Bargalhao Posted January 24, 2009 Share Posted January 24, 2009 In your opinion, which book is better for a course in Mathematical Economics at PhD level with the ususal topics? -Takayama´s "Mathematical Economics" -De La Fuentes "Mathematical Methods and Models for Economists" -Carter´s "Foundations of Mathematical Economics" And why?' Quote Link to comment Share on other sites More sharing options...
Canuckonomist Posted January 24, 2009 Share Posted January 24, 2009 Simon and Blume Comes up a lot, too. Sundaram's "Optimization Theory" is used in half of the math review for Rochester. (and I like this one.) Quote Link to comment Share on other sites More sharing options...
SquareSquare Posted January 24, 2009 Share Posted January 24, 2009 Simon and Blume is on the same level as Chiang - undergraduate. I say De La Fuente, but that book has so many typos! You've got to stay alert. Quote Link to comment Share on other sites More sharing options...
econofrosh Posted January 24, 2009 Share Posted January 24, 2009 We're using Carter for our undergraduate math econ class. It is pretty readable, but I'm not sure if it's the best out there. I think De La Fuente covers more material than Carter does so in that respect, Mathematical Methods and Models for Economists might be better. Quote Link to comment Share on other sites More sharing options...
leguan Posted January 24, 2009 Share Posted January 24, 2009 Simon and Blume is on the same level as Chiang - undergraduate. If you are saying that Chiang is for undergraduate, would you it still consider sufficient as preparation for phd coursework in economics? Quote Link to comment Share on other sites More sharing options...
asianeconomist Posted January 24, 2009 Share Posted January 24, 2009 The Math Appendices of MWG are good too. Quote Link to comment Share on other sites More sharing options...
YoungEconomist Posted January 24, 2009 Share Posted January 24, 2009 Are there any "higher level" math econ books? I bought Chiang back when I was taking Calc 1 and when I looked through that book I was so confused because I had never seen most of that stuff before. But now that I've taken diff eq, linear algebra, probability, real analysis, etc, it seems that most of the stuff in that book is merely a review of the simpler material I've learned in these courses. Are there any math econ books that will review important concepts of real anlaysis and probability (as well as the usual calc and linear algebra)? Quote Link to comment Share on other sites More sharing options...
Oikos-nomos Posted January 24, 2009 Share Posted January 24, 2009 Those books are not about mathematical economics, they are about mathematics for economists. A book on mathematical economomics would be "Theory of Value" by Debreu. I haven't read it though, but I studied some notes based on that book and I loved the topological applications that the author uses. Of those books that you mentioned, I find De la Fuente to be best. He's very comprehensive, short (look at the size of Simon & Blume) and it's the most rigorous one. Quote Link to comment Share on other sites More sharing options...
Oikos-nomos Posted January 24, 2009 Share Posted January 24, 2009 Are there any "higher level" math econ books? I bought Chiang back when I was taking Calc 1 and when I looked through that book I was so confused because I had never seen most of that stuff before. But now that I've taken diff eq, linear algebra, probability, real analysis, etc, it seems that most of the stuff in that book is merely a review of the simpler material I've learned in these courses. Are there any math econ books that will review important concepts of real anlaysis and probability (as well as the usual calc and linear algebra)? De la Fuente's does that job, and quite well. Quote Link to comment Share on other sites More sharing options...
YoungEconomist Posted January 24, 2009 Share Posted January 24, 2009 Those books are not about mathematical economics, they are about mathematics for economists. Can you explain the difference between the two? Quote Link to comment Share on other sites More sharing options...
ssendam Posted January 24, 2009 Share Posted January 24, 2009 Are there any "higher level" math econ books? I bought Chiang back when I was taking Calc 1 and when I looked through that book I was so confused because I had never seen most of that stuff before. But now that I've taken diff eq, linear algebra, probability, real analysis, etc, it seems that most of the stuff in that book is merely a review of the simpler material I've learned in these courses. Are there any math econ books that will review important concepts of real anlaysis and probability (as well as the usual calc and linear algebra)? Real Analysis with Economic Applications, by Efe A. Ok also has parts of a book on probability: ---Professor Efe A. OK---RESEARCH Quote Link to comment Share on other sites More sharing options...
treblekicker Posted January 24, 2009 Share Posted January 24, 2009 Are there any "higher level" math econ books? I bought Chiang back when I was taking Calc 1 and when I looked through that book I was so confused because I had never seen most of that stuff before. But now that I've taken diff eq, linear algebra, probability, real analysis, etc, it seems that most of the stuff in that book is merely a review of the simpler material I've learned in these courses. Are there any math econ books that will review important concepts of real anlaysis and probability (as well as the usual calc and linear algebra)? Any book on Measure and Probability would cover almost all of the probability and analysis you'd need to know throughout your PhD (for a very very small number of people, functional analysis would be useful). Measure, Integral, and Probability by Capinnski and Knopp is said to be a good book for this material. Obviously, this is a pure math text, but I doubt you'll find a text out there which constructs measure theory and advanced probability while providing economics examples along the way. Quote Link to comment Share on other sites More sharing options...
SquareSquare Posted January 24, 2009 Share Posted January 24, 2009 If you are saying that Chiang is for undergraduate, would you it still consider sufficient as preparation for phd coursework in economics? In my opinion, it's necessary but by no means sufficient for a PhD at a top50 or so school. These books cover the necessary basics, but micro and macro these days require more sophisticated math. I'm not mentioning econometrics, since Chiang/Blume don't go into statistics. Somebody here could probably argue that if you are comfortable with Blume/Chiang you'll be fine with picking up more advanced math later, but I'd disagree. It won't be that easy, and I would strongly recommend people to go at least one step beyond that. Quote Link to comment Share on other sites More sharing options...
leguan Posted January 24, 2009 Share Posted January 24, 2009 Somebody here could probably argue that if you are comfortable with Blume/Chiang you'll be fine with picking up more advanced math later, but I'd disagree. It won't be that easy, and I would strongly recommend people to go at least one step beyond that. So what would the step beyond that be? And thanks for the comments on chiang, squaresquare! Quote Link to comment Share on other sites More sharing options...
