Mathematics and Mathematica for Economists

Rating:
Summary: Great Introduction...
Review: Here is a practical comment for the typical economics graduate student: Buy this book if you want to start using Mathematica!

What does a typical economics graduate student need? First, s/he needs to review her/his knowledge of mathematics. Second, s/he needs to learn how to use the tool (math) to solve an economic problem. Cliff J. Huang and Philip S. Crooke's book is helpful in both respects. While they are introducing the basic language of Mathematica they review most of the undergraduate math. And they teach with a hands-on approach--that is, you solve almost every problem using Mathematica.

Mathematica is a great tool for economics graduate students, it helps you out in understanding the basic intuitions behind mathematical concepts--because you do not have to solve complex problems (Mathematica solves them for you), you just have to understand them. Of course, students are advised to consult their professors to choose the right computer software or programming language. Mathematica can do a lot, but some other software might be much more practical for your PhD thesis project...

[Also consider Differential Equations: An Introduction with Mathematica by Clay C. Ross]

Rating:
Summary: Exceptionally valuable contribution to graduate economics
Review: This book covers mathematical methods topics that would ordinarily constitute the core of a one semester course at the first year graduate level in economics. The book could also be used at the advanced undergraduate level. It is the first book to fully integrate Wolfram Research's Mathematica software into a study of mathematical methods for economists. The authors' stated objective in this integration is to relieve students, via use of computer software, of the rather tedious computations typically associated with mathematics for economists coursework so that attention can be focused on underlying principles. To further this objective, a Mathematica notebook, MathEcon, comprised of functions commonly implemented in mathematics for economists courses accompanies the book.

The book features fifteen chapters including coverage of topics in linear algebra, quadratic forms, vector calculus, functional properties, mathematical programming, and differential and difference equations. The first two chapters provide an introduction to Mathematica and a review of calculus. Chapters are divided into sections and subsections and all chapters include exercises at the conclusion of each subsection. Many, though not all, of the exercises involve use of the Mathematica software. Numerous examples are included in all chapters and the use of Mathematica to illustrate concepts and problem solving is prevalent throughout the book. In this regard, the numeric, symbolic, and, in particular, graphic capabilites of Mathematica are used extensively to explain concepts and example problem solutions.

This book can only be regarded as an exceptionally valuable contribution to graduate education in economics. The choice and coverage of topics is appropriate for the mathematics for economists course. Mathematical concepts are presented with uncommon clarity. For example, the chapter on eigensystems is perhaps the best treatment of this topic in the mathematics for economists literature. The many examples contained in the book provide for enhanced comprehension of related concepts and would by themselves elevate this book above the field as an educational device. Exercises are generally well suited for reinforcement of material covered in the chapter subsections. The thoughtful integration of related computer capabilities and provision of the MathEcon package fully achieve the authors' stated objective. This book is an obvious first choice as a textbook in mathematics for economists courses.