A Concise Course in Advanced Level Statistics: With Worked Examples

A Concise Course in Advanced Level Statistics: With Worked Examples
Nelson Thornes | 2001-01-01 00:00:00 | Nelson Thornes | 704 | Mathematics
This title is fully revised and updated for complete coverage of statistics at Advanced Level. The use of a second color highlights key areas and formula. Summaries are included to provide consolidation of learning and understanding. Further practice sections of questions are offered for thorough exam preparation and practice. New ICT support for this key area is provided throughout
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The Jacobson Radical of Group Algebras (North-Holland Mathematics Studies)

The Jacobson Radical of Group Algebras (North-Holland Mathematics Studies)
G. Karpilovsky | 1987-04-15 00:00:00 | North Holland | 532 | Mathematics
Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.

The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.



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Statistical Shape Analysis

Statistical Shape Analysis
I. L. Dryden, Kanti V. Mardia | 1998-01-01 00:00:00 | Wiley | 376 | Mathematics
Statistical Shape Analysis involves methods for the geometrical study of random objects where location, rotation and scale information can be removed. The book lays the foundations of the subject discussing key ideas and the very latest developments, as well as offering practical guidance and comparisons of techniques. There is a vast range of applications of shape analysis and the authors introduce the field to statisticians and applied researchers through important examples and data analysis in Biology, Medicine and Image Analysis. The text primarily concentrates on landmark data key points of correspondence located on each object. Careful consideration of the similarity invariances requires methods appropriate for non-Euclidean data analysis. In particular, multivariate statistical procedures cannot be applied directly, but can be adapted in certain instances. The book begins with introductory material on shape, size and coordinate systems. Planar Procrustes analysis is then discussed to highlight the main components of shape analysis. The shape space and general Procrustes methods are introduced, probability distributions for shape are described and statistical inference is discussed. Some deformation methods for shape change are also given and a special chapter is devoted to shape in image analysis. Finally, various alternative procedures including landmark-free methods are critically discussed and compared. Definitions and important results are highlighted throughout to assist the reader in learning about this new, exciting and important area.
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Index Theory, Determinants and Torsion for Open Manifolds

Index Theory, Determinants and Torsion for Open Manifolds
Jurgen Eichhorn | 2009-01-01 00:00:00 | World Scientific Publishing Company | 352 | Mathematics
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.
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Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type (Oxford Lecture Series in Mathematics and Its Applications)

Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type (Oxford Lecture Series in Mathematics and Its Applications)
Juan Luis Vázquez | 2006-10-12 00:00:00 | Oxford University Press, USA | 248 | Mathematics
This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.

Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.

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Multivariate Statistics: A Vector Space Approach

Multivariate Statistics: A Vector Space Approach
Morris L. Eaton | 2007-12-31 00:00:00 | Inst of Mathematical Statistic | 512 | Mathematics
Reviews
Eaton provides a well-written treatment of multivariate analysis but with the geometric rather than the algebraic approach. For those who are better at geometry than algebra this approach that involves Euclidean spaces may be easier to understand than the algebraic approach that is common in many leading texts including Anderson. I find this approach to be a little more natural. It is much like the Hilbert space approach to stochastic processes where orthogonality equates to zero correlation or independence in the Gaussian case.

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Schaum's Outline of Theory and Problems of Graph Theory

Schaum's Outline of Theory and Problems of Graph Theory
McGraw-Hill | 1997-01-01 00:00:00 | McGraw-Hill | 288 | Mathematics
Student's love Schaum's--and this new guide will show you why! Graph Theory takes you straight to the heart of graphs. As you study along at your own pace, this study guide shows you step by step how to solve the kind of problems you're going to find on your exams. It gives you hundreds of completely worked problems with full solutions. Hundreds of additional problems let you test your skills, then check the ansers. So if you want to get a firm handle on graph theory--whether to ace your graph course, to supplement a course that uses graphs, or to build a solid basis for future study--there's no better tool than Schaum's. This guide makes a wonderful supplement to your class text, but it is so comprehensive that it can even be used alone as a complete graph theory independent study course!
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Determining Spectra in Quantum Theory

