd printing edition (August 15, 1998) | ISBN: 3540620435 | 587 pages | PDF | 5,2 Mb

For many years, algebraic topology rests on three legs: "ordinary" cohomology, K-theory, and cobordism. This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra.

From the Foreword by Haynes Miller

The author has also performed a service to the history of science in this book, giving detailed attributions. This same care makes the book easy to use by the student, for when proofs are not given, specific references are.

From the reviews:

" This is an important, formidable monograph ..... The readers interested in pursuing this line of research will find it enormously helpful to have the results assembled in one place with an unified, brilliant exposition."

Zentralblatt Math 906.1999

"This book provides an excellent and thorough treatment of various topics related to cobordism. It should become an indispensable tool for advanced graduate students and workers in algebraic topology. "

MathSciNet MR1627486

Patrizia Pucci , James Serrin, "The Maximum Principle (Progress in Nonlinear Differential Equations and Their Applications)"
Birkhäuser Basel; 1 edition (October 23, 2007) | ISBN: 3764381442 | 234 pages | PDF | 1,7 Mb

Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.

Morris Kline, "Mathematics and the Search for Knowledge"
Oxford University Press, USA (November 20, 1986) | ISBN: 0195042301 | 272 pages | PDF | 13,3 Mb

Review
"Requires a minimum of technical knowledge and gives an illuminating oversight of the historical developments...with many interesting observations along the way."--Proceedings of the Edinburgh Mathematical Society

"The lively writing makes this suitable supplementary reading for advanced undergraduates from many disciplines. An extensive and often technical bibliography is included for those who want to go further."--Zentralblatter/Abstract Journals

Book Description
In this book Kline examines the development of mathematics as our most powerful instrument for exploring the physical world. He probes our existing world of mathematics and illuminates its workings as a science enabling us to penetrate the secrets of the world's natural phenomena.

LearningExpress Editors, "501 Quantitative Comparison Questions"
LearningExpress, LLC; | ISBN: 1576854345 | 176 pages | PDF | 1,3 Mb

501 Quantitative Comparison Questions helps prepare students for key academic aptitude tests-including the PSAT/NMSQT, the SAT, and the GRE-which feature a quantitative comparison section within the math portion of the exam. 501 Quantitative Comparison Questions is designed to help students prepare for this specialized math section, mastery of which is essential for acceptance to desirable schools and jobs. By completing the exercises in this book, students can increase their math knowledge and gain familiarity with specialized questions needed to score high. The book features complete answers, each with a full explanation.

LearningExpress Editors, "501 Math Word Problems"
LearningExpress, LLC | ISBN: 1576855635 | 192 pages | PDF | 1 Mb

This test-prep book from the experts at LearningExpress, based on real-world tests, presents methods and practice for quickly and dramatically improving math word problem skills. Structured in a multiple-choice format with numerous tips, 501 Math Word Problems emphasizes a self-paced approach that moves from basic questions to more difficult ones. Ideal for anyone taking the PSAT, SAT, GRE, GMAT, LSAT, or other standardized tests, the book covers such topics as basic math, fractions, decimals, percents, algebra, and geometry.

Walter Rudin, «Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics)»
McGraw-Hill | ISBN: 007054235X | DJV | 2,59 Mb | 325 Pages | 1976 Year


The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.

John B. Conway, "A Course in Functional Analysis"
Springer-Verlag | ISBN 3540960422 | 1st edn (1985) | 404 pages | DjVu | 3.6 MB


Description
This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.

Review
The author begins his Preface with the statement, "Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other." As a corollary, it is possible to find two books or courses that bear the title "Functional Analysis" and have little in common. In the present book the author has decided to follow what he calls the "common thread" of functional analysis, namely the existence of a linear space with a topology. Throughout, the emphasis is placed on the study of bounded operators on a Hilbert space. The author begins by discussing the basic properties of Hilbert spaces and operators on them. He follows this with Banach spaces and locally convex spaces. Chapters are devoted to the weak topology on a Banach space and the weak star topology on its dual, bounded linear operators on a Banach space, Banach algebras, C* algebras, normal operators on a Hilbert space (bounded and unbounded) and Fredholm theory for bounded operators on a Hilbert space. Many examples are given, including some from other branches of mathematics. Numerous exercises are provided. The author has also included several important applications and topics such as Fourier transforms, invariant subspaces, Sturm-Liouville systems, Banach limits, Runge's theorem, ordered vector spaces, inductive limits, distributions, the Stone-Cech compactification, the Krein-Milman theorem, the Stone-Weierstrass theorem, the Schauder fixed point theorem, the Ryll-Nardzewski fixed point theorem, Haar measure, the Krein-Smulian theorem, and moments.
The exposition is clear, although definitions are not always easy to come by. The reader should have a thorough knowledge of measure and integration theory, a good background in topology and familiarity with the basics of analytic function theory. There are two remarks whch the reviewer is forced to make. The first is that (g) of Theorem 2.5 of Chapter XI is not due to the references cited, but rather to the reviewer [Bull. Amer. Math. Soc., 74 (1968), pp. 1139-11441. The second concerns the term Weyl spectrum which has found its way into the literature. The set which it represents was introduced by the reviewer (ibid., 71 (1965), pp. 365-367; J. Math. Anal. Appl., 13 (1966), pp. 205-215) and not by Weyl. (Martin Schechter, University of California at Irvine)

Uploader's note: The cover shown in this news post belongs to the 2nd edition of this book. The book posted here is the 1st edn (I couldn't find either the 2nd edition to upload, or the cover to the 1st edn)

Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica
CRC; 1 edition | ISBN: 084932016X | 384 pages | August 28, 1998 | PDF | 3 Mb

This book provides a concise introduction to numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. Discussions include: o matrix algebra and analysis o solution of matrix equations o methods of curve fit o methods for finding the roots of polynomials and transcendental equations o finite differences and methods for interpolation and numerical differentiation o numerical computation of single and double integrals o numerical solution of ordinary differential equations Engineering Analysis: o teaches readers to become proficient in FORTRAN or QuickBASIC programming to solve engineering problems o provides an introduction to MATLAB and Mathematica, enabling readers to write supplementary m-files for MATLAB and toolkits for Mathematica using C-like commands The book emphasizes interactive operation in developing computer programs throughout, enabling the values of the parameters involved in the problem to be entered by the user of the program via a keyboard. In introducing each numerical method, Engineering Analysis gives minimum mathematical derivations but provides a thorough explanation of computational procedures to solve a specific problem. It serves as an exceptional text for self-study as well as resource for general reference.

Guo Chun Wen, "Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types"
CRC (August 22, 2002) | ISBN: 0415269717 | 264 pages | 1,8 Mb

This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discussed. Mixed complex equations are included in the quasilinear case, and the text considers both boundary value conditions in the general oblique derivative case and multiply connected domains. Complex analytical methods are used to investigate various problems as well. In particular, hyperbolic numbers and hyperbolic complex functions are introduced to handle hyperbolic complex equations. Researchers and graduate students in mathematical analysis will find this text indispensable.

Jorge Nocedal,«Numerical Optimization»
Springer | ISBN: 0387987932 | PDF | 2,81 Mb | 656 Pages | 2000 Year

NUMERICAL OPTIMIZATION presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.