I'm looking for a good introduction to basic economics from a mathematically solid(or, even better, rigorous) perspective. I know just about nothing about economics, but I've picked up bits and pieces in the course of teaching Calculus for business and social sciences, and I'd like to know more, both for my personal culture and to incorporate into my courses. My Platonic ideal of such a book would be along the lines of T W Körner's Naive Decision Making, but I'll take what I can get.

1$\begingroup$ This may not be exactly what you are looking for, but for a history of how the solid mathematical foundations of economics have being built, perhaps "More Heat Than Light" is a nice source. amazon.com/MoreHeatthanLightPerspectives/dp/0521426898/… $\endgroup$– James OCommented Apr 5, 2011 at 15:09

5$\begingroup$ Dear Gordon, If you indeed persue it, please tell us, some months from now, which book you tried and what were your impressions. $\endgroup$– Gil KalaiCommented Apr 5, 2011 at 15:46

1$\begingroup$ @Gordon Craig: You may probably get even more book suggestions on the sister site quant.stackexchange.com which is specifically devoted to mathematical finance. $\endgroup$– Andrey RekaloCommented Apr 5, 2011 at 21:08

2$\begingroup$ Zen's comments are inappropriate and indeed offensive, (in addition to their poor content). When there is a question over MO about how to go about learning a mathematical area or an academic area where mathematics is applied it is inappropriate to use this as a stage to express negative opinions about the entire area and to invite people to argue. It is certainly inappropriate to do it in an offensive way. (On top of it, indeed, as he himself testifies, Zen does not know anything about these topics.) – $\endgroup$– Gil KalaiCommented Apr 7, 2011 at 11:48

2$\begingroup$ @Gil: I'll have to get back to you in a few years rather than a few months, since this is more of a weekend and holiday project than everything else. (Somewhat) in defense of the content of Zen's post, I don't find his comments offensive(although they sounds a bit farfetched, and may well violate MO protocol) and his comment about Nobel's descendants is accurate(I heard one say it on the radio,) although the relevance what someone's greatgrandson has to say is questionable. $\endgroup$– Gordon CraigCommented May 18, 2011 at 19:48
6 Answers
My real advice is to start with something less mathematical and more intuitive so that you understand the motivations for the more mathematical approaches.
That having been said, if you're looking for a mathematically rigorous approach to ideas of central importance in economic theory, I'd start with Debreu's Theory of Value. MasColell (suggested in another answer) is a massive textbook that touches on a gazillion different topics; Debreu reads like a math paper. It's dated, but only in the same sense that, say, Serre's FAC is dated. It's a seminal work, it's the inspiration for a lot of what's come since, and you can still learn a lot from it.

2$\begingroup$ If I had a question on economic theory, I would take heed of Steven's advice: he really knows what he is talking about! $\endgroup$ Commented Apr 5, 2011 at 14:43

$\begingroup$ Dear Steven, could you add any concrete suggestions for something less mathematical and more intuitive? Thanks. $\endgroup$ Commented May 6, 2011 at 13:26

1$\begingroup$ Michael: Throwing modesty to the winds, I can recommend either my own textbook on Price Theory or The Armchair Economist. The textbook uses very little formal math, but the reasoning is essentially mathematical. I am a great believer that when you're seeing this stuff for the first time, it's important not to rely on formal math, but to be forced to work through what's really going on at a verbal level. $\endgroup$ Commented May 6, 2011 at 17:08

3$\begingroup$ @Steven: Thanks for the recommendation. I'll look at the textbook on Price Theory, but I read the first few chapters of the Armchair Economist, and in all honesty, I was uncomfortable with some of the implicit assumptions. I'd be happier with something where the axioms are laid out explicitly, which is one of the reason that I'm interested in a mathematical treatment. $\endgroup$ Commented May 18, 2011 at 20:00
Let me first tell you that there are three types of economic theory:
 price theory
 general equilibrium
 game theory
Nowadays, the last type of theory is by far the most popular, but maybe you need some familiarity with the other two to appreciate game theory as an economist does. I guess you could say the mathematics is very easy judged from what mathematicians are used to. What is difficult is the economic interpretation. For that you need a bit economic intuition and a bit of culture about classic economic models.
My recommendations for a mathematically mature neophyte would be:
 george stigler's price theory for the first
 debreu's classic for general equilibrium; there is also a book by JWS Cassels
 Fudenberg & Tirole or Vega Redondo for game theory
The book Lecture Notes in Microeconomics theory by Ariel Rubinshtein is a nice place to start. (And it can be downloaded freely.) It describes matter in a formal way, it is mathematically precise, and it is rather short. It gives a good feeling of what theoretical economics is about and how theoretical economists go about it.

$\begingroup$ Yay for free books! Even better when they're short! $\endgroup$ Commented Apr 5, 2011 at 16:43

$\begingroup$ @Gil: Thanks very much. And I second Thierry's comments. $\endgroup$ Commented May 18, 2011 at 19:51
Some work in economics is very technical, but ultimately, economics is not a formal science. There is no canonical mathematical model for economic behavior as there is for, say, quantum mechanics. I think one needs to acquire some sense for the subject first. A perfect book for that, from someone who has a formal perspective, is "Rational Choice" by Itzhak Gilboa. It is by far the best introduction to economics I know of, and it has references to more formal work you can follow up later.
I would recommend the following three books:
 Microeconomic Theory by MasColell et al.
 Stochastic Calculus for Finance vol I and II by Shreve
Good luck!

$\begingroup$ Thanks! I'll investigate both, although I'm more interested in the economic theory than the Finance aspect. $\endgroup$ Commented May 18, 2011 at 19:50
Microeconomic Theory by Mas Colell et al. Game Theory by Fudenberg and Tirole.