Reddit reviews Mathematics for Economists

The pure mechanics component consists of multivariable differential calculus, a little bit of multivariable integral calculus, and a bit of linear algebra; plus substantial comfort what might be called "systems of equations differential calculus." The fastest way to cover this material is to work through the first five or so chapters of Kaplan's advanced calculus book or something similar. Do the exercises. Your basic Stewart Calculus doesn't adequately cover the systems-of-equations part and Kreyszig's Advanced Engineering Mathematics book is at the right technical level but has all the wrong emphasis and coverage for economists. Kaplan's book isn't ideal, but it's about as close as you're going to get. (This is a hole in the textbook market...)

The theoretical portion mainly consists of basic point-set topology and elementary real analysis. The fastest way to cover this material is to chop through the first eight chapters of Rudin's undergraduate book.

Yale has a lovely set of Math Camp notes that you should also work through side-by-side with Kaplan and Rudin.

To see economic applications, read those two books side-by-side with Simon and Blume's book.

The first chapter of Debreu's Theory of Value covers all the math you need to know and is super slick, but is also far too terse and technical to realistically serve as your only resource. Similarly you should peek at the mathematical appendices in MWG but they will likely not be sufficient on their own.

Math econ isn't a sub-field of, it's a set of mathematical tools used in econ. You can't specialize in math econ in grad school.

Chiang and Wainright and Simon and Blume are what you want to at least cover the basics. Although most if not all of it will be review which is the intention.

"Masters Level" Economic Textbooks.
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I've picked these texts as they are ones that I ran across in the year I spent as a masters student, or in advanced economics classes when I was an undergraduate/undergraduate tutor.

Hal Varian, Microeconomic Analysis Relatively outdated graduate level textbook in microeconomic theory. I'd imagine his intermediate book would prepare you well for this text. It requires understanding of partial derivatives and some matrix notation to get through, but compared to today's texts comes off comparably light. I'd imagine it'd old and used enough that there exists comprehensive answer guides online that you can track down.

David Romer, Advanced Macroeconomics Romer's Advanced Macroeconomics is used in some undergraduate programs, and some masters/graduate programs. Again, compared to standard texts, it is wanting, but does a good job of covering many of the introductory models that are used in modern economic analysis. This text requires knowledge of at least single variable integration (might require multiple in the later chapters, but when I was tutoring students with it classes never got that far), and the usual multivariate calculus.

Jeffrey Wooldridge, Introductory Econometrics: A Modern Approach this was the textbook that I first saw econometrics through, and I still think its a fantastic applied text. It has a decent mathematical appendix covering some probability and math topics required for the text. On the flip side, the text gives you some pretty good how-to methods to implement a lot of the common econometric techniques and some intuition behind why they are used.

Simon & Blume, Mathematics for Economists This text is usually used in graduate programs math camps as a book saying "you should feel comfortable using these techniques before entering the program." Covers a wide range of topics from calculus, optimization, and linear algebra, to differential equations and some topics in real analysis. It has a fair amount of exercises to work through, and again, the book has been used enough that answer guides may be available online.

As you've probably heard, graduate school is very mathematical, and very little that I learned in intermediate micro ends up bridging the gap outside of some of the intuition I gathered through it. Most of the books I cited above are a solid jump up in difficulty from most intermediate books I've seen, and still a solid jump away from the common PhD level texts (Mas-Colell, Whinston, and Green "Microeconomic Theory". Sargent and Ljungqvist "Recursive Macroeconomic Theory". Greene "Econometric Analysis", respectively).

As a result, depending on what you plan on doing in the near to short term, its usually better to take more calculus, linear algebra, and other mid level mathematics classes.

The standard grad school text these days for dynamic macro is Ljungqvist & Sargent's Recursive Macroeconomic Theory. You won't need to go through the whole thing necessarily, but to be able to tackle the Woodford book, I would think chapters 1-4, 7-8, 12-13, 16-17 and 24-26 would be quite helpful.

There's also Simon & Blume's Mathematics for Economists, which is a good reference book should you need it. For example, the discussion and motivation of Lagrange multipliers and the Kuhn-Tucker optimization conditions is very good.

One noteable omission from both of those books which you will likely encounter at some point is continuous-time optimization/optimal control. This topic is often covered in the appendices of various grad-level macro textbooks, but perhaps the best I've come across is Chapter 7 of Daron Acemoglu's Introduction to Modern Economic Growth. The appendix to Barro & Sala-i-Martin's Economic Growth also has some pretty good coverage.

By the way, if you hunt around, all of these textbooks can be found online for "free".

The only possible issue I see is your selection of textbook: Principles of Mathematical Economics - I've honestly never heard of this book.

The graduate school go-to textbook is Mathematics for Economists by Simon and Blume. However, I think this book would be overkill for you, as it is geared towards pure, PhD level, economics. Also, I was in a similar place to you, with respect to mathematical training at one point, and Simon & Blume proved to be too large a leap.

