I study pure mathematics at university and I'm looking to get into economics, with pretty much no background knowledge about it.
Are there good sources to learn from with a decent mathematical background in mind, or should I just start learning from "normal" sources, like watching video lectures from introductory courses, which don't assume much mathematical knowledge? Preferably, I'd like to embrace economics without those limitation.
McCloskey's Applied Theory of Price is somewhat legendary as a model of clarity. It is, sadly, no longer in print. However, a PDF is available here: http://www.deirdremccloskey.com/docs/price.pdf. The level of mathematical sophistication in this book (like in most good economics!) is not that high, but the book gives a deeper look at the important concepts than is to be found in most extant introductory undergraduate texts.
If you really want a more mathematically formalised treatment then you are going to have to turn to graduate-level econ books. For microeconomics, the classic text of choice is Microeconomic Theory by Mas-Colell et al.
If you do go down the more formal route, I would urge you not to give up on simpler treatments altogether; they're great for building intuition. More than a decade of experience in economics has taught me that good intuition built through simple models is often far more valuable than a less intuitive understanding of a more sophisticated model.
A good introductory text might be something like Preston McAfee's Introduction to Economic Analysis if you want something that might substitute for the average principles text.
http://www.mcafee.cc/Introecon/
There are two versions available there. I understand the earlier version might be preferable if you're already comfortable with math. From the beginning of the 2006 draft:
"This book presents introductory economics (“principles”) material using standard mathematical tools, including calculus. It is designed for a relatively sophisticated undergraduate who has not taken a basic university course in economics. It also contains the standard intermediate microeconomics material and some material that ought to be standard but is not. The book can easily serve as an intermediate microeconomics text. The focus of this book is on the conceptual tools and not on fluff. Most microeconomics texts are mostly fluff and the fluff market is exceedingly overserved by $100+ texts. In contrast, this book reflects the approach actually adopted by the majority of economists for understanding economic activity. There are lots of models and equations and no pictures of economists."
Foundations of Economics Analysis, by Paul Samuelson
or
Economics, by Paul Samuelson (and William Nordhaus) or here for the original.
Maybe I should at least mention this for historical reasons. The book is very old by now (though it has seen some updates with Nordhaus becoming a co-author on later editions), but it's amazing how many Nobel laureates in economics cite this book as an inspiration to go into economics---many of them coming from a background in math.
From Roger Myerson's prize biographical,
I have always loved to read about history and found a fascinating beauty in historical maps. But I hoped for something more analytical, and so I was naturally intrigued when I first heard about economics. I began reading Paul Samuelson's basic economics textbook in a high school vacation. When I got to college, I chose to concentrate in economics and applied mathematics...
From James Heckman's prize biographical,
Samuelson's Foundations of Economic Analysis, was an exciting experience that shaped my desire to learn more economics...
From Samuelson's biography, the mention this about his textbook:
His Economics: An Introductory Analysis, first published in 1948, has become the best selling economics textbook of all time. The textbook has sold more than a million copies and has been translated into French, German, Italian, Hungarian, Polish, Korean, Portuguese, Spanish and Arabic. It is now in its fifth edition. "The book's emphasis on different themes has changed with the changing of the nation's economic problems," wrote Business Week in 1959. "The first edition was dominated by the end-of-the-war worry that widespread unemployment would return... later editions put growing stress on fiscal and monetary controls over inflation. In the later editions Samuelson has worked toward what he calls a 'neoclassical synthesis' of ancient and modern economic findings. Briefly, his synthesis is that nations today can successfully control either depression or inflation by fiscal and monetary policies... Some economists feel that Samuelson's book... is really his greatest contribution. It has gone a long way toward giving the world a common economic language."
Complementary to the other answers, my suggestion would also be to check more than one book entitled "Mathematics for Economics" or alike.
It will give you an idea of what parts of mathematics does Economics use more often, and also, of how Economics translates into economic concepts the mathematical ones.
Some very different books on the subject (without any particular order)
2) A. Takayama
4) A.C. Chiang
...and of course Samuelson's Foundations (already suggested).
A note of warning: if you are a "pure math" person, you may not like what you see into these books.
In general you will find more abstract mathematics into Game Theory and Theoretical Micro, although Stochastic Macro, as well as Finance (especially the latter with its insistence on using continuous time) can be pretty heavily mathematized.
Finally, there is the sub-field of "Mathematical Economics" if you want to feel more at home as regards approach and style. A journal of the filed is Journal of Mathematical Economics.
From a mathematical perspective i highly advice learning about econometrics it's a very useful and somewhat lucrative aspect of economics. I've done a moderate amount of maths in my degree and the more abstract linear algebra material with matrices and markov chains plays into it quite a bit.
But to start you'd probably should begin with basic microeconomics such as supply/demand, indifference curves, game theory and competitive markets. As for books most first year and second year economics textbooks are supremely accessible honestly high school kids shouldn't have too much of a problem with it. Look up the first year subjects on economics in your uni and try to read the textbook set for them.
