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EDIT: I just want to point out that /u/x0vash0x made a really good point lower in the chain of comments responding to this. The things I say below pertain to what you should do to to understand the mathematics that other microeconomic theorists have used. If you want to be a good theorist, I think /u/x0vash0x is absolutely right when they said you need "to be an applied mathematician who loves economics." Below this is my original comment.

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Speaking as someone who just finished a masters in econ and is now studying math full time (starting a math phd program in the fall), the "all of it" answer unfortunately hasn't matched with my experience. Not that my experience gives me omniscience about the mathematics in economics, but I haven't seen economists use much in the way of topology, complex analysis, number theory, abstract algebra, category theory, functional analysis, or harmonic analysis. Granted, I certainly wish economists used those things and if anyone knows of examples of those being used in economics, please let me know!

Here's my take. The most important three for microeconomics are at the bottom.

• Linear algebra is going to become important if you start studying advanced optimization material, which I mention below. It will also be useful to you for studying econometrics which, if you get a PhD in economics, you will absolutely need to study.
  
  
• If you plan on doing research that involves probability, you will almost certainly need to know measure theory. Any lecture notes that come up when you google "Measure and integration lecture notes filetype:pdf" will work. The thing about measure theory is it's a lot of work, but each step can be presented in a way that's relatively easy, so if one source presents something in a confusing way, find another source that presents it in a relatively clear way.
  
  
• Most important thing #1: If it's in a first semester real analysis class, you need to become very comfortable with it. I would study this first. I like "Principles of Mathematical Analysis" by Walter Rudin because I hate myself it's very, very concise. It's a book where at the beginning, Rudin's written all of it, and by the time you're done, Rudin's written about half of it; the rest was written by you in the margins. He skips steps in proofs and lets you fill in the rest. It makes you go through the book very slowly, but you learn more that way. Just make sure you understand the justification for everything before moving on. Don't worry about the exercises; the book itself is hard enough. You can find a pdf online of it for free. For microeconomics, I'd say you really only need the first 6 chapters.
  
  
• Most important thing #2: Game theory. This is, to my understanding, the primary tool of a modern microeconomist, but you seem to already know that since you want to learn it. This is a subject with a large supply of lecture notes online (just google "game theory lecture notes filetype:pdf"). I would make this your second priority after first semester real analysis. You'll learn plenty of other math in the context of game theory, if you study it enough. Once you're pretty comfortable with game theory and really want to learn the advanced math used by microeconomists in game theory and elsewhere, though, you'll have to learn:
  
  
• Most important thing #3: Optimization. I don't just mean first order conditions. At the top of your must read list is Supermodularity and Complementarity by Topkis. This contains some pretty new mathematics (as in, theorems which were only just proved in 1993). Understanding the material in this book will made a great deal of recent microeconomics literature make more sense to you. I want to stress: this is advanced. However, this is a gateway to a lot of math that modern microeconomists use. After that, you should have less trouble figuring out which material about optimization is relevant to you. I believe convex optimization is particularly important (specifically, the kind of stuff in part 1 of this book which came up when I just googled convex optimization). Note, it uses linear algebra. There are probably better sources, but this is a subject I know relatively less about. I just know I saw some convex analysis/optimization stuff when I took a PhD microeconomics class (and the teaching assistant admitted that it was more advanced math than they were familiar with).
  
  I hope this helps! To the extent I'm able to answer further questions, feel free to ask.

I think it may help to be a little more specific here. Different industries face different marginal costs. I'll copy an excerpt from Ch 7 of Goolsbee, Levitt and Syverson's Microeconomics at the end of this post.
Broadly speaking however, firms face falling marginal costs. If I manufacture lightbulbs, wine, cars, or CPUs then that first unit I produce costs me alot more than my 1,000th or 10,000th unit.
If I am making a car then I have to have many designers and engineers to decide what it is going to look like and how it is going to work, what parts it is going to need. I will need to build a factory to assemble it, I will need to invest in production equipment---some of it which must be special ordered/designed just for this car model. I will need to test it, etc, etc etc. Same goes with making a wine or a lightbulb (less so, but still holds true especially if I make those cool firework lightbulbs).
However as I make more and more I can order more and more of the raw materials at a cheaper price since I am buying in bulk (again, generalizing here) and my workers become better experienced and specialized in the production processes: i.e., the first time you change your spark plugs and wires it may take you an hour, then 45 min then 30 min.

This has it's limits of course based on demand and diminishing marginal productivity of labor/capital but I won't get into that. In broad terms what I just described above has a limit, where unit output costs begin to rise. This is why firms do not make unlimited output and generally try to set output to where MC = MR.