Golden Rule Posted January 24, 2009 Share Posted January 24, 2009 My judgment is that Simon+Blume is a bit more advanced than Chiang, though I do agree with SquareSquare that you should have mathematical maturity beyond the level of those two books before entering grad school. As for what that "step beyond" is, I don't think it really matters, and no one here should lose sleep over it. Bottom line is you need some comfort with mathematical language and proofs at the level of any undergrad pure math class, whether it be real analysis or number theory or whatever. The details beyond that I don't think are too important. It's just a matter of maturity being able to understand the proofs that you read and how to solve some problems yourself. The exact details of what you cover in your preparation don't matter so much, because you're always going to encounter unfamiliar problems and need to cope with them. As for my experience, I reviewed Simon+Blume material before math camp (I thougt Chiang was too basic and worthless), and during math camp I read some of De La Fuente and that Optimization book that was mentioned, and I thougt this was more than enough. Maybe someone doing hard core theory of some sort would want to do more, but this was more than enough to complete the first year of the PhD program. Quote Link to comment Share on other sites More sharing options...
buckykatt Posted January 24, 2009 Share Posted January 24, 2009 I'm also a fan of Silberberg. Quote Link to comment Share on other sites More sharing options...
Bargalhao Posted January 25, 2009 Author Share Posted January 25, 2009 Those books are not about mathematical economics, they are about mathematics for economists. A book on mathematical economomics would be "Theory of Value" by Debreu. I haven't read it though, but I studied some notes based on that book and I loved the topological applications that the author uses. Not entirely true, actually. Mathematical economics refers to the application of mathematical methods to represent economic theories and analyze problems posed in economics. So, all of the four books do it. De La Fuente´s, Carter´s and Takayama´s just present a different kind of math than Debreu´s book, (and are more pedagogical, of course) which focuses more on topology, like you mentioned. Otherwise, why would two of the three books have "Mathematical Economics" on their titles? Not like Carter and Takayama wouldn´t know the difference. Quote Link to comment Share on other sites More sharing options...
SquareSquare Posted January 25, 2009 Share Posted January 25, 2009 My judgment is that Simon+Blume is a bit more advanced than Chiang, though I do agree with SquareSquare that you should have mathematical maturity beyond the level of those two books before entering grad school. As for what that "step beyond" is, I don't think it really matters, and no one here should lose sleep over it. Bottom line is you need some comfort with mathematical language and proofs at the level of any undergrad pure math class, whether it be real analysis or number theory or whatever. The details beyond that I don't think are too important. It's just a matter of maturity being able to understand the proofs that you read and how to solve some problems yourself. The exact details of what you cover in your preparation don't matter so much, because you're always going to encounter unfamiliar problems and need to cope with them. As for my experience, I reviewed Simon+Blume material before math camp (I thougt Chiang was too basic and worthless), and during math camp I read some of De La Fuente and that Optimization book that was mentioned, and I thougt this was more than enough. Maybe someone doing hard core theory of some sort would want to do more, but this was more than enough to complete the first year of the PhD program. Yes, it's crazy how many people on this board stress out about taking very advanced courses in math - topology, combinatorics and what not. Given prior (negative) experience, I think it's better to build a solid foundation, rather than start taking classes when some of the prereqs are shaky. So, Chiang -> Blume -> RA (e.g. Oak) -> De La Fuente. I would stop the math for math's sake right about here. (Again, I'm skipping econometrics, because that's a different story.) Quote Link to comment Share on other sites More sharing options...
secondsforlunch Posted January 25, 2009 Share Posted January 25, 2009 Yes, it's crazy how many people on this board So, Chiang -> Blume -> RA (e.g. Oak) -> De La Fuente. I would stop the math for math's sake right about here. (Again, I'm skipping econometrics, because that's a different story.) Ok's preface says that the book can actually be used concurrently with De La Fuente. Real analysis with economic applications is really a tough read unless you've covered Rudin. Quote Link to comment Share on other sites More sharing options...
SquareSquare Posted January 25, 2009 Share Posted January 25, 2009 Sorry, but Rudin's entirely different league. The rigorous (abstract) approach is not exactly helpful to budding economists. Quote Link to comment Share on other sites More sharing options...
Oikos-nomos Posted January 26, 2009 Share Posted January 26, 2009 Not entirely true, actually. Mathematical economics refers to the application of mathematical methods to represent economic theories and analyze problems posed in economics. So, all of the four books do it. De La Fuente´s, Carter´s and Takayama´s just present a different kind of math than Debreu´s book, (and are more pedagogical, of course) which focuses more on topology, like you mentioned. Otherwise, why would two of the three books have "Mathematical Economics" on their titles? Not like Carter and Takayama wouldn´t know the difference. Mmm, as you define Math Econ (or as Wikipedia does ;)) there would be no distinction between Economics and Mathematical Economics, because math has become the main tool (the language?) of Economics. I guess the line that separates one from another is vanishing, but certainly the mere application of math to Economics can't be called Math Econ, if it were so, we would be applying to Math Econ Phds and this forum would need a name correction. But as I said, the difference between the two is narrowing as Economics becomes more mathematical. I think this quote reflects very well what I'm trying to say: "Yesterday's advanced mathematical economics is today's mathematical economics, and will be tomorrow's economic analysis." K. Lancaster, in Mathematical Economics (1968) Quote Link to comment Share on other sites More sharing options...
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