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Markov Chain Monte Carlo in Practice
Markov Chain Monte Carlo in Practice
(Interdisciplinary Statistics)
Pages: 512
In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation. Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains. Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.


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Handbook of Typography for Mathematical Sciences

Handbook of Typography for Mathematical Sciences
Pages: 192
You know mathematics. You know how to write mathematics. But do you know how to produce clean, clear, well-formatted manuscripts for publication? Do you speak the language of publishers, typesetters, graphics designers, and copy editors? Your page design-the style and format of theorems and equations, running heads and section headings, page breaks, fonts, and spacing-makes the difference between, awkward, hard-to-read publications and coherent, professional ones. The Handbook of Typography for the Mathematical Sciences is your key to exercising control over how your books and articles look, read, and ultimately communicate your ideas. Focusing on TeX, today's medium of choice for producing mathematical documents, the author illuminates all of the issues associated with page design and seeing your manuscript smoothly and accurately through each step of its publication. · Learn how to format, edit, and layout a page · Examine a variety of graphics options: Postscript®, bitmaps, *.jpg, *.gif, and *.pdf files · Discover powerful tools available for indexing, bibliographies, tables, and diagrams · Access a compendium of all TeX commands commonly used in mathematical writing · Explore ways to include diskettes, source code, or software available on the Internet with you publications Becoming acquainted with this material will make you a well-informed author equipped to deal with publishers, compositors, editors, and typesetters, with TeX consultants, copy editors, and graphics designers-an author who has a better understanding of the publishing process and is able to create better mathematics books.


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Algebra VIII: Representations of Finite-Dimensional Algebras
Algebra VIII: Representations of Finite-Dimensional Algebras
Pages: 168
The monograph aims at a general outline of old and new results on representations of finite-dimensional algebras. In a theory which developed rapidly during the last two decades, the lack of textbooks is the main impediment for novices. Therefore special attention is paid to the foundations, and proofs are included for statements which are elementary, serve comprehension or are scarcely available. In this manner the authors try to lead the reader up to a point where he can find his way through the original literature. The discourse is centered around the fairly complete theory of finitely-represented posets and algebras. The monograph provides many examples and all the needed background on decomposition theorems, quivers, almost split sequences and derived categories. It includes a survey on representations of tame and wild quivers, lists of critical algebras and a proof of the old conjectures of Brauer and Thrall.


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Algebra II: Noncommunicative Rings, Identities
Algebra II: Noncommunicative Rings, Identities
Pages: 234

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Algebras, Rings and Modules: Volume 2
Algebras, Rings and Modules: Volume 2
(Mathematics and Its Applications)
Pages: 400

As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.
Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined.
The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings.
Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest.

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Advanced Linear Algebra, Third Edition
Advanced Linear Algebra, Third Edition
Pages: 526
This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.

For the third edition, the author has:
* added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem);
* polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products);
* upgraded some proofs that were originally done only for finite-dimensional/rank cases;
* added new theorems, including the spectral mapping theorem and a theorem to the effect that , dim(V)<=dim(V*) with equality if and only if V is finite-dimensional;
* corrected all known errors;
* the reference section has been enlarged considerably, with over a hundred references to books on linear algebra.

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A History of Abstract Algebra
A History of Abstract Algebra
Pages: 168

Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century algebra came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the history of the basic concepts, results, and theories of abstract algebra.

The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing context from which the reader may gain a deeper appreciation of the mathematics involved.

Key features:

* Begins with an overview of classical algebra

* Contains separate chapters on aspects of the development of groups, rings, and fields

* Examines the evolution of linear algebra as it relates to other elements of abstract algebra

* Highlights the lives and works of six notables: Cayley, Dedekind, Galois, Gauss, Hamilton, and especially the pioneering work of Emmy Noether

* Offers suggestions to instructors on ways of integrating the history of abstract algebra into their teaching

* Each chapter concludes with extensive references to the relevant literature

Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. The book may also serve as a supplemental text for courses in abstract algebra or the history of mathematics.

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Mathematics: Powerful Patterns into Nature and Society
Mathematics: Powerful Patterns into Nature and Society
Pages: 192

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Partial Differential Equations IX
Partial Differential Equations IX: Elliptic Boundary Value Problems
Pages: 281

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Partial Differential Equations VIII
Partial Differential Equations VIII
Overdetermined Systems Index of Elliptic Operators
Pages: 265

This volume contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples

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Fundamental Program of the Calculus



Fundamental Program of the Calculus

Table Of Contents:

1. Real Numbers
2. Real Sets
3. The Fundamental Covering Lemma Of The Calculus
4. Real Functions
5. The Derivate
6. The Integral
7. Littlewood's Three Principles
8. Measure & Integral: Lebesgue's Program
9. Theory For The Integral
10. Dini Derivates
11. The Vitali Covering Theorem
12. Jordan Variation Of A Real Function
13. Variational Measures
14. The Integral
15. The Stieltjes Integral
16. Appendix: Formal Theory Of The Calculus

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Lectures on Algebra, Number Theory, etc.



