Statistical Properties of Deterministic Systems

rgodic theory is a mathematical subject that studies the statistical proper- ties of deterministic dynamical systems. It is a combination of several branches of pure mathematics, such as measure theory, functional analysis, topology, and geometry, and it also has applications in a variety of fields in science and engineering, as a branch of applied mathematics. In the past decades, the ergodic …

Planning with Complexity

The book you have in your hand culminates a journey that began over forty years ago (though time may show it is merely a way station). The journey mirrors developments in planning and policy making during that time – the effort to integrate theory and practice, the search for more effective ways to conduct policy, and the growing role of collaboration. This journey began in 1967 when author I…

Random Walks, Boundaries and Spectra

This book contains the joint proceedings of the workshop on Boundaries that took place in Graz, from June 29–July 3, and the Alp-Workshop that was held immediately afterwards in Sankt Kathrein am Offenegg, on the weekend July 4–5, 2009

Positive Polynomials and Sums of Squares

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Q-Squared

I am deeply grateful to Ravi Kanbur, who initiated the Q-Squared initiative, and invited me to join on. The momentum in favour of mixed method analysis of poverty over the past decade has been highly influenced by Ravi’s efforts. In the absence of such, this book would not exist. I am also extremely appreciative of the support provided by the International Development Research Centre (IDRC),…

Spectral Analysis on Graph-Like Spaces

In this monograph, we analyse thin tubular structures, so-called “graph-like spaces”, and their natural limits, when the radius of a graph-like space tends to zero. The limit space is typically a metric graph, i.e. a graph, where each edge is associated a length, and therefore, the space turns into a one-dimensional manifold with singularities at the vertices. On both, the graph-like spaces…

Rigidity and Symmetry

The thematic program on Discrete Geometry and Applications took place at the Fields Institute for Research in Mathematical Sciences in Toronto between July 1 and December 31, 2011. The papers included in this book are based on some research conducted during the semester and on some of the lectures there, in particular those related to the part of the program under the heading “Rigidity and Sy…

Statistical Physics

This book is essentially based on the lecture course on “Statistical Physics”, which was taught by the author at the physical faculty of the Ural State University in Ekater- inburg since 1992. This course was intended for all physics students, not especially for those specializing in theoretical physics. In this sense the material presented here contains the necessary minimum of knowledge o…

Modern Statistics

There are two general goals in this book. Assuming the reader has had no prior training in statistics, the first is to provide a graduate-level introduction to basic, routinely used statistical techniques relevant to the social and behavioral sciences. As can be seen from the Table of Contents, a wide range of topics is covered. Included is a nontechnical description of three major insights reg…

Blind Equalization and System Identification

Discrete-time signal processing has appeared to be one of the major momenta to the advances of science and engineering over the past several decades be- cause of the rapid progress of digital and mixed-signal integrated circuits in processing speed, functionality, and cost effectiveness. In many science and engineering applications, the signals of interest are distorted by an unknown physical s…

Computational Statistics Handbook with MATLAB

Statistics is concerned with the science of uncertainty and can help the scientist deal with these questions. Many classical methods (regression, hypothesis testing, parameter estimation, confidence intervals, etc.) of statistics developed over the last century are familiar to scientists and are widely used in many disciplines [Efron and Tibshirani, 1991]. Now, what do we mean by computational…

Calculus Light

The first question we may face is: “Another Calculus book?” We feel that the an- swer is quite simple. As long as students find mathematics and particularly calcu- lus a scary subject, as long as the failure rate in mathematics is higher than in all other subjects, except maybe among students who take it as a major in College and as long as a large majority of the people mistakenly believe …

Applied and Numerical Harmonic Analysis

This book is concerned with signal analysis in its broadest sense. Usually, signals are modeled as functions in suitable spaces such as L2, the space of square integrable functions, or Sobolev spaces. Signals might be given explicitly as, for example, in image analysis or implicitly, as solutions of operator equations. In either case, the problem of interest is to analyze and process these sign…

DVANCED ENGINEERING MATHEMATICS

This book springs from class notes, I developed for a course called Engineer- ing Analysis which I have taught every other fall semester since 1983 at the University of Akron. The course is targeted to students who are beginning graduate study in engineering. The students enrolled are first- and second-year graduate students in the Department of Mechanical Engineering, although I have taught st…

