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I'm coming from a math background (so my mind is set up for Definitions-Observation-Lemma-Proof frameworks) and looking for recommendations of a Macroeconomics textbook mainly devoted to growth models and foreign exchange rates.

Any recommendations?

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    $\begingroup$ I have always thought it interesting that while there are hundreds of Mathematics for Economists books, the only Economics for Mathematicians book still seems to be JWS Cassels's typewritten notes from a 12 hour course he gave in the 1980s at Cambridge, and that was naturally microeconomics where you can set up plausible assumptions and prove interesting results. Macroeconomics does not lend itself to proof beyond some national accounting tautologies. $\endgroup$ – Henry Feb 11 at 0:20
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I really think a great place to start in general is Olivier Blanchard's "Macroeconomics". However, this is an economics undergraduate text and may not be optimal for a mathematician, especially given the structure you expect.

More to your taste may be the following standard texts:

"Introduction to modern economic growth" by Daron Acemoglu.

"Recursive Macroeconomic Theory" by Lars Ljungqvist and Thomas J. Sargent

"Recursive Methods in Economic Dynamics" by Nancy L. Stokey, Robert E. Lucas and Edward C. Prescott

"Foundations of international macroeconomics" by Maurice Obstfeld and Kenneth Rogoff. A bit old by now, but a classic and a good place to start for international economic topics. Alternatively, try:

"Open Economy Macroeconomics" by Martín Uribe and Stephanie Schmitt-Grohé.

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I would also add the following books to the @BBKing list:

David Romer. Advanced Macroeconomics - the first three chapters devoted to growth are excellent (but it does not contain much about exchange rates).

Nelson Mark. International Macroeconomics and Finance - this is very good book for catching up with the research on exchange rates. It’s quite short but surprisingly thorough and it has very good balance between theory and empirical/statistical models.

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    $\begingroup$ Romer has an especially good treatment regarding the type of math you see at a higher level and would better suit your interests more than a typical undergrad textbook $\endgroup$ – Brennan Feb 10 at 18:27
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"Definitions-Observation-Lemma-Proof" is not the right perspective for macro, and one will not, and should not, get that in a proper introduction. Start with an undergraduate text, such as Blanchard, for proper economic perspective.

(If a macro-economist wants a beginner's reference on algebraic geometry, one would recommend an undergraduate text, not Hartshorne.)

Same goes for the two sub-topics you specifically refer to---growth and international finance/international macro. Two suggestions are:

International Macroeconomics, Feenstra et al,

Introduction to Modern Economic Growth, Acemoglu.

Romer and Ljungqvist/Sargent are standard graduate texts. Romer to macro is what (baby) Rudin is for analysis. Stokey/Lucas is one of very few economics textbooks that are rigorous by mathematical standard, but it's meant to communicate some basic mathematics to economists, not for those with no economics background.

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I would suggest that you also read books by Richard Duncan, e.g. The Dollar Crisis, to get a lucid explanation of the global economy from one of the few people who anticipated the 2006/7 financial crisis.

I have also seen approaches where economists use dynamic physics simulators to identify areas of the economy as being stable or unstable, though I am not sure who to recommend. Perhaps Steve Keen.

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