Mathematical background

This topic reviews the basic mathematics required in this course: A justification for a mathematical framework, the ceiling and floor functions, L’Hôpital’s rule, logarithms, arithmetic and other polynomial series, geometric series, recurrence relations, weighted averages, combinations.
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Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "realworld" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.
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Solve Two of the Toughest Problems When Preparing for the Stockbroker’s Exam Those wishing to become licensed as stockbrokers must pass the series 7 examination. This exam, known officially as the General Securities Registered Representative Examination, is very rigorous. Traditionally, students without a financial background have a difficult time with the mathematical calculations peculiar to the world of stocks, bonds, and options. Many are also relatively unfa miliar with proper use of the calculator and thus are dou bly hampered in their efforts to become registered.
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The aim of this book is to bring students of economics and finance who have only an introductory background in mathematics up to a quite advanced level in the subject, thus preparing them for the core mathematical demands of econometrics, economic theory, quantitative finance and mathematical economics, which they are likely to encounter in their finalyear courses and beyond. The level of the book will also be useful for those embarking on the first year of their graduate studies in Business, Economics or Finance.
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Based on a streamlined presentation of the author’s successful work, An Introduction to Frames and Riesz Bases, this book develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The book presents basic results in an accessible way and includes extensive exercises.
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This is the third volume in the series “Tutorial in Mathematical Biosciences”. These lectures are based on material which was presented in tutorials or developed by visitors and postdoctoral fellows of the Mathematical Biosciences Institute (MBI), at The Ohio State University. The aim of this series is to introduce graduate students and researchers with just a little background in either mathematics or biology to mathematical modeling of biological processes. The first volume was devoted to mathematical neuroscience, which was the focus of the MBI program in 2002–2003.
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We have attempted to explain the concepts which have been used and developed to model the stochastic dynamics of natural and biological systems. While the theory of stochastic differential equations and stochastic processes provide an attractive framework with an intuitive appeal to many problems with naturally induced variations, the solutions to such models are an active area of research, which is in its infancy. Therefore, this book should provide a large number of areas to research further.
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This thesis will attempt to describe in detail the concepts of digital signatures and the related background issues. We will begin with a general introduction to cryptography and digital signatures and follow with an overview of the requisite math involved in cryptographic applications.
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This chapter collects some fundamental mathematical concepts that we will use in our study of probability and statistics. Most of these concepts should seem familiar, although our presentation of them may be a bit more formal than you have previously encountered. This formalism will be quite useful as we study probability, but it will tend to recede into the background as we progress to the study of statistics.
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The purpose of this text is to provide the basis for an upperlevel undergraduate or graduate course over one or two semesters, covering basic concepts and examples of fluid mechanics with particular applications in the natural environment. The book is designed to meet a dual purpose, providing an advanced fundamental background in the fluid mechanics of environmental systems and also applying fluid mechanics principles to a variety of environmental issues.
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This text is aimed at students of economics and the closely related disciplines of accountancy and business, and provides examples and problems relevant to those subjects, using real data where possible. The book is at an elementary level and requires no prior knowledge of statistics, nor advanced mathematics. For those with a weak mathematical background and in need of some revision, some recommended texts are given at the end of this preface.
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The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.
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This new text, intended for the senior undergraduate finite element course in mechanical, civil and aerospace engineering departments, gives students a solid, practical understanding of the principles of the finite element method within a variety of engineering applications. Hutton discusses basic theory of the finite element method while avoiding variational calculus, instead focusing upon the engineering mechanics and mathematical background that may be expected of senior engineering students.
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The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers, Prentice Hall, 1986. This book began as a second edition to the earlier book and the basic goal remains unchanged  to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suce to get the basic ideas across....
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The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization …).
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Ato Z of Mathematicians contains the fascinating biographies of 150 mathematicians: men and women from a variety of cultures, time periods, and socioeconomic backgrounds, all of whom have substantially influenced the history of mathematics. Some made numerous discoveries during a lifetime of creative work; others made a single contribution. The great Carl Gauss (1777–1855) developed the statistical method of least squares and discovered countless theorems in algebra, geometry, and analysis.
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This book is designed for a onesemester course on Nano and Microelectromechanical Systems or Nano and Microengineering. A typical background needed includes calculus, electromagnetics, and physics. The purpose of this book is to bring together in one place the various methods, techniques, and technologies that students and engineers need in solving a wide array of engineering problems in formulation, modeling, analysis, design, and optimization of highperformance microelectromechanical and nanoelectromechanical systems (MEMS and NEMS).
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The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers, Prentice Hall, 1986. This book began as a second edition to the earlier book and the basic goal remains unchanged — to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reflects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suffice to get the basic ideas across.......
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This book is designed for students and researchers who want to develop professional skill in modern quantitative applications in nance. The Center for Applied Statistics and Economics (CASE) course at HumboldtUniversitat zu Berlin that forms the basis for this book is oered to interested students who have had some experience with probability, statistics and software applications but have not had advanced courses in mathematical nance.
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Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the NavierStokes equations for incompressible viscous fluids.
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