Determining Spectra in Quantum Theory
Michael Demuth and Chennai Mathematical Institute | 2005-01-01 00:00:00 | | 219 | Mathematics
The spectral theory of Schrodinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components a la Lebesgue decomposition. Key features and topics: * Well-developed exposition of criteria that are especially useful in determining the spectra of deterministic and random Schrodinger operators occurring in quantum theory * Systematically uses measures and their transforms (Fourier, Borel, wavelet) to present a unifying theme * Establishes criteria for identifying the spectrum * Examines a series of applications to show point spectrum and continuous spectrum in some models of random operators * Presents a series of spectral-theoretic results for the perturbed operators introduced in the earlier chapters with examples of localization and delocalization in the theory of disordered systems * Presents modern criteria (using wavelet transform, eigenfunction decay) that could be used to do spectral theory * Unique work in book form combining the presentation of the deterministic and random cases, which will serve as a platform for further research activities This concise unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials in particular. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.
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An Introduction to Mathematical Finance: Options and Other Topics, 1 edt.

An Introduction to Mathematical Finance: Options and Other Topics, 1 edt.
Sheldon M. Ross | 1999-01-01 00:00:00 | Cambridge University Press | 200 | Mathematics
An Introduction to Mathematical Finance: Options and Other Topics by Sheldon M. Ross (Author)
Publisher: Cambridge University Press (August 28, 1999) | ISBN-10: 0521770432 | PDF | 39 Mb | 200 pages

This mathematically elementary introduction to the theory of options pricing presents the BlackScholes theory of options as well as introducing such topics in finance as the time value of money, mean variance analysis, optimal portfolio selection, and the capital assets pricing model. The author assumes no prior knowledge of probability and presents all the necessary preliminary material simply and clearly. He explains the concept of arbitrage with examples, and then uses the arbitrage theorem, along with an approximation of geometric Brownian motion, to obtain a simple derivation of the Black-Scholes formula. In the later chapters he presents real price data indicating that this model is not always appropriate and shows how the model can be generalized to deal with such situations. No other text presents such topics in a mathematically accurate but accessible way. It will appeal to professional traders as well as undergraduates studying the basics of finance.
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Similarity Solutions of Nonlinear Partial Differential Equations (Research Notes in Mathematics Series)

Similarity Solutions of Nonlinear Partial Differential Equations (Research Notes in Mathematics Series)
Lawrence Dresner | 1900-01-01 00:00:00 | Longman Group United Kingdom | 136 | Mathematics

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Introduction to Lambda Trees

Introduction to Lambda Trees
Ian Chiswell | 2001-01-03 00:00:00 | World Scientific Publishing Company | 328 | Mathematics
Introductory text for mathematicians and research students in algebra and topology, introducing the fundamental concepts and theory of A-Trees, including the origins and history of the theory. Discusses connections with other theories such as model theory and R-Trees.

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Flows in Networks

Flows in Networks
L. R. Ford, D. R. Fulkerson | 1962-01-01 00:00:00 | Princeton Univ Press | 198 | Mathematics
In this classic book, first published in 1962, L. R. Ford, Jr., and D. R. Fulkerson set the foundation for the study of network flow problems. The models and algorithms introduced in Flows in Networks are used widely today in the fields of transportation systems, manufacturing, inventory planning, image processing, and Internet traffic.

The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction. Flows in Networks is rich with insights that remain relevant to current research in engineering, management, and other sciences. This landmark work belongs on the bookshelf of every researcher working with networks.

Review
[Flows in Networks] should . . . be of great value to the expert and a standard reference source for many years to come.
(H. J. Ryser Management Science )

The book stands as the principal work on network flow theory. Its authors have performed almost as great a service in preparing this volume for publication as they did in originally developing much of its contents.
(Ronald A. Howard Proceedings of the IEEE )

The book should be of value not only to those interested in linear programming but also those who are concerned with graph theory.
(Arthur Ziffer Physics Today )

The book is a natural meeting ground for persons interested in communication engineering or combinatorial mathematics.
(Journal of Data Management )

The book is a very welcome addition to the literature and should be of extreme value to anyone interested in operations research, communication theory, or combinatorial mathematics.
(A. Newhouse Computing Review )
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Real Variables with Basic Metric Space Topology

Real Variables with Basic Metric Space Topology
Robert B. Ash | 2009-05-21 00:00:00 | Dover Publications | 224 | Mathematics

Designed for a first course in real variables, this text encourages intuitive thinking and offers background for more advanced mathematical work. Topics include complex variables, measure theory, differential equations, functional analysis, and probability. Detailed solutions to the problems appear at the back of the book, making it ideal for independent study. 1993 edition.

