Fundamental Methods of Mathematical Economics

Book Description

The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. the book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.

Customer Reviews:

Great introduction to mathematical economics!.......2007-07-18

I enjoy Chiang's writing style. I've been reading up on mathematical methods in preparation for a masters econ program, and feel very comfortable with the material thanks to this textbook. The international edition is a good bargain.

A must read text book for any economics undergrad student.......2006-04-02

I found it extremely easy to read and at the same time rigorous enough to settle the bases. The author knows very deeply the economics students needs of mathematical methods and achieves a precise and complete explanation of all notions I needed to know for my undergrad course. I strongly recommend it during the first or second year.

A must read for graduate students in economics.......2006-02-26

Alpha Chiang's text should serve as the foundation for all quantitive analysis done in economic theory. It is an invaluable teaching tool for graduate students in economics and will help them better understand the mathematical techniques that have become so necessary for economic modeling.

I am not a highly quantitative person myself, but I found Chiang's book comprehensible and a useful reference guide in my gradaute economics classes. Along with Hal Varian's "Microeconomic Theory" and Jan Kmenta's "Econometrics", I would say that Chiang's "Fundamentals of Mathematical Economics" should serve as sacred literature for any prospective graduate student in economics.

not so good.......2005-10-14

the text carries to excess the concept of "keeping the presentation as simple as possible". but in general you cannot understand or solve problems with a fifth grader's ability to abstract them.
especially the relunctance to use matrix notation makes some topics actually harder to understand once they become more complicated.
furthermore I find the structure quite confusing since the text amounts to a monotous blabla - clear definitions might be helpful and some rigor would keep the reader conscious instead of drifting off. after all the text is not so bad but I think we deserve something better. blume might be better.

The best math textbook for economist.......2005-09-30

That is why it used everywhere, in nearly all economic departments. I strongly recommend you buy this book. It really helped me in my undergrad, and it is helping in my graduate courses. If you want to buy another book to accompany this, get Simon and Blume book. One person (probably little masochistic) was saying that Chiang has so many examples, blah, blah, blah. Look, not everyone is a math genius, undergraduate student's need Chiang, it's even useful for graduates. Math is used quite too excessively in economics...showing off?

Quantitative Models for Performance Evaluation and Benchmarking: Data Envelopment Analysis with Spreadsheets and DEA Excel Solver (International Series ... in Operations Research & Management Science)

Average customer rating:

GREAT BOOK...THE BEST DEA CD
very good DEA book and software

Quantitative Models for Performance Evaluation and Benchmarking: Data Envelopment Analysis with Spreadsheets and DEA Excel Solver (International Series ... in Operations Research & Management Science)
Joe Zhu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software
Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References
Handbook on Data Envelopment Analysis (International Series in Operations Research & Management Science)
Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research
Stochastic Frontier Analysis

Accessories:

Models, Methods, Concepts & Applications of the Analytic Hierarchy Process (International Series in Operations Research and Management Science, Volume ... in Operations Research & Management Science)
Spatial Econometrics: Methods and Models (Studies in Operational Regional Science)
Macroeconomic Patterns and Stories: A Guide for MBAs
New Introduction to Multiple Time Series Analysis

ASIN: 1402070829

Product Description

This book introduces DEA as a multiple-measure performance evaluation and benchmarking tool. The focus of performance evaluation and benchmarking is shifted from characterizing performance in terms of single measures to evaluating performance as a multidimensional systems perspective. This book also provides easy-to-use DEA software - DEA Excel Solver. This DEA Excel Solver is an Add-In for Microsoft® Excel and provides a custom menu of DEA approaches, which include more than 150 different DEA models. It is an extremely powerful tool that can assist decision-makers in benchmarking and analyzing complex operational efficiency issues in manufacturing organizations as well as evaluating processes in banking, retail, franchising, health care, e-business, public services and many other industries. The DEA Excel Solver does not set limit on the number of units, inputs or outputs. With the capacity of Excel Solver, the DEA Excel Solver can deal with large sized performance evaluation tasks. For a free version of DEA Excel Solver, please visit www.deafrontier.com.

Customer Reviews:

GREAT BOOK...THE BEST DEA CD.......2004-05-20

The book is excellent with a nice mix of theory and applications in DEA. I believe this is the best book on DEA. Of special interest is the CD that looks at many DEA models. The CD has no competitor and is by far the best around. I have used this CD in many of my academic papers on DEA. If you need DEA software this is the book.

very good DEA book and software.......2003-02-01

This is the DEA book has many DEA models that you can apply with the software supplied. The software is an Excel Add-In which can be easily used. The book also has good intro. on DEA. It is a book for both DEA beginner and advanced users.

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Differential Models
Alexander Solodov , and Valery Ochkov
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540208526

Book Description

Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering.