Excerpt from "Microeconomics" by Goolsbee, et al
Economists use the term returns to scale to describe what happens to the amount of
output in response to a proportional increase or decrease in all of the inputs.
A production function is said to have constant returns to scale if changing the
amount of capital and labor by some multiple changes the quantity of output by exactly
the same multiple. (For example, a doubling of capital and labor results in a doubling of
output.) ......
A production function has increasing returns to scale instead if changing all inputs
by some multiple changes output more than proportionately. (Doubling capital
and labor more than doubles output.) Finally, decreasing returns to scale exist if
adjusting all inputs by the same multiple changes output by less than that multiple.
(Output does not fully double when inputs are doubled.)
We assumed earlier in the chapter that inputs have diminishing returns — their marginal
products fall as firms use more of them. So, how can returns to scale be constant or
increasing when there are diminishing returns to inputs? The key difference between the
two concepts is that marginal products refer to changes in only one input while holding
the other input constant, but returns to scale is about changes in all inputs at the same
time. In other words, diminishing marginal returns refers to short-run changes, while returns
to scale is a long-run phenomenon because we are changing all inputs simultaneously.
......

A number of aspects of a production technology determine a production function’s
returns to scale.
In some ways, it is natural for a production function to have constant returns to scale.
If a production process can easily be replicated lock, stock, and barrel, output should
expectedly grow proportionately with inputs. For example, if a firm has a factory that
makes 1,000 cars a day using 3,000 units of labor and 4,000 units of capital, it seems
reasonable that the firm could build an identical factory somewhere else (maybe even
next door) and, having doubled all of its inputs, double its output. Adding a third identical
factory and set of workers should again increase output commensurately, and so on.
But there are other influences than can push production functions toward increasing
or decreasing returns to scale as well. For example, a common source of increasing
returns to scale is fixed costs. These are payments to inputs that must be used
no matter what the output quantity is, even if it is zero. If a certain quantity of inputs must be used before the firm can
produce its first unit of output, increasing inputs after these fixed costs are paid will
increase output more than proportionately. Consider the example of a firm that uses
three inputs to earn its revenues: capital, labor, and a Web page. We assume the Web
page input is a fixed cost, because the cost of its upkeep is basically the same whether
the firm makes a lot of product or just a little. If the firm doubles its capital and labor
inputs while keeping the same Web page, it will probably double its output. Therefore,
the firm was able to double its output without having to double all its inputs. This is
just another way of stating the definition of increasing returns to scale.
A firm can also experience increasing returns to scale if there is learning by doing.
As a company makes more of a good, it tends to become more and more efficient at
production. This sort of learning takes place with virtually any task that is repeated
over and over (as you’ve probably learned from your own personal experience). If a firm
gets better at producing the more output it makes, then it may be able to produce the
second batch of output using fewer resources than it required for the first batch. That
is, it will be able to double its output without having to double its inputs.
Decreasing returns to scale are possible but should be unlikely for the same reason
that constant returns to scale are natural. If inputs are measured properly, and the
firm has ample time to adjust all its inputs, the firm should be able to replicate its current
production operation, allowing it to increase output by the same factor as inputs.
Nevertheless, economists sometimes measure firms’ production functions and find that
they exhibit decreasing returns to scale. Most often, such a finding indicates that not
all inputs are being fully measured. For instance, suppose a company builds a seemingly
identical second factory with the same number of workers and capital as its first one,
yet the second is less efficient. This might be because the second factory’s manager
is not as talented as the manager at the first, or because the company’s productive
corporate culture isn’t as well established as at the original factory. Managerial talent
and corporate culture are inputs to the firm’s production, but are often too difficult
to measure to include in standard labor and capital inputs measures. To have true decreasing
returns to scale, the second factory would have to be less efficient even if the
managerial talent and corporate culture were at the same level as at the first factory.
One reason a firm might have true decreasing returns to scale is regulatory burden.
Many business regulations exempt small companies. As a result, as a company grows, it
often has to comply with additional rules and regulations. Because the cost of complying
with these regulations can be substantial, small firms that expand the scale of their
operations above the threshold find themselves having to deal with a new set of costs
now that they are no longer exempt.

Disclaimer: I am referring to US PhD programs. Things are a bit different in Europe/Canada, but not in terms of material, only structure.

So what you learn in an Econ PhD is drastically different from undergrad. Unless you go to a heterodox PhD program, an Econ PhD is a “STEM” PhD whereas the same can’t be said for most undergrad Econ degrees. I wouldn't say it's impossible to learn the material on your own; however, 1) only wannabe researchers will gain from learning the material at the level of rigor of a Ph.D. program (some of the exercises are just intellectual exercises rather than providing you with tools you can use at a "normal job") and 2) the material is rather high level and it can be difficult to grasp if not being explained by someone who really understands it. The first year sequence at almost all schools is Micro 1, Macro 1, and Econometrics 1 in the fall, the the corresponding “course_title 2” course in the spring.

The first year sequence essentially lays the standard models/techniques in each of the overarching fields (micro, macro, Econometrics) along with the assumptions that those models rely on. The goal is for you to not just be able to memorize the assumptions and solve the standard models, but to truly understand why we need each assumption, what we gain by using it, and what limitations it imposes on the model. That way when we’re doing our own research and we have to relax an assumption or derive a completely new model, we understand what we’re doing.

