I have found many thousands more readers than I ever looked for. I have no right to say to these, You shall not ?nd fault with my art, or fall asleep over my pages; but I ask you to believe that this person writing strives to tell the truth. If there is not that, there is nothing. William Makepeace Thackeray, The History of Pendennis This is a monograph/textbook on the probabilistic aspects of gambling, intended for those already familiar with probability at the post-calculus, p- measure-theory level. Gambling motivated much of the early development of probability the- 1 ory (David 1962). Indeed, some of the earliest works on probability include Girolamo Cardano's [1501-1576] Liber de Ludo Aleae (The Book on Games of Chance, written c. 1565, published 1663), Christiaan Huygens's [1629- 1695] "De ratiociniis in ludo aleae" ("On reckoning in games of chance," 1657), Jacob Bernoulli's [1654-1705]Ars Conjectandi (The Art of Conject- ing, written c. 1690, published 1713), Pierre R' emond de Montmort's [1678- 1719] Essay d'analyse sur les jeux de hasard (Analytical Essay on Games of Chance, 1708, 1713), and Abraham De Moivre's [1667-1754]TheDoctrineof Chances (1718, 1738, 1756). Gambling also had a major in?uence on 20- century probability theory, as it provided the motivation for the concept of a martingale.

This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics.

The book gives a comprehensive account of a variety of topics including - Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems; Advances on collocation based numerical methods for Ordinary Differential Equations and Volterra Integral Equations; Basic Methods for Computing Special Functions, Melt Spinning: Optimal Control and Stability Issues; Brief survey on the CP methods for the Schrodinger equation; Symplectic Partitioned Runge-Kutta methods for the numerical integration of periodic and oscillatory problems.

"Recent Advances in Computational and Applied Mathematics" is aimed at advanced undergraduates and researchers who are working in these fast moving fields.

Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commentedPiola s work and compared it to modern theories in mechanics in order to stress Piola s impact on modern science and proofs that he has set milestones in applied mathematics.
This book presents Piola's original Italian text together with ist translations and their comments. It shows impressively that Gabrio Piola s work must still be regarded as a modern theory."

This English version of Ruslan L. Stratonovich's Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.

The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author's past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

These lecture notes are dedicated to the most recent theoretical applications of Black Hole solutions in high-energy physics. The main motivation of this volume is to present the latest black hole backgrounds that are relevant for gauge/gravity correspondence. Leading scientists in the field explain effective techniques for finding singular and cosmological solutions embedded in gauged supergravity, shedding light on underlying properties and symmetries. Starting from a basic level, the mathematical structures underlying black holes and cosmologies are revealed, helping the reader grasp the connection between theoretical approaches and physical observations with insights into possible future developments from both a theoretical and experimental point of view. The topics covered in this volume are based on lectures delivered during the "Theoretical Frontiers in Black Holes and Cosmology" school, held in Natal in June 2015.

The book shows a very original organization addressing in a non traditional way, but with a systematic approach, to who has an interest in using mathematics in the social sciences.

The book is divided in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D'Amore which considers the relationship between mathematics and art.

The title of the book "Mathematics and Society" was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities.

The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project "Creative Cities Network" of UNESCO).

This contributed volume presents computational models of diabetes that quantify the dynamic interrelationships among key physiological variables implicated in the underlying physiology under a variety of metabolic and behavioral conditions. These variables comprise for example blood glucose concentration and various hormones such as insulin, glucagon, epinephrine, norepinephrine as well as cortisol. The presented models provide a powerful diagnostic tool but may also enable treatment via long-term glucose regulation in diabetics through closed-look model-reference control using frequent insulin infusions, which are administered by implanted programmable micro-pumps. This research volume aims at presenting state-of-the-art research on this subject and demonstrating the potential applications of modeling to the diagnosis and treatment of diabetes. The target audience primarily comprises research and experts in the field but the book may also be beneficial for graduate students.

The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature.

The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functional analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods and discusses the quantization of factorization algebras. The book is primarily intended for pure mathematicians (and in particular graduate students) who would like to learn about the mathematics of quantum field theory.

Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.

The future of oncology seems to lie in Molecular Medicine (MM). MM is a new science based on three pillars. Two of them are evident in its very name and are well known: medical science and molecular biology. However, there is a general unawareness that MM is firmly based on a third, and equally important, pillar: Systems Biomedicine. Currently, this term denotes multilevel, hierarchical models integrating key factors at the molecular, cellular, tissue, through phenotype levels, analyzed to reveal the global behavior of the biological process under consideration. It becomes increasingly evident that the tools to construct such complex models include, not only bioinformatics and modern applied statistics, as is unanimously agreed, but also other interdisciplinary fields of science, notably, Mathematical Oncology, Systems Biology and Theoretical Biophysics.

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

The model-based investigation of motions of anthropomorphic systems is an important interdisciplinary research topic involving specialists from many fields such as Robotics, Biomechanics, Physiology, Orthopedics, Psychology, Neurosciences, Sports, Computer Graphics and Applied Mathematics. This book presents a study of basic locomotion forms such as walking and running is of particular interest due to the high demand on dynamic coordination, actuator efficiency and balance control. Mathematical models and numerical simulation and optimization techniques are explained, in combination with experimental data, which can help to better understand the basic underlying mechanisms of these motions and to improve them. Example topics treated in this book are * Modeling techniques for anthropomorphic bipedal walking systems * Optimized walking motions for different objective functions * Identification of objective functions from measurements * Simulation and optimization approaches for humanoid robots * Biologically inspired control algorithms for bipedal walking * Generation and deformation of natural walking in computer graphics * Imitation of human motions on humanoids * Emotional body language during walking * Simulation of biologically inspired actuators for bipedal walking machines * Modeling and simulation techniques for the development of prostheses * Functional electrical stimulation of walking.