As a hands-on approach to learn how to pose a differential mathematical model the authors have selected 9 examples with important practical application and treat them as following:
- Problem-setting and physical model formulation
- Designing the differential mathematical model
- Integration of the differential equations
- Visualization of results

Each step of the development of a differential model is enriched by respective Mathcad 11 commands, todays necessary linkage of engineering significance and high computing complexity.

To support readers of the book with respect to changes that might occur in future versions of Mathcad (Mathcad 12 for example), updates of examples, codes etc. can be downloaded from the following web page www.thermal.ru. Readers can work with Mathcad-sheets of the book without any Mathcad by help Mathcad Application Server Technology.

Introduction to Dynamic Systems: Theory, Models, and Applications

Average customer rating:

Good book, but consider a used copy!
Excellent treatment of dynamic systems
Excellent supplementary reading of Linear System Theory
The best mathematical textbook ever written

Introduction to Dynamic Systems: Theory, Models, and Applications
David G. Luenberger
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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Schaum's Outline of Feedback and Control Systems (Schaum's)
Optimization by Vector Space Methods (Series in Decision and Control)
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Investment Science
The Object Primer: Agile Model-Driven Development with UML 2.0

ASIN: 0471025941

Book Description

Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.

Customer Reviews:

Good book, but consider a used copy!.......2007-06-14

This "2001 edition" (according to Amazon) was actually copyrighted in 1979. While the book remains very useful, prospective consumers may wish to consider a good used copy in order to save some money.

Although the publication date is misleading, at least Wiley correctly prints the original copyright date within its "new" texts (there are other examples of this practice). Springer-Verlag performs still greater magic. In "Linear and Nonlinear Programming", also by Luenberger, Springer decided to print the copyright date as 2003 instead of 1984, thus giving the impression that the text contains an up-to-date treatment of the subject matter. If I were buying a copy of "Green Eggs and Ham", I would not care about an incorrect copyright date. However, where technical subjects are concerned, this practice borders on fraud (in my view). It is a deliberate attempt to deceive its customers into believing that they are purchasing something more current and relevant than is actually the case.

Excellent treatment of dynamic systems.......2001-05-03

This introduction to dynamic systems is presented with an algebraic formalism which makes things clear and concise. All concepts are explained intuitively as well as formally, having in mind the objective of making things clear. Few books exhibit such a good approach and other reviewers are right when they emphasize the highly pedagogical quality of Luenberger's books ! This is no overstatement.

The advantage of using this algebraic formulation lies in the simplicity as well as the understandability of the state-space approach, which is best explained in those terms. Most books assume that everyone knows what a state space is without explicitly showing what it is really about. This book just uses the reverse assumption, in that you're not asssumed to know everything before getting into it.

Only some basic knowledge in algebra (undergraduate-level) is required but even without experience in algebraic formalism, it is possible to go through the content thanks to the important number of examples and the intuitive explanations.

A must-read !

Excellent supplementary reading of Linear System Theory.......1999-04-24

The economic application examples are interesting for engineering students.

The best mathematical textbook ever written.......1999-02-19

I studied this book for two semesters as a doctoral student, and consider it the best mathematical textbook ever written. Luenberger writes concisely and with great clarity and elegance. His notation is crisp and easy to follow. The book begins with basic concepts of matrix algebra and dynamic equations, and then builds step-by-step to encompass an enormously broad set of applications. The examples are drawn from all over the map, and are great fun to explore. This is a truly mind-expanding text.

Book Description

Infectious diseases are continuing to threaten humankind. While some diseases have been controlled, new diseases are constantly appearing. Others are now reappearing in forms that are resistant to drug treatments. A capacity for continual re-adaptation furnishes pathogens with the power to escape our control efforts through evolution. This makes it imperative to understand the complex selection pressures that are shaping and reshaping diseases. Modern models of evolutionary epidemiology provide powerful tools for creating, expressing, and testing such understanding.

Bringing together international leaders in the field, this volume offers a panoramic tour of topical developments in understanding the mechanisms of disease evolution. The volume's first part elucidates the general concepts underlying models of disease evolution. Methodological challenges addressed include those posed by spatial structure, stochastic dynamics, disease phases and classes, single- and multi-drug resistance, the heterogeneity of host populations and tissues, and the intricate coupling of disease evolution with between-host and within-host dynamics. The book's second part shows how these methods are utilized for investigating the dynamics and evolution of specific diseases, including HIV/AIDS, tuberculosis, SARS, malaria, and human rhinovirus infections.

This volume is particularly suited for introducing young scientists and established researchers with backgrounds in mathematics, computer science, or biology to the current techniques and challenges of mathematical evolutionary epidemiology.

Book Description

This book describes mathematical techniques for interpreting measurements of greenhouse gases in order to learn about their sources and sinks. The majority of the book gives general descriptions of techniques, but the last third covers the applications to carbon dioxide, methane, chlorofluorocarbons and other gases implicated in global change.

Download Description

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Earth systems science.

Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)

Average customer rating:

A practical approach to finite difference methods
Well Done
Need more books like this one

Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series)
Daniel J. Duffy
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit (Springer Finance)

ASIN: 0470858826

Book Description

In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature:

Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options
Early exercise features and approximation using front-fixing, penalty and variational methods
Modelling stochastic volatility models using Splitting methods
Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work
Modelling jumps using Partial Integro Differential Equations (PIDE)
Free and moving boundary value problems in QF

Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Download Description

The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: * Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options * Early exercise features and approximation using front-fixing, penalty and variational methods * Modelling stochastic volatility models using Splitting methods * Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work * Modelling jumps using Partial Integro Differential Equations (PIDE) * Free and moving boundary value problems in QF

Customer Reviews:

A practical approach to finite difference methods.......2006-11-10

This book proved to be a useful reference for practical implementation of finite-difference methods for PDEs: several one- and multi-factor financial derivatives pricing models, including local volatility models and models with stochastic volatilities. The methods described in the text are stable, accurate and reasonably efficient. Stability of FD methods is obviously of top concern to the author (as it should be to readers as well), and he goes into extensive detail evaluating the stability of various techniques. The writing is clear and consistent, though a "notational" index or glossary would have been helpful, particularly in the early going. The author provides several practical examples, which lends a refreshing degree of concreteness to the book.

Well Done.......2006-11-06

Daniel J.Duffy introduces Finite Difference methods for solving partial differential equations that arise in numerical pricing of derivatives. There are seven sections in the book. They are:
Part I The Continuous Theory of Partial Differential Equations - A short introduction to partial differential equations and their applications to financial engineering.
Part II Finite Difference Methods: the Fundamentals - There are three chapters that introduce Finite Difference methods to approximate initial value and initial boundary value problems. Another two chapters apply the methods to Black-Scholes equation. He did a nice job to approximate the solutions to problems with small volatility or large drift,...
Part III Applying FDM to One-Factor Instrument Pricing
Part IV FDM for Multidimensional problems
Part V Applying FDM to Multi-Factor Instrument Pricing and
Part VI Free and Moving Boundary Value Problems
There are altogether 18 chapters (about 180 pages) that thoroughly introduce the application of FDM techniques to a wide range of options (pricing) modelling. The exposition is clear and concise.
The last part
Part VII Design and implementation In C++ - The last four chapters design for readers having programming literacy.
To fully appreciate the materials of the book, readers should have at least one year training in partial differential equations and knowledge in financial derivatives at about the same level as John Hull's book - Options, Futures and Other Derivatives, 5e.
If the book contains a few applications to real world data, it will be perfect to primers in this field.

Need more books like this one.......2006-07-05

Having bought many books in Financial Engineering this is one of the most useful. The source code is atleast alot better than the other books that claim to be the best. I give this book 4 stars and recommend quants to buy this book.

Evolutionary Games and Population Dynamics

Average customer rating:

The Best There Is On Evolutionary Dynamics

Evolutionary Games and Population Dynamics
Josef Hofbauer , and Karl Sigmund
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Evolutionary Dynamics: Exploring the Equations of Life
Evolution and the Theory of Games
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Individual Strategy and Social Structure: An Evolutionary Theory of Institutions
Mathematical Models of Social Evolution: A Guide for the Perplexed

ASIN: 052162570X

Book Description

Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.

Customer Reviews:

The Best There Is On Evolutionary Dynamics.......2000-07-14

When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.

The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.

There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.

The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.

Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.

Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).

Book Description

The use of actual observations to infer the properties of a model is an inverse problem, which are often difficult as they may not have a unique solution. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, including many heuristic arguments. Prompted by recent developments in inverse theory, this text is a completely rewritten version of a 1987 book by the same author, and includes many algorithmic details for Monte Carlo methods, least-squares discrete problems, and least-squares problems involving functions. In addition, some notions are clarified, the role of optimization techniques is underplayed, and Monte Carlo methods are taken much more seriously.

Differential Equations: Graphics, Models, Data

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One of the best Differential Equations textbooks ever

Differential Equations: Graphics, Models, Data
David O. Lomen , and David Lovelock
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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University Physics with Modern Physics with MasteringPhysics(TM) (12th Edition) (MasteringPhysics Series)

ASIN: 0471076481

Book Description

Viewing stained glass from different angles or in various lights is necessary to discover its many qualities. Likewise, viewing solutions of differential equations from several points of view is essential to fully understand their behavior. Lomen and Lovelock provide an active environment for students to explore differential equations by using analytical, numerical, graphical, and descriptive techniques, and for students to use ODEs as a natural tool for modeling many interesting processes in science and engineering.

Customer Reviews:

One of the best Differential Equations textbooks ever.......2001-10-12

As a student of Professors Lomen and Lovelock I can say with confidence that this is one of the best Differential Equations textbooks I've worked with. The book clearly explains all the concepts, provides numerous examples, and covers everything that there is to be known. Perfect as a supplement to your class lectures or as a way to teach yourself what you might not have learned in the past.

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