Great Price "An Introduction to Mathematical Analysis for Economic Theory and Econometrics" for $57.82 Today
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 all kinds of useful limit theorems and 0-1 laws, and a cool application to quantile estimation on page 405 and state dependent preferences on page 445. Chapter 8 introduces Lp spaces with applications to Statistics and Econometrics including a theoretical discussion of parametric and non-parametric regression. This chapter also includes an application to Artificial Neural Networks.
I haven't spent much time on the final 3 chapters, though I look forward to studying Chapter 11 on expanded spaces (Nonstandard Analysis) which Berkeley's Robert M. Anderson claims can be very useful in the future. In his manuscript on Nonstandard Analysis, Anderson writes "a very large number of papers could be significantly simplified using nonstandard arguments."
The applications make this the only book of its kind that I have seen. Efe Ok's text on Real Analysis assumes a stronger background than this text, and doesn't include such an eclectic collection of applications. Ok's text is more suitable for someone who wants to work in pure theory.
I would have liked to have seen additional material on general topological spaces covered earlier in the text so for example their discussion of open sets in Euclidean space can be seen as a special type of topological space.
I would strongly recommend this book to anyone who wants to see how mathematical analysis can be applied to economics.
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An Introduction to Mathematical Analysis for Economic Theory and Econometrics Overviews
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
Customer Review
easy to read; good exercise questions - T. Chen -
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.
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