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Mathematics 2006 - Mathematical Modeling

Elements of Mathematical Ecology

Elements of Mathematical Ecology

Mark Kot, University of Washington

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology, and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems throughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

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Calculated Bets

Calculated Bets
Computers, Gambling, and Mathematical Modeling to Win

Steven Skiena, State University of New York, Stony Brook

Calculated Bets describes a gambling system that works. Steven Skiena, a jai-alai enthusiast and computer scientist, documents how he used computer simulations and modeling techniques to predict the outcome of jai-alai matches and increased his initial stake by 544% in one year. Skiena demonstrates how his jai-alai system functions like a stock trading system, and includes examples of how gambling and mathematics interact in program trading systems, how mathematical models are used in political polling, and what the future holds for Internet gambling. With humor and enthusiasm, Skiena explains computer predictions used in business, sports, and politics, and the difference between correlation and causation. An unusual presentation of how mathematical models are designed, built, and validated, Calculated Bets also includes a list of modeling projects with online data sources.

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Mathematical Modeling
Case Studies from Industry

Edited by Ellis Cumberbatch, Claremont Graduate School, California
Edited by Alistair Fitt, University of Southampton

Industrial Mathematics is growing enormously in popularity around the world. This book deals with real industrial problems from real industries. Presented as a series of case studies by some of the world's most active and successful industrial mathematicians, this volume shows clearly how the process of mathematical collaboration with industry can not only work successfully for the industrial partner, but also lead to interesting and important mathematics. The book begins with a brief introduction, where the equations that most of the studies are based upon are summarized. Thirteen different problems are then considered, ranging from the cooking of cereal to the analysis of epidemic waves in animal populations. Throughout the work the emphasis is on telling industry what they really want to know. This book is suitable for all final year undergraduates, master's students, and Ph.D. students who are working on practical mathematical modeling.

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Modelling with Differential and Difference Equations

Modelling with Differential and Difference Equations

Glenn Fulford, University College, Australian Defence Force Academy, Canberra
Peter Forrester, La Trobe University, Victoria
Arthur Jones, La Trobe University, Victoria

The theme of this book is modeling the real world using mathematics. The authors concentrate on the techniques used to set up mathematical models and describe many systems in full detail, covering both differential and difference equations in depth. Among the broad spectrum of topics studied in this book are: mechanics, genetics, thermal physics, economics and population studies.

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Mathematical Models in Biology

Mathematical Models in Biology
An Introduction

Elizabeth S. Allman, University of Southern Maine
John A. Rhodes, Bates College, Maine

Focusing on discrete models across a variety of biological subdisciplines, this introductory textbook includes linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction from DNA sequence data, genetics, and infectious disease models. Assuming no knowledge of calculus, the development of mathematical topics, such as matrix algebra and basic probability, is motivated by the biological models. Computer research with MATLAB is incorporated throughout in exercises and more extensive projects to provide readers with actual experience with the mathematical models.

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Mathematical Explorations with MATLAB

Mathematical Explorations with MATLAB

K. Chen, University of Liverpool
Peter J. Giblin, University of Liverpool
A. Irving, University of Liverpool

Mathematical Explorations with MATLAB examines the mathematics most frequently encountered in first-year university courses. A key feature of the book is its use of MATLAB, a popular and powerful software package. The book's emphasis is on understanding and investigating the mathematics by putting the mathematical tools into practice in a wide variety of modeling situations. Even readers who have no prior experience with MATLAB will gain fluency. The book covers a wide range of material: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations from the basic mathematics. These lessons are applied to a rich variety of investigations and modeling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

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An Elementary Introduction to Mathematical Finance

An Elementary Introduction to Mathematical Finance
Options and other Topics

Sheldon M. Ross, University of California, Berkeley

This original text on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this second edition are: a new chapter on optimization methods in finance, a new section on Value at Risk and Conditional Value at Risk; a new and simplified derivation of the Black-Scholes equation, together with derivations of the partial derivatives of the Black-Scholes option cost function and of the computational Black-Scholes formula; three different models of European call options with dividends; a new, easily implemented method for estimating the volatility parameter.

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