My advice would be to use one of the following books (in order of my preference):
1. Essential Mathematics for Economic Analysis by Sydsaeter
2. Mathematics for Economics
by Hoy
3. Fundamental Methods of Mathematical Economics
by Chiang

They'll bring your basic command, of the basic required mathematics up to scratch AND these books cover linear algebra. You will also then be in a good place to tackle Simon & Blume if you ever need to in the future. Another piece of advice: PRACTISE PRACTISE PRACTISE. For what you are doing, you don't need to have a deep understanding of the mathematics you are using BUT, you do need to be very comfortable with applying the techniques.

So, as you are working through (for instance) Sydsaeter, I would be attempting the related practice questions you find in:

1. Schaum's Outline of Calculus
   
2. Schaum's Outline of Linear Algebra
   
3. Schaum's Outline of Introduction to Mathematical Economics
   
   Hope this helps.
   
   P.S. Almost all of these books are available for 'free' on Library Gensis

just done something very similar. Took a year off and on my Msc now (broad core econ, haven't specialised). echoing whats been said below:

Was in a similar position with recommendation letters. pretty large UG cohort and I never went to office hours because i just liked to get on by myself. I recommend sending big essays or project examples of work from the classes with those professors. or just sending something you're proud of and reflects your style. that saves them having to dig it up and lecturers can glean a lot from just skimming a students work. dont worry about it, lecturers are such pros and will be happy you want to study more!
obviously give them lots and lots of forewarning.

get into the maths. depending on your program of choice, i would read any level UG econometrics book just to keep you fresh with the methods and lingo. I did quite a bit of metrics at UG but forgot it all after the exams; so useful to go through it at your own pace and see how it fits together.
Pure maths-wise i've stuck with Simon and Blume and the appendix of Greene for some techniques. Greene is pretty dry and scary though, don't be put off! both books and their solutions are available in pdf form everywhurrr

i'm in the UK (from your spelling and tone it looks like you're in the US/Canada?) but at masters level it's just a lot more technical. no more UG waffling about intuition and graphical analysis! I've only been going for a couple weeks but you're expected to derive that equation and really play around with it. a lot of programs i looked at offered preparatory maths courses beforehand but students with solid maths are a lot more confident now real econ has started. just being familiar with the concepts means you're not shocked by them as they're introduced in the micro/macro class. You can follow the lecturer rather than getting derailed at some earlier step.

do an internship, try and think where it's going to lead but failing that, do anything. just anything. they're easy to get, getting some part time work on the side will pay your bills. there really is no excuse. bit daunting applying for them initially and it can be a slog but its worth it.

good luck!

This. Chiang is the easiest to read and comprehend, while Simon and Blume go into the technical aspects with more proofs and rigor. I took the graduate level mathematical economics as an undergrad and we used Chiang. As a PhD student now, we use Simon and Blume; although I certainly reference Chiang a lot.

Chaing : http://www.amazon.com/Fundamental-Methods-Mathematical-Economics-Wainwright/dp/0070109109/ref=sr_1_1?ie=UTF8&qid=1382493346&sr=8-1&keywords=chiang+economics


S& B : http://www.amazon.com/Mathematics-Economists-Carl-P-Simon/dp/0393957330/ref=sr_1_1?ie=UTF8&qid=1382493357&sr=8-1&keywords=simon+and+blume

My pleasure! Again, this is just my experience and I only have a masters in econ, not a PhD, so someone researching in the field could probably be more insightful.

If you're getting ready for a master's, your immediate best friend is something like this guy. This is the textbook we used in my program.

Before my masters, I focused almost exclusively on real analysis and as a result, found myself over prepared in the math that I wasn't tested on and underprepared in the math I was tested on. This book (and books like it) will make you much more prepared for the stuff you'll be tested on than the advanced math used in modern microeconomic research. Pay special attention to the chapters on optimization.

If you're well versed in Lagrange multipliers, KKT conditions, and optimization using matricies, you're probably all set.

Edit: I should add, this book is neither very advanced nor very rigorous, but I would have had an easier time in my masters program if I prepared with a book like that instead of the more rigorous stuff I was focusing on.

I think this is a difficult question to answer without more of an idea where you stand now.

In general, assuming someone has a bachelor's degree and didn't completely skip on all the math, I'd suggest Mathematics for Economists by Simon & Blume, and after or concurrently with that, Advanced Microeconomic Theory by Jehle & Reny. Simon & Blume should cover most of the math that you need to understand Jehle & Reny in sufficient detail.

If you want to read and understand macro papers, I'm pretty sure things are going to be a lot harder. I'm not the person to ask in that case, anyway.

[edit] Also I should mention that acquiring these books in a perhaps less than legitimate fashion is possible, and not very hard.

Chiang is a classic. Another good one is this: http://www.amazon.com/Mathematics-Economists-Carl-P-Simon/dp/0393957330

Try and get either one used.

I know this is a bit old but maybe it still helps. Simon and Blume is a very good book, I think at a similar level than A. Chiang. Also, Sundaram's book is very good for everything related to optimization. It's much narrower in terms of topics but it's great and pretty cheap for a textbook. Finally, you may be able to find Silverberg's book in your library. It's great for the mathematical approach to microeconomics. It's probably to advanced for an into to micro class but keep it in mind for more advanced classes.

I would also recommend Mathematics for Economists. It covers a lot of the different fields, but only as they apply to economics.

It's not as rigorous as a whole course in optimization or real analysis, but it covers the important bits.