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A First Course in Modular Forms
This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include • elliptic curves as complex tori and as algebraic curves, • modular curves as Riemann surfaces and as algebraic curves, • Hecke operators and Atkin–Lehner theory, • Hecke eigenforms and their arithmetic properties, • the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, • elliptic and modular curves modulo p and the Eichler–Shimura Relation, • the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.
A First Course in Harmonic Analysis
This book is a primer in harmonic analysis using an elementary approach. Its first aim is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Secondly, it makes the reader aware of the fact that both, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. There are two new chapters in this new edition. One on distributions will complete the set of real variable methods introduced in the first part. The other on the Heisenberg Group provides an example of a group that is neither compact nor abelian, yet is simple enough to easily deduce the Plancherel Theorem.
A First Course in Differential Equations
This text is designed for the standard post-calculus course in elementary differential equations. It is a brief, one-semester treatment of the basic ideas, models, and solution methods. The book, which serves as an alternative to existing texts for instructors who want more concise coverage, emphasizes graphical, analytical, and numerical approaches, and is written with clear language in a user-friendly format. It provides students with the tools to continue on to the next level in applying differential equations to problems in engineering, science, and applied mathematics.
A Course in Enumeration
This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject.
A Course in Derivative Securities : Introduction to Theory and Computation
This book aims at a middle ground between the introductory books on derivative securities and those that provide advanced mathematical treatments. It is written for mathematically capable students who have not necessarily had prior exposure to probability theory, stochastic calculus, or computer programming. It provides derivations of pricing and hedging formulas (using the probabilistic change of numeraire technique) for standard options, exchange options, options on forwards and futures, quanto options, exotic options, caps, floors and swaptions, as well as VBA code implementing the formulas. It also contains an introduction to Monte Carlo, binomial models, and finite-difference methods.
A Course in Credibility Theory and its Applications
It covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. The first four chapters contain plenty of material The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. The models are worked out in detail (including the estimation of structural parameters) so that they can immediately be applied in practice. Most exercises are based on real insurance data and real situations from practice and many of them have the characteristics of a case study. The extension to practical problems arising from the general area of finance is often quite straightforward. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.for a first course on Credibility.
A Course in Calculus and Real Analysis
This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. It highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis.
A Concise Introduction to Mathematical Logic
This book is unique in that it is more concise than most others; the material is treated in a streamlined fashion. This allows the lecturer to select the material for a one-semester course on a topic more easily. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. Chapter 3 is partly of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and related subjects. The other chapters contain material on logic programming for computer scientists, model theory, recursion theory, Gödel's Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed where appropriate.
A Comprehensible Universe : The Interplay of Science and Theology
Why is our world comprehensible? This question seems so trivial that few people have dared to ask it. In this book we explore the deep roots of the mystery of rationality. The inquiry into the rationality of the world began over two-and-a-half-thousand years ago, when a few courageous people tried to understand the world with the help of reason alone, rejecting the comforting fabric of myth and legend.
A companion to astronomy and astrophysics : Chronology and glossary with data tables
Astronomy and Astrophysics is a comprehensive, fundamental, up-to-date reference book. It is filled with vital information and basic facts for amateur astronomers and professional astrophysicists, and for anyone interested in the Universe, from the Earth and other planets to the stars, galaxies and beyond. Although serious and thorough, the language, and ideas will attract the general reader, as well as students and professionals. Astronomy and Astrophysics consists of two main parts, a Timeline and a Dictionary. The Timeline is a concise history, arranged chronologically, which provides the complete story of cosmic discovery from early Chinese and Greek astronomy to the latest findings of modern astrophysics and robotic spacecraft.
A Common Consolidated Corporate Tax Base for Europe = Eine einheitliche Körperschaftsteuerbemessungsgrundlage für Europa
This book contains the proceedings of the International Tax Conference on the c- th th mon consolidated corporate tax base (CCCTB) that was held in Berlin Three panels of tax experts evaluated the common tax base with respect to structural elements, consolidation, allocation, international aspects and administration.
A Climate of Justice : An Ethical Foundation for Environmentalism
This book helps readers combine history, politics, and ethics to address the most pressing problem facing the world today: environmental survival. In A Climate of Justice, Marvin Brown connects the environmental crisis to basic questions of economic, social, and racial justice. Brown shows how our current social climate maintains systemic injustices, and he uncovers resources for change through a civic ethics of repair and reciprocity.
A Buddhist Approach to International Relations : Radical Interdependence
This book. Many scholars have wondered if a non-Western theory of international politics founded on different premises, be it from Asia or from the “Global South,” could release international relations from the grip of a Western, “Westphalian” model.
A Biomass Future for the North American Great Plains : Toward Sustainable Land Use and Mitigation of Greenhouse Warming
The Great Plains of North America is a major global breadbasket but its agriculture is stressed by drought, heat spells, damaging winds, soil erosion and declining ground water resources. This book explores the possibility that the ecology and economy of the Plains region (and similar regions) would benefit from the introduction of perennial biomass crops. Biomass production and processing on the Plains (possibly aided by genetic engineering) would partially restore a perennial vegetative cover and create new employment opportunities. Biomass also offers a means of reducing fossil fuel use, providing fuel to local power plants and a feedstock for production of cellulosic ethanol, a gasoline substitute. Interest in biofuels is growing rapidly in public, political and business circles with rising fossil fuel prices and because of a growing recognition of the need for energy independence in petroleum importing countries.
A Benchmark Approach to Quantitative Finance
The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.
A Basic Course on Probability Theory
The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. Theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference.
3D-Position Tracking and Control for All-Terrain Robots
Rough terrain robotics is a fast evolving field of research and a lot of effort is deployed towards enabling a greater level of autonomy for outdoor vehicles. This book demonstrates how the accuracy of 3D position tracking can be improved by considering rover locomotion in rough terrain as a holistic problem. In this work, a mechanical structure allowing smooth motion across obstacles with limited wheel slip is used. In particular, it enables the use of odometry and inertial sensors to improve the position estimation in rough terrain. A method for computing 3D motion increments based on the wheel encoders and chassis state sensors is developed. The algorithm runs online and can be adapted to any kind of passive wheeled rover. Finally, sensor fusion using 3D-Odometry, inertial sensors and visual motion estimation based on stereovision is presented. The experimental results demonstrate how each sensor contributes to increase the accuracy and robustness of the 3D position estimation.
25 Years of Transformations of Higher Education Systems in Post-Soviet Countries : Reform and Continuity
A result of the first ever study of the transformations of the higher education institutional landscape in fifteen former USSR countries after the dissolution of the Soviet Union in 1991. It explores how the single Soviet model that developed across the vast and diverse territory of the Soviet Union over several decades has evolved into fifteen unique national systems, systems that have responded to national and global developments while still bearing some traces of the past. The book is distinctive as it presents a comprehensive analysis of the reforms and transformations in the region in the last 25 years; and it focuses on institutional landscape through the evolution of the institutional types established and developed in Pre-Soviet, Soviet and Post-Soviet time. It also embraces all fifteen countries of the former USSR, and provides a comparative analysis of transformations of institutional landscape across Post-Soviet systems.
104 Number Theory Problems : From the Training of the USA IMO Team
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