Superstring theory is a promising theory which can potentially unify all the forces and the matters in particle physics. A new multi-dimensional object which is called "D-brane" was found. It drastically changed our perspective of a unified world. We may live on membrane-like hypersurfaces in higher dimensions ("braneworld scenario"), or we can create blackholes at particle accelarators, or the dynamics of quarks is shown to be equivalent to the higher dimensional gravity theory. All these scenarios are explained in this book with plain words but with little use of equations and with many figures. The book starts with a summary of long-standing problems in elementary particle physics and explains the D-branes and many applications of them. It ends with future roads for a unified ultimate theory of our world.

In Computed Tomography: Algorithms, Insight, and Just Enough Theory, readers will learn about the fundamental computational methods used for image reconstruction in computed tomography (CT). Unique in its emphasis on the interplay of modeling, computing, and algorithm development, the book presents underlying mathematical models for motivating and deriving the basic principles of CT reconstruction methods, along with insight into their advantages, limitations, and computational aspects. Computed Tomography: Algorithms, Insight, and Just Enough Theory: Develops the mathematical and computational aspects of three main classes of reconstruction methods. Emphasizes the link between CT and numerical methods, which is rarely found in current literature. Describes the effects of incomplete data using both microlocal analysis and the singular value decomposition (SVD). Contains computer exercises using MATLAB that allow readers to experiment with the algorithms and make the book suitable for teaching and self-study. This book is aimed at students, researchers, and practitioners. As a textbook, it is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps.

The text examines the maps positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout."

Quadratic equations, Pythagoras' theorem, imaginary numbers, and pi - you may remember studying these at school, but did anyone ever explain why? Never fear - bestselling science writer, and your new favourite maths teacher, Michael Brooks, is here to help. In The Maths That Made Us, Brooks reminds us of the wonders of numbers: how they enabled explorers to travel far across the seas and astronomers to map the heavens; how they won wars and halted the HIV epidemic; how they are responsible for the design of your home and almost everything in it, down to the smartphone in your pocket. His clear explanations of the maths that built our world, along with stories about where it came from and how it shaped human history, will engage and delight. From ancient Egyptian priests to the Apollo astronauts, and Babylonian tax collectors to juggling robots, join Brooks and his extraordinarily eccentric cast of characters in discovering how maths made us who we are today.

As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, on its five principles, i. e. : the inertia, the forces action, the action and reaction, the parallelogram and the initial conditions principle, respectively. Other models, e. g. , the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler's laws brilliantly verify this model in case of velocities much smaller than the light velocity in vacuum. The non-classical models are relativistic and quantic. Mechanics has as object of study mechanical systems. The first volume of this book dealt with particle dynamics. The present one deals with discrete mechanical systems for particles in a number greater than the unity, as well as with continuous mechanical systems. We put in evidence the difference between these models, as well as the specificity of the corresponding studies; the generality of the proofs and of the corresponding computations yields a common form of the obtained mechanical results for both discrete and continuous systems. We mention the thoroughness by which the dynamics of the rigid solid with a fixed point has been presented. The discrete or continuous mechanical systems can be non-deformable (e. g.

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog's theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz's rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.

This book contains selected papers of Jurg Frohlich, one of the most outstanding mathematical physicists of our time, on the subject of statistical mechanics. In an extensive introduction, Jurg Frohlich sets his results into a wider context and gives precious information on the genesis of his work from both a historical and a methodological perspective. It is not only an overview of current and future research directions in statistical mechanics, but also relates this subject with other branches of contemporary physics and mathematics.

All papers in this collection bear Jurg Frohlich s signature in terms of a delicate balance between mathematical rigor and physical significance. They cover thirty years of his work on statistical physics, ranging from the most basic foundational questions in atomism and thermodynamics via the description of phase transitions and critical phenomena up to disordered systems and the study of many-body systems in condensed matter physics, including the quantum Hall effect. The wide range of topics covered in this compendium reflects the breadth of Jurg Frohlich s interests, and the last chapters reveal an outlook towards some of his more recent research areas."

This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included.

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "Mathematical Methods for Extracting Quantifiable Information from Complex Systems." This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Classical Mechanics teaches readers how to solve physics problems; in other words, how to put math and physics together to obtain a numerical or algebraic result and then interpret these results physically. These skills are important and will be needed in more advanced science and engineering courses. However, more important than developing problem-solving skills and physical-interpretation skills, the main purpose of this multi-volume series is to survey the basic concepts of classical mechanics and to provide the reader with a solid understanding of the foundational content knowledge of classical mechanics. Classical Mechanics: The Universal Law of Gravitation focuses on the notion that forces act through their associated fields, which is first introduced when discussing Newton's universal law of gravitation. A huge conceptual leap is required from the reader: an object can cause another object to move without even touching it. This is a difficult concept to reconcile with our everyday experiences but it makes perfect sense when we realize that is exactly how the Earth acts on us. Gravity is able to pull on us even though we are not in direct contact with the Earth. Also, the concept of super-position (and when it is applicable) is introduced. Super-position is crucial to the development of problem-solving skills so it will be illustrated in a number of example problems.

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more.

The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.

The book benefits a broad audience of researchers and advanced students.