Yet another Sheep

Her´s the reading list. I split the list in two types of books: Those written for an economics audience and those written for others.

Specifically for Economists

Mathematics for Economists by Carl P. Simon and Lawrence Blume

This is a very basic book and one should know it´s content, even if one has no interest in doing mathematical economics. This is the stuff all grad students have to learn anyways. Still, it is a great book that deserves to be in the list.

Foundations of Mathematical Economics by Michael Carter

If you don't know what to do this summer, working through this book may be the right thing to do. It assumes almost nothing and by the last page, the reader has learned a lot. The book is exercise driven, there are more than 800 exercises with solutions on the homepage of the book. There are a lot of economic examples, so the reader will also learn a lot about economics. The book is however less useful as a reference book because of it´s odd organization (a large chapter on spaces and then a chapter on functions...). It´s also not really possible to read the book fast, because much is outsourced to the exercises.

Real Analysis with Economic Applications by Efe A. Ok

I actually haven't read this book, but from what I´ve seen on it´s homepage, it seems to be a real gem. It certainly contains everything that should be included, is pretty self contained and does real math. If someone has access to it, it is probably worth checking out.


Fixed Point Theorems with Applications to Economics and Game Theory by Kim Border

This book contains everything one needs to know in order to do fixed point arguments in a finite dimensional setting. It is however not that easy to read, reqires already some familiarity with real analysis and is useful mostly in solving problems that were of interest in the seventies. Read it later if you are reall into classical general equilibrium theory (I am).

Infinite Dimensional Analysis: A Hitchhiker's Guide by Charalambos D. Aliprantis and Kim C. Border

This book is by far the most advanced book in this section. It is a great reference, but not that much fun to read. The math is excellently written, but the chapters are long and it takes more than 200 pages until one can read about normed spaces. It is however a book every mathematical economist should keep around. Knowing it´s content should be enough to read everything in the Journal of Mathematical Economics that isn't based on diffeentiability or algebraic topology, two areas missing from this post (don't enough about them).

General Math books

Introduction to Analysis by Maxwel Rosenlicht

This is the most basic of all the books in this section. I is a gentle introduction to serious real analysis and is also dirt cheap. This is the book I recommend tofriends starting out.

Principles of Mathematical Analysis by Walter Rudin

This book is beautiful, elegant- and very terse. You may need to supplement it with something else, but reading it teaches how good proofs ought to look.

Real Analysis by Halsey Royden

Gentle graduate textbook. Gives a well-rounded introduction for those who want to do more avanced stuff.

Handbook of Analysis and Its Foundations by Eric Schechter

My favorite math book. It is for those who really, really like analysis and want to understand all aspects of it. Most of the stuff is not directly useful for economists but makes one a much better in mathematics which should help indirectly. Not a first introduction though.

Geometric Functional Analysis and Its Applications by Richard B. Holmes

Out of print, but a real gem for those who want to work in infinite dimensional spaces in economics. Lot´s of stuff on convex sets, separating hyperplanes and fixed points. One can read this after Royden, it´s a tough book.

Topological Spaces: Including a Treatment of Multi-Valued Functions by Claude Berge

A cheap book on general topology that contains material that is especially useful for economists such as multifuctions (aka correspondences). Not a introduction though.