An Introduction to Mathematical Analysis for Economic Theory and Econometrics

By Juraj Zeman, Maxwell B Stinchcombe, P. Dean Corbae, et al.

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory.

Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics.

Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra.

Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers
Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem
Focuses on examples from econometrics to explain topics in measure theory

• Format: Hardcover
• Language: English
• ISBN: 0691118671
• ISBN13: 9780691118673
• Release Date: March 2009
• Publisher: Princeton University Press
• Length: 688 Pages
• Weight: 3.60 lbs.
• Dimensions: 2.0" x 7.1" x 10.3"

Customer Reviews

Probably the best math-econ book for anyone who wishes to pursue a Ph.D. in economics

As a junior economics professor, I have been through a number of math-econ books (which means quite a lot of torture in the learning history). CSZ (Corbae, Stinchcombe, and Zeman) ranks the top place on my recommendation list of math-econ books for anyone who wishes to pursue a Ph.D. in economics. I can not agree with the authors more that "this books bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today." They have done a fantastic job in building up this bridge. During the learning of math econ, a common problem (insofar as I know) is that after you finish the class with a good grade, you still do not know how to apply those math tools in the research practice. A first group of math-econ books are just all abstract math (sometimes, there are pure math books), including tough and intimidating real analysis, functional analysis, etc.... Yes, you can really learn a lot of math (after many many sleepless nights like I did before), but...but, those math are not coupled with econ questions. Such a course might help you understand the technical papers, but might not teach you well how to construct econ models by yourself. A second group of math-econ books do not set a high-level of technical requirements. They might teach a lot of comparative statics and linear algebra, followed by very limited of real analysis. If you merely take a math-econ book in the second group, I guess you will not make sense of SLP (Stokey, Lucas and Prescott). Now CSZ fills the gap between the two groups among math-econ books. Starting from the very beginning, real analysis with its econ application is introduced in a step-by-step, self-contained, and sometimes entertaining approach. If you have a solid undergraduate background in calculus and linear algebra (do not tell me you got a C in those courses!), you should be able to completely understand the beginning chapters which provides proofs of theorems, (remarkably!) examples, and inspiring exercises. Once you work out those exercises in the beginning chapters, more profound math stuffs in the later chapters should be In an accessible approach, it introduces rigorous math that is demanded by advanced econ research. Interestingly this textbook does not even have a chapter called "comparative statics", "constrained optimization", etc., but it beautifully embeds those stuffs into the discussions of logic, set theory, etc. In a similar approach does CSZ provide a math foundation for econometrics after Chapter 6. CSZ's introduction to metric spaces in the second and third sections of the textbooks makes me very conformable (i.e. better equipped) when I go back to those graduate econometrics textbooks (especially, if you want to study Paul Ruud's Introduction to Classical Econometrical Theory). So, it is perhaps a must-read material before you touch those popular graduate econometrics textbooks, such as Greene, Hayas

An excellent math econ book

I am not currently teaching Math Econ, but when I do again I intend to use this book. One problem with the typical first-year econ grad student is that they have little experience with theorem-proof mathematics; they are more familiar with applied mathematics, meaning that they set about to solve a given problem, than they are with the logical process of proving that problem has a solution. CSZ do a nice job of easing the student into this process, starting with the basics of mathematical logic. And they manage to cover the basics as well as some advanced topics. My only quibble is that the book gives too little attention to dynamic programming and recursive competitive equilibria. These methods are now a standard part of any macroeconomist's toolkit, but students rarely get a mathematically careful presentation that is also appropriate as a textbook (SLP is more like a reference book, albeit one where the reader must provide their own proofs). CSZ of course cannot do everything in one book, even one that is 670 pages long, but I personally would have liked to see more on these topics. As a whole, the book fills a clear need in the profession and recommend it to all incoming PhD econ students -- you should read the first couple of chapters before arriving at school in the fall. It will give you a leg up over your classmates (or catch you up) and make the transition to grad school a bit easier.

An impressive collection of tools from Mathematical Analysis applied to different fields of economic

Every undergraduate who wishes to pursue a PhD in economics is told to take a sequence of certain math classes, the hardest of which is usually real analysis. I took a real analysis course based on Rudin's blue book and found it a painful transition from my previous courses. I had to quickly get used to reading and writing proofs. It was unclear if and how these tools can be used in economics. This book is a great solution because it helps the reader to gently transition to writing proofs and is chock-full of applications at every step. This book has three parts: The first 3 chapters introduce the reader to abstract math and proof writing techniques. The second part, chapters 4-8, teach standard material that is often covered in a 2-semester sequence on real analysis. This includes metric spaces, measure theory and probability, and Lp spaces. This also includes a chapter on convex analysis which is rarely covered in books on real analysis designed for math students. The last 3 chapters cover advanced material which is useful for readers interested in economic and econometric theory. The thing that I liked most about this book is its impressive collection of applications to economics, here are some: The first chapter on Logic discusses general equilibrium and proves the first fundamental theorem of welfare economics. In the second chapter on set theory they discuss lattices and apply these tools to introduce Monotone Comparative Statics (MCS) (which was a hot topic in the 90's and hasn't even been introduced into most microeconomics textbooks yet, not even in MasColell). They explain how MCS is a generalization of regular Comparative Statics based on the implicit function theorem, which requires strong assumptions about differentiability. The discussion of real numbers in chapter 3 is very thorough, so an econ student doesn't need to follow every detail but in case he gets curious about some property of the real numbers he can always refer back to it. In chapter 4 they talk about the finite dimensional vector space of real numbers. This is a more gentle approach than I experienced when I learned analysis, because we jumped straight into general metric spaces. They apply these tools to Linear Dynamical Systems, Markov Chains, and most notably to Dynamic Programming. Chapter 5 covers finite-dimensional convex analysis, which includes all kinds of convex separation theorems and applies these tools to prove the second fundamental theorem of welfare economics. They also cover everything you ever wanted to know about constrained optimization, the implicit function theorem and Kuhn Tucker conditions in horrendous detail. The authors proceed to discuss general metric spaces and include more applications to dynamic programming generalizing many of the topics discussed in previous chapters. Chapter 7, which is a bit more technical than the previous chapters, discusses measure theory and measure-theoretic probability. This includes applications to

easy to read; good exercise questions

I'm currently a economics graduate student. I was in Max's class when he used the manuscript of this textbook as the course material. This book definitely covers what an economics student will need during the infancy of research. I especially like the questions in the book. They help a lot in understanding. I highly recommend this book to any economics graduate student.