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Business Math For Dummies (For Dummies (Business & Personal Finance))

Business Math For Dummies (For Dummies (Business & Personal Finance))
Jane Sterling, Mary | 2008-01-01 00:00:00 | For Dummies | 388 | Mathematics
Now, it is easier than ever before to understand complex mathematical concepts and formulas and how they relate to real-world business situations. All you have to do it apply the handy information you will find in Business Math For Dummies. Featuring practical practice problems to help you expand your skills, this book covers topics like using percents to calculate increases and decreases, applying basic algebra to solve proportions, and working with basic statistics to analyze raw data. Find solutions for finance and payroll applications, including reading financial statements, calculating wages and commissions, and strategic salary planning.
Navigate fractions, decimals, and percents in business and real estate transactions, and take fancy math skills to work. You’ll be able to read graphs and tables and apply statistics and data analysis. You’ll discover ways you can use math in finance and payroll investments, banking and payroll, goods and services, and business facilities and operations. You’ll learn how to calculate discounts and markup, use loans and credit, and understand the ins and outs of math for business facilities and operations. You’ll be the company math whiz in no time at all! Find out how to:
- Read graphs and tables
- Invest in the future
- Use loans and credit
- Navigate bank accounts, insurance, budgets, and payroll
- Calculate discounts and markup
- Measure properties and handle mortgages and loans
- Manage rental and commercial properties

Complete with lists of ten math shortcuts to do in meetings and drive your coworkers nuts and ten tips for reading annual reports, Business Math For Dummies is your one-stop guide to solving math problems in business situations.
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Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs)

Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs)
Kenji Ueno | 2003-06-20 00:00:00 | American Mathematical Society | 222 | Mathematics
Algebraic geometry plays an important role in several branches of science and technology. This is the last of three volumes by Kenji Ueno algebraic geometry. This, in together with Algebraic Geometry 1 and Algebraic Geometry 2, makes an excellent textbook for a course in algebraic geometry.

In this volume, the author goes beyond introductory notions and presents the theory of schemes and sheaves with the goal of studying the properties necessary for the full development of modern algebraic geometry. The main topics discussed in the book include dimension theory, flat and proper morphisms, regular schemes, smooth morphisms, completion, and Zariski's main theorem. Ueno also presents the theory of algebraic curves and their Jacobians and the relation between algebraic and analytic geometry, including Kodaira's Vanishing Theorem.

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CR Submanifolds of Complex Projective Space (Developments in Mathematics)

CR Submanifolds of Complex Projective Space (Developments in Mathematics)
Mirjana Djoric,Masafumi Okumura | 2009-10-28 00:00:00 | Springer | 176 | Mathematics

This book covers the necessary topics for learning the basic properties of complex manifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader to topics of current research and to more advanced publications.

The first half of the book provides an introduction to complex differential geometry and the properties of complex manifolds. The second half describes the properties of hypersurfaces of various complex spaces and CR submanifolds, with particular emphasis on CR submanifolds of maximal CR dimension.

Key features of CR Submanifolds of Complex Projective Space:

-Presents many recent developments and results in the study of CR submanifolds not previously published.

-Special topics explored include: the Kähler manifold, submersion and immersion, and the structure equations of a submanifold.

-Provides relevant techniques, results and their applications, and presents insight into the motivations and ideas behind the theory.

-Presents the fundamental definitions and results necessary for reaching the frontiers of research in this field.

This slim text is largely self-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced undergraduates, graduate students and researchers in differential geometry will benefit from this concise approach to an important topic.

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Growth Theory of Subharmonic Functions

Growth Theory of Subharmonic Functions
V. S. Azarin | 2008-01-01 00:00:00 | | 259 | Mathematics
In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables.

The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function.

All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.
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Mathematical Statistics (Springer)

Mathematical Statistics (Springer)
Jun Shao | 1999-01-01 00:00:00 | Springer | 545 | Mathematics
This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to the classical results that are typically covered in a textbook of a similar level, this book introduces some topics in modern statistical theory that have been developed in recent years, such as Markov chain Monte Carlo, quasi-likelihoods, empirical likelihoods, statistical functionals, generalized estimation equations, the jackknife, and the bootstrap.
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The Art of the Infinite: The Pleasures of Mathematics

The Art of the Infinite: The Pleasures of Mathematics
Robert Kaplan | 2004-01-01 00:00:00 | Oxford University Press | 336 | Mathematics
Here's human imagination at work. The flights of fancy the Kaplans show us are not about dragons and wizards, but about imaginary numbers, square roots, triangles, and infinite series.

