Methods of Mathematical Economics

Alpha C. Chiang is a professor at the University of Connecticut

Professor Chiang's "Fundamental Methods of Mathematical Economics" has become the classic preparatory text for students beginning a course of quantitative study in economics and finance. It has been in print for nearly a generation, and with good reason. Chiang's achievement is to have created a learning programme that can take a modestly numerate person all the way from basic matrix algebra through limits, continuity and derivatives past simple differential equations all the way to optimisation theory and linear programming. And all in one volume! Little prior training is required for this journey - all you need is basic algebra. The explication is admirably clear, there are plenty of good practice examples and the pace is moderate. "Mastering Chiang," as one of my old professors used to call it, provides an excellent foundation for the economics or finance student and will admirably equip him or her to deal with the more rigorous challenges ahead.

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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.(p)
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.

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I used this book in my Mathematical Economics textbook in an Economics Masters program. This book covers ALOT of basic math material needed in economics. It is an excellent text/reference/review math book for a graduate level student in economics and possibly other areas in the social sciences. I highly recommend this book to any economics student (though it may be difficult for some undergraduates).
It covers the basics of number theory, economics related math (i.e. market equilibriums, etc.), linear (matrix) algebra, comparative static analysis, differentiation, integration, logarithmic & exponential functions, differential equations, and more that we did not cover in the class like programming. Even if you have taken many math classes outside of the field in economics, this book is a great bridge to apply that math to economics.
While most of the math in this book is not specific to economics, I would not strongly recommend it to science majors since only math that is commonly used in economics is discussed (i.e. no trig functions). In addition, this book does not cover econometrics (statistics) or probability at all.
For a hard-cover textbook, this book is small and relatively light so it would make a great reference book to keep in your bookbag.