\[KernelIcon]    PREFACE	
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Economics is a science with many diversified fields and topics of interest such as the  theory of firm, consumer theory, welfare economics, international trade, etc. It is also a science with topics of interest that change from  time to time.  Economic issues of interest today are quite different from those in the 1960s, 1970s, and 1980s. The diversity of the fields and the changing nature of the economic issues make the study of economics a challenging, and at times, a laborious task.  However, most of these seemingly diverse fields and subjects have striking similarities and common elements, especially if they are cast into simple mathematical models.
 
As a tool, mathematics can be used to facilitates a clear and organized presentation and test of economic theories and problems.  It provides a basis for setting up a model, making explicit assumptions about the model, finding optimal solutions, and extending the results by varying the parameters and assumptions of the model. A large gain in clarity and economy of effort can be achieved by incorporating mathematics into economic analysis.  Today, it is critical for students of business and economics to be fully equipped with major mathematical tools. Once a student has learned the mathematical tools, s/he can apply them in analyzing  many diverse problems in the subject. 

Unfortunately,  many students entering colleges and universities do not have enough preparation in mathematics to allow them to manipulate mathematical symbols, to do numerical calculations and to graph the mathematical relationships.  These techniques are basic tools of economic analysis and students lacking them, often, do poorly in economic studies.  In many schools, the lack of preparation by students has resulted in cancellation of quantitative parts of the economic curriculum, lowering the course standards, and omitting some of the advanced topics.  Even if students had enough preparation in mathematical methods, presenting certain topics in the class room using the traditional methods is often very time consuming and sometimes tedious.  To deal with these problems, many colleges and universities have attempted to incorporate use of computers and software into their curriculum to enhance the efficiency of teaching and learning quantitative economics. 

For the past ten years I have been using my manuscript, Mathematical Methods in Economics,  in mathematical economics courses at Cal Poly-Pomona. During the fall quarter, 1995, I experimented with the use of the Mathematica in this course.  The results were beyond my expectations.  The use of the Mathematica resulted in covering more chapters of the book than I was ever able to cover in the past.  Students enjoyed the course more than ever and their progress and positive responses were outstanding.  In 1996, in consultation with the Wolfran Research, the publishers of the Mathematica software,  I incorporated Mathematica into the manuscript, revised several chapters, added new material and changed the name of the manuscript to Mathematical Methods in Economics Using Mathematica.

I find Mathematica to be a comprehensive software package that helps to remove student handicaps in mathematical analysis and allows them to concentrate more on the economic concepts, economic theories, and the structure of economic optimization rather than worrying about details of numerical calculations and symbolic manipulations.  Mathematica allows the students to experiment with economic theories and concepts using a very powerful and comprehensive software without being tied up by time consuming mathematical manipulations and calculations. Students can experiment dynamics of economic theories using this powerful, and user friendly software which can handle dynamic and stochastic economic models.  The two-dimensional and three-dimensional graphic features of the program brings economic theories of dynamic market analysis to life.  With Mathematica, I believe that for the first time economic students have access to a wealth of laboratory to experiment economic theories and models.

The unifying and simplifying property of the mathematical methods together with the power and facilitating features of the Mathematica is the basic reason for writing this bookware (book software).  I have attempted to present a number of mathematical methods which are useful in analyzing various business and  economic problems and use Mathematica to show how easily they can be handled and solved using a current computer software.

Each chapter begins with a  tool box presenting all the Mathematica commands used in that chapter.  To practice the commands, click on the hyperlink key on the page.  This will provide you with a practice notebook that contains several examples.  As well, the Magenta-colored hyperlinks link you directly to the description of the command in the Help menu of Mathematica.  It is highly advisable to practice the commands by changing the parameters and the assumptions of the models and by rerunning the programs.  The chapters follow with a clear statement of pertinent definitions, principles and theorems. Then a number of examples in applications of the concepts to the most common business and economic problems in the theory of price, markets, and the allocation of resources are provided.  These examples help to  illustrate and amplify the theory.  The manual solution to the examples are followed by the Mathematica commands and solutions which can be run as you read the material from the screen.  You can always do more practice by changing the parameters in the example and test for the consistency of the results or experiment with the theory.   At the end of each chapter, there are a number of numerical exercises for further practice by the students.  
 
This bookware is written for intermediate undergraduate and beginning graduate students in business and economics.  The requirements include rudimentary knowledge of calculus, elementary matrix algebra, and  intermediate economics.  An attempt is made to keep the exposition of mathematical theorems brief and as simple as possible. Proofs of theorems are given whenever they are instructive and are not too tedious to follow. The emphasis is on the application of the  mathematical theorems and techniques to problem solving in business and economics.   

The bookware is essentially divided into four parts.  Chapters 1 through 5 are the beginning chapters that review the fundamental concepts necessary for developing the materials in other chapters.  I intentionally made the introduction to Mathematica and the Mathematica commands in Chapter 1 so brief.   I believe that the Mathematica commands can be learned gradually as students study chapters of the book and solve the examples.  For students who would like to learn Mathematica commands at a faster pace than the chapters, I refer them to the Mathematica, The Student Book, by Stephen Wolfran, Addison Wesley Publishing Company.   Other concepts considered in chapter 1 are the number system, sets, and mathematical relations. Chapter 2 introduces the concept of function and different types of functions and their graphs.  Chapter  3 deals with fitting equations to sets of data.  Chapter 4 concentrates on the elements of linear algebra.  Chapter 5 discusses some of the advanced topics in linear algebra.  Teaching this chapter or parts of it may be optional in the undergraduate courses.  The concepts in the beginning chapters 1-5 are needed as working knowledge throughout the book. Chapters 6  through 8 are concerned with  optimizing techniques, unconstrained  and constrained. These techniques are the fundamental tools of many economic analysis and problem solving.  Chapters 9 and 10 are devoted to linear programming and its applications to input-output systems and the theory of games.  Chapters 11 through 14 concentrate on dynamic analysis including integral calculus, differential equations, and difference equations.

I would like to thank the many colleagues and students who have given me the benefit of their comments and suggestions.  My special thanks to Dr. David Park (California State Polytechnic University-Pomona) who set the cornerstone of this book and encouraged me to create it. Dr. Maureen Burton (California State Polytechnic University-Pomona), and Osman Yurekli (University of North Carolina, Wilmington) who read the first draft and made many useful comments and suggestions.  Professor James E. Sutton (California State Polytechnic University-Pomona) generously devoted his time to reading chapters and making many valuable contributions to the development of this book  Ted Krueger, and Bunchon Songsamphant, graduate students at the California State Polytechnic University-Pomona, helped me with homework problems and were the  source of many suggestions.  I especially acknowledge my debt to Dr. Daniel C. Vandermuelen's (Claremont Graduate School) lectures in mathematical economics and Dr. Thomas D. Willett's (Claremont McKenna College) lectures in economics.