I bought this book to mine for ideas to use in the notes I am writing to accompany the Third Edition of Geometry by Harold Jacobs, and I struck a rich lode. My professional interests made me look at material of a more technical nature, such as the proof of the theorem of Pappus. Pappus noticed that if you take six points A, B, and C on one side of an angle and a, b, and c on the other side of this angle and join each point to the two points labeled by *different* letters, then the three points of intersection of these six segments lie on a straight line. I knew this as a fact since my high school days, but it is not easy to give a proof that is reasonable at that level. The Kaplans have a beautiful explanation of this result, putting it in context and giving a gentle proof. Very nice indeed.

They have found just the right diagram or line of argument for many things I have seen before. Those of us who have suffered through the terrors of trigonometry will remember that there are some angle sum formulas, though we may not remember exactly what they are. The diagram at the top of page 187 tells you why these formulas are true and will make them unforgettable, if you decide to remember it. The path to this figure is made easy and natural in the book. What was new to me was the idea of adding a box around the tipped triangle --- suggested in the throw away line at the top of page 186. This gives us just what we need, neither too much nor too little.

One virtue of this book is that you can leaf through it and dive into the text wherever you see an interesting illustration or some idea you have been wondering about. The topics are mostly self-contained and there is always a nice story or bit of historical context to give you a sense of where you are and how this fits into the larger picture.

Buy this book, browse it, read it, and now and then get out your paper and pencil and puzzle through whatever tickles your fancy. This book is not just *about* mathematics, it gives you the real stuff.
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Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics (Dover Books on Physics)

Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics (Dover Books on Physics)
N. I. Muskhelishvili | 2008-05-19 00:00:00 | Dover Publications | 464 | Mathematics

This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Intended for graduate students and professionals, its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other areas. 1992 edition.

Reviews
To be honest, I have not gone into a thourough and complete reading of the texbook, but I picked up several and sparse subjects in order to get a better understanding about some issues relating linear transport theory. But also in a limited use like that I cannot help recognizing that, even after half a century, this book remains a milestone in integral equations and boundary problems. Deep, clear, and available also to ready-to-use requests, it may seem a bit out of fashion for the light use of geometrical formalism, but also this latter feature makes it to be very strict to the point, if you need to strengthen the theoretical building of numerical calcualtions to be performed.
Reviews
Eventhough this text dates from 1946 it is difficult to find a more complete and accurate discussion on the boundary value problems raised up by the Cauchy integral.

Being one of the most outstanding pupils of the Vekua school (as Gakhov), Muskhelishvili explores every single particular case of the classical boundary value problems of complex analysis giving a complete solution to each, sometimes employing highly ingenious arguments. It includes also several applications.

As in the case of the book by Gakhov (also reviewed by myself) I wonder why this material is not standard in usual complex analysis courses, at least in the American continent. When you read this kind of books you realize that all your previous knowledge on the subject was almost useless, to say the least. My suggestion for the material to be mastered by complex analysis students is: First read an introductory classic like Ahlfors, Lang, or Markushevitch, and then proceed to Kress (Linear Integral Equations), Gakhov, and Muskhelishvili. Then you will be ready for the next step: Hypercomplex analysis.

The contents of the book are: The Hölder condition; Integrals of the Cauchy type; Some corollaries on Cauchy integrals; Cauchy integrals near the ends of the line of integration; The Hilbert and Riemann-Hilbert boundary problems; Singular integral equations with Cauchy kernels (case of contours); The Dirichlet problem; Various representations of holomorphic functions by Cauchy and analogous integrals; Solution of the generalized Riemann-Hilbert-Poincaré problem; The Hilbert problem in the case of arcs or discontinuous boundary conditions; Inversion formulae for arcs; Effective solution of some boundary problems of the theory of harmonic functions; Effective solution of the principal problems of the static theory of elasticity for the half-plane, circle and analogous regions; Singular integral equations for the case of arcs and continuous coefficients; Singular integral equations in the case of discontinuous coefficients; Application to the Dirichlet problem and similar problems; Solution of integro-differential equations of the theory of aircraft wings of finite span; The Hilbert problem for several unknown functions; Systems of singular integral equations with Cauchy type kernels and some supplements; + 3 appendices.

Includes full motivation for each topic, historical notes, and extensive references.

Please read some of my other reviews (just click on my name above).

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