Overall, this is a well-written book. It covers a variety of topics, from preference maximization through existence and stability of eq'ia, to optimal control and growth models.

However, I'm not sure what its niche is -- what this book provides that others don't, or that it covers more thoroughly. If you want math, read Simon and Blume or a math book. If you want micro theory, read Mas-Collel or Silberberg. If you want neoclassical macro theory, read Sargent. For optimal control, read Kamien/Schwarz or Seierstad/Sydsaeter. This book covers selected topics from each. Though it covers them well, much is left out.

Noticeably absent from the book is any uncertainty, randomness, or probability. There is also no game theory. These seek huge omissions for a book which seeks to show the usefulness of mathematical techniques in economic analysis.

Notation is also a bit unusual. I was a bit confused by some of the author's own notation for partial orderings and Cartesian products.

Economists can be divided into those who have read "Mathematical Economics" and those who are going to read it. I believe this book can furhter your knowledge as no other book can do. Usually it takes many months, or even years to be fully understood. I would advice undergraduate students to start with books like K. Lancaster 's "Mathematical Economics" or maybe Simon and Blume's book, to get the best out of Takayama's wisdom. The challenge of reading this book is something that no good economists can avoid.

This is an excellent book for every economist who want to learn more than what is taught in classic courses. It is true that its lecture demands solid knoeledge of the topic, but the author gives full explanations and foundations after each teorem or development, and it has helped me to get the necessary mathematical skills for building models. If you are not sure of your math abilities, try first simon and blume ones, which is easier. I highly recommend it!

This book is more readable than his "Mathematical Economics" since it is not based on an axiomatic approach in dealing with the problems.

This book attempts to introduce some of the mathematical tools that are relevant to economics (espically micro). Proofs of the theorems are mostly omitted. There is a chapter introducing or reviewing some basic mathematics. Main topics are non-linear programming, uncertainty, differential equation and optimal control theory.

The treatment on non-linear programming is excellant. It is a good book for graduate students major in economics. But it requires some basic knowledge in mathematics.