Bücher der Reihe Springer Undergraduate Texts in Mathematics and Technology

Calculus with Vectors

This text introduces upper division undergraduate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles. Monte Carlo is the uniquely appropriate tool for modeling the random factors that drive financial markets and simulating their implications.The Monte Carlo method is introduced early and it is used in conjunction with the geometric Brownian motion model (GBM) to illustrate and analyze the topics covered in the remainder of the text. Placing focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications. Coverage includes investment science, mean-variance portfolio theory, option pricing principles, exotic options, option trading strategies, jump diffusion and exponential Levy alternative models, and the Kelly criterion for maximizing investment growth.Novel features:inclusion of both portfolio theory and contingent claim analysis in a single textpricing methodology for exotic optionsexpectation analysis of option trading strategiespricing models that transcend the Black-Scholes frameworkoptimizing investment allocationsconcepts thoroughly explored through numerous simulation exercisesnumerous worked examples and illustrationsThe mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. Also by the author: (with F. Mendivil) Explorations in Monte Carlo, (c)2009, ISBN: 978-0-387-87836-2; (with J. Herod) Mathematical Biology: An Introduction with Maple and Matlab, Second edition, (c)2009, ISBN: 978-0-387-70983-3.

This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony's problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

He has held academic positions at University of Alaska Fairbanks, Ball State University, and Florida State University.

This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets;

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets;

This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon's information theory, discussing the fundamental concepts and indispensable results of Shannon's mathematical theory of communications.

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world.

This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines.

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications.

This book introduces the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles.

This book starts with concrete topics and applications based on everyday experiences that naturally lead students to algebraic questions and concepts. The down-to-earth presentation is accessible to an audience with no previous knowledge of the subject.

This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow.

Modeling and Simulation

This book provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It features many examples and exercises.

Rather than being a 'how to' manual for making computations, this book places primary importance on the mathematics. It covers number theory, calculus of one and several variables, linear algebra, and visualization and interactive geometric computation.

An essential read for mathematicians, this volume looks beyond the syntax and semantics of Mathematica and other programs. It focuses on why they are necessary tools for anyone who engages in mathematics, as well as showing how to create better proofs.

Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A.

The authors present elegant mathematical concepts such as Markov chains, function iteration and simple groups, and develop these concepts, applying them to important practical problems such as web-navigation, data compression and error correcting codes.

The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering.

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization.

Structured in a problem-solution format, this undergraduate text motivates the student to think through the programming process. New to the second edition are added chapters on suffix trees, games and strategies, and Huffman coding as well as an appendix illustrating the ease of conversion from Pascal to C.

This book offers a balanced presentation of Optimization, focusing on theory and including algorithms and real-world examples. Detailed examples and counter-examples are provided - with exercises, solutions and helpful hints, and Matlab/Maple supplements.

This book offers a simple, no-frills approach to differential equations, with some 400 exercises that can be solved without a calculating device. Each worked example includes Mathematica commands for checking results and generating graphical representations.

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences.