
Mathematics 2006  Mathematical Modeling

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 spatiallystructured population models (with a focus on reactiondiffusion models), agestructured models, and twosex 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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Steven Skiena, State University of New York, Stony Brook
Calculated Bets describes a gambling system that works. Steven Skiena, a jaialai enthusiast and computer scientist, documents how he used computer simulations and modeling techniques to predict the outcome of jaialai matches and increased his initial stake by 544% in one year. Skiena demonstrates how his jaialai 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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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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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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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 nonlinear 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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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 firstyear 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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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 BlackScholes 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 BlackScholes equation, together with derivations of the partial derivatives of the BlackScholes option cost function and of the computational BlackScholes formula; three different models of European call options with dividends; a new, easily implemented method for estimating the volatility parameter.
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