Lectures on Algebra, Number Theory, etc.

1. Lectures on Commutative Algebra

2. Lectures on Topics in Algebraic Number Theory

3. A Quick Review of Commutative Algebra

4. Primary Decompositions of Modules

5. Lectures on Field Theory and Ramification Theory

6. Notes on Galois Theory

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Completely Bounded Maps and Operator Algebras
Completely Bounded Maps and Operator Algebras
Pages: 320

In this book the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.

http://rapidshare.com/files/57040639/0521816696.rar

Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis
Pages: 314

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.

The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.

This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works.

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Harcourt Mathematics 12 - Geometry and Discrete Mathematics

CHAPTER 2
Plane Figures and Proof
Review of Prerequisite Skills
Rich Learning Link
2.1 Proofs Using Congruent Triangles
2.2 Conditional Statements
2.3 The Converse of a Conditional Statement
2.4 Indirect Proof and Parallel Lines
2.5 Ratio and Proportion
2.6 Similar Figures
Key Concepts Review
Review Exercise
Rich Learning Link Wrap-Up
Chapter 2 Test
Extending and Investigating

http://rapidshare.com/files/55806620/algeo.zip

Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis
Pages: 314

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.

The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.

This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works.

http://rapidshare.com/files/57039680/0817643397.rar
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http://mihd.net/q18p0f
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Harcourt Mathematics 12 - Geometry and Discrete Mathematics

CHAPTER 2
Plane Figures and Proof
Review of Prerequisite Skills
Rich Learning Link
2.1 Proofs Using Congruent Triangles
2.2 Conditional Statements
2.3 The Converse of a Conditional Statement
2.4 Indirect Proof and Parallel Lines
2.5 Ratio and Proportion
2.6 Similar Figures
Key Concepts Review
Review Exercise
Rich Learning Link Wrap-Up
Chapter 2 Test
Extending and Investigating

http://rapidshare.com/files/55806620/algeo.zip

Matrix Algebra
Matrix Algebra: Theory, Computations, and Applications in Statistics
Pages: 530
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained.


The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics.


The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations.


The book includes a large number of exercises with some solutions provided in an appendix.


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Mathematics of Data Management

Mathematics of Data Management v2
Pages: 676
This text provides students with a basic foundation in the concepts and skills of managing data. The major objective of the text is to provide students with the mathematical foundation, and the research and technological skills, to successfully complete a major culminating project on a topic of interest to them.


Students access data through print and internet sources to use in the exercise questions as well as the completion of small projects that prepare them for the successful completion of the culminating project. The text integrates the optional use of technology tools such as dynamic statistical software, graphing calculators, and spreadsheets in such a way that classes and students with limited access to these technology tools are accommodated.


Features


- Built on the very best of McGraw-Hill Ryerson's math texts: numerous exercises to maximize student comprehension; quality investigations for both concept development and assessment; concepts developed in the context of meaningful real world applications
- Easy-to-follow process integrated throughout the text for accomplishing the course culminating project that integrates the expectations of the course
- Four smaller projects provide students with the opportunity to develop the skills required to successfully complete their culminating project
- Projects provide an opportunity for open-ended assessment of students' application of the skills and comprehension of the concepts of the course
- Assessment tools, both in-text and TR support
- All concepts are summarized at the end of each section for easy reference and reviewed with thought provoking communication questions
- Exercise set and chapter test questions are correlated to the Achievement Chart
- Prerequisite Skills and Technology appendices to support independent learning, and provide quick how-to references for previously learned skills and technology tool key strokes
- Fully integrated technology
- Comprehensive review of previously learned skills and concepts prepare students for the new concepts in each chapter
- Comprehensive chapter reviews provide section-by-section review of concepts learned in the chapter
- Chapter tests provide a sample test-taking experience based on the concepts in the chapter
- Cumulative reviews


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Theory and Applications of Numerical Analysis, Second Edition

Theory and Applications of Numerical Analysis, Second Edition
Pages: 447
This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.

* a unique blend of theory and applications
* two brand new chapters on eigenvalues and splines
* inclusion of formal algorithms
* numerous fully worked examples
* a large number of problems, many with solutions

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Numerical Methods for Linear Control Systems

Numerical Methods for Linear Control Systems
Pages:640
Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. MATLAB-based software is included for implementing all of the major algorithms from the book.

* Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions
* Background material in linear algebra, numerical linear algebra, and control theory included in text

* Step-by-step explanations of the algorithms and examples

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