Advances in Algebraic Quantum Field Theory

Relativistic quantum field theory was conceived in the late 1920s as a framework unifying the two fundamental theories that revolutionized physics in the twentieth century: Quantum Mechanics and the Special Theory of Relativity. Algebraic Quantum Field Theory (AQFT) is relativistic quantum field theory regarded from a certain perspective, emphasizing localization of observables in space and tim…

A Brief History of Numbers

This book tells the story of the development of the idea of number since the days of the Pythagoreans and up until the turn of the twentieth century. The latter is more or less the time when currently prevailing conceptions about numbers reached their actual state, for all of their complexity (or perhaps we should rather say, for all of their simplicity). This is not the first book to tell a si…

Symplectic Methods in Harmonic Analysis and in Mathematical Physics

Harmonic analysis is one of the most active and fastest growing parts of both pure and applied mathematics. It has gone far beyond its primary goal, which was to study the representation of functions or signals as superpositions of trigonometric functions (Fourier series). The interest in harmonic analysis has always been great because of the wealth of its applications, and it plays nowadays a …

Statistical Inference

Statistical distances have two very important uses in statistical analysis. Firstly, they can be applied naturally to the case of parametric statistical inference. The idea of minimum distance estimation has been around for a while and there are many nice properties that the minimum distance estimators enjoy. Minimum distance estimation was pioneered by Wolfowitz in the 1950s (1952, 1953, 195…

The Mathematics of Networks of Linear Systems

In this introductory chapter, the subject of the book is explained in more detail by focusing on two central issues of the control of networks: open-loop control of interconnected systems and synchronization. While the first topic emphasizes the computational aspects involved in controlling interconnected systems, the second theme of synchronization discusses the impact of couplings on the shap…

Algorithms

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Algorithms

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Mathematical Models in Portfolio Analysis

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1st Edition

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9788740303704

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Mathematical Models in Portfolio Analysis

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Mathematics in A level assessments

In the UK fewer students engage with mathematics after the age of 16 than do their peers in other countries. This is a serious problem and the Foundation shares the Secretary of State’s view that: “…within a decade the vast majority of pupils [should be] studying maths right through to the age of 18.”1 One way of addressing this issue is to consider what kinds of free-standing mathe…

Natural Computing Algorithms

Although there is no unique definition of the term natural computing, most commonly the field is considered to consist of three main strands of enquiry: see Fig. 1.1. The first strand concerns the use of natural materials and phenomena for computational purposes such as DNA and molecular computing (computing in vivo); the second strand concerns the application of computer simulations to replica…

Mathematical Modeling and Optimization of Complex Structures

A Fluid-Structure Interaction model is studied for aortic flow, based on Koiter’s shell model for the structure, Navier–Stokes equations for the fluid and transpiration for the coupling. It accounts for wall deformation while yet working on a fixed geometry. The model is established first. Then a numerical approximation is proposed and some tests are given. The model is also used for optima…

Statistics

Statisticians refer to an entire group that is being studied as a population. Each member of the population is called a unit. In this example, the population is all Galapagos Tortoises, and the units are the individual tortoises. It is not necessary for a population or the units to be living things, like tortoises or people. For example, an airline employee could be studying the population o…

Introduction to Complex Numbers

This workbook is designed to be used in conjunction with the author’s free online video tutorials. Inside this workbook each chapter is divided into learning modules (subsections), each having its own dedicated video tutorial. View the online video via the hyperlink located at the top of the page of each learning module, with workbook and paper or tablet at the ready. Or click on the Introdu…

Improving Student Learning in Mathematics and Science: The Role of National S…

In Spring 1997, the National Education Goals Panel (NEGP) requested a report on standards-based reform from the Center for Science, Mathematics, and Engineering Education (the Center) of the National Research Council (NRC) and a report from the National Council of Teachers of Mathematics (NCTM). The request stemmed from NEGP's belief that the organizations that developed the national standards …

Fundamental of Algebra

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1st Edtion

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978-0-8215-8207-7

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1-473

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Fundamental of Algebra

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Introduction to Complex Numbers

This workbook is designed to be used in conjunction with the author’s free online video tutorials. Inside this workbook each chapter is divided into learning modules (subsections), each having its own dedicated video tutorial. View the online video via the hyperlink located at the top of the page of each learning module, with workbook and paper or tablet at the ready. Or click on the Int…

Discrete Mathematics for Computer Science Some Notes

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