After the first year, you choose a subfield of specialization (micro theory, macro theory, applied micro, Industrial Organization, behavioral economics, Econometrics, etc) and take courses which continue doing what you learned in your first year, but specifically for your subfield. Then after the second year, you write your dissertation.

If you’re curious what you learn in a first year micro class, here’s a link to download Ariel Rubinstein’s book Lecture Notes in Microeconomic Theory: The Economic Agent. It’s free on his website as long as you provide an email address. While Microeconomic Theory by MWG is a more standard book for first year Micro, I think Rubinstein’s book is better written, especially when compared to the consumer/producer theory sections of MWG. Also, it’s free :)

It's not as unrealistic as you might think. This is something that Bernanke & Co. actually worried about at the beginning of the crisis when they were "sterilising" the liquidity injections. From Courage to Act Chapter 11:

>The sales of Treasuries drained reserves from the banking system, offsetting the increase in reserves created by our lending. This procedure, known as sterilization, allowed us to make loans as needed while keeping short-term interest rates where we wanted them. But this solution would not work indefinitely. We had already sold many of our Treasury securities. If our lending continued to expand—and the potential appetite for our loans at times seemed infinite—we could run out of Treasuries to sell, making sterilization infeasible.

>At that point, the funds injected by any additional loans would increase the level of bank reserves, and we could lose control of interest rates. This concern was very much on our minds, and it provided additional ammunition to FOMC participants who were uncomfortable with our growing array of lending programs...

From Chapter 15:

>In 2006, Congress had granted the Fed the authority to pay banks interest on the reserves that they hold at the Fed. However, for budgetary reasons, the authority had been set to become effective five years later, in 2011. But we asked, as part of the TARP legislation, that we be allowed to pay interest on reserves immediately.
We had initially asked to pay interest on reserves for technical reasons. But in 2008, we needed the authority to solve an increasingly serious problem

>Until this point we had been selling Treasury securities we owned to offset the effect of our lending on reserves (the process called sterilization). But as our lending increased, that stopgap response would at some point no longer be possible because we would run out of Treasuries to sell. At that point, without legislative action, we would be forced to either limit the size of our interventions, which could lead to further loss of confidence in the financial system, or lose the ability to control the federal funds rate, the main instrument of monetary policy. The ability to pay interest on reserves (an authority that other major central banks already had), would help solve this problem. Banks would have no incentive to lend to each other at an interest rate much below the rate they could earn, risk-free, on their reserves at the Fed. So, by setting the interest rate we paid on reserves high enough, we could prevent the federal funds rate from falling too low, no matter how much lending we did.

TLDR: Manipulate IOER.

Where are you in economics right now? Undergraduate? Graduate?

Advanced mathematics appears everywhere in economics, though your mileage may vary depending on your definition of "advanced". As a mathematician, I suspect that quantitative finance contains the most advanced mathematics, since in modern mathematics research the majority of interaction with economics is through quantitative finance. But unless you plan on doing the most advanced math, there's more than enough advanced math in non-finance economics to keep you interested.

Generally speaking, professional economists build up some skill in real and functional analysis, as well as a variety of other skills like optimization, stochastics, and PDEs, depending on their specific research interests. These are all graduate-level math topics, so I'd consider them reasonably advanced. Take a look into econ PhD prelim coursework. When I took the sequence, we used the texts Microeconomic Theory by Mas-Colell-Whinston-Green, Recursive Macroeconomic Theory by Ljungqvist and Sargent, and Econometrics by Hayashi. I think they're good springboards for you to evaluate the math in higher economics.

In quantitative finance, I'd maybe start by checking out Portfolio Risk Analysis by Connor, Goldberg, and Korajczyk, then if you're still interested, I'd pick up measure-theoretic probability. I recommend Probability with Martingales by Williams. Once you're comfortable with measure theory, look through Stochastic Calculus and Financial Applications by Steele. You'll very quickly enter the area of research mathematics while studying quantitative finance, e.g. jump-diffusion models and Levy processes appear in the pricing of exotic derivatives, and they're heavily studied by even pure mathematicians.

https://www.amazon.com/Naked-Economics-Undressing-Dismal-Science/dp/0393356493/ref=dp_ob_title_bk

Chicago uses it alongside the Mankiw text in the intro micro/macro classes. Great readable intro to the economics concepts get defined more rigorously in the textbooks. You can just pick it up and read it casually, like you would Freakonomics, but its goal is to teach intro concepts rather than give "neat" examples of economics at play.

I 100% agree that suggesting textbooks to people who ask questions like this is just completely out of touch. Half of the kids in an intro econ class don't even read most of the textbook...they learn from the lectures/supplementary readings and only review the textbook enough to finish the homework assignments.

Maybe /u/grok_it is one of the few people who wants to actually crack a textbook in their free time, but most people would be better served by something like Naked Economics.

I copypaste here an old comment of mines. It was about laws in economics in general, rather than financial economics, but I think it still stand:







I arrive a bit late to the party, but I will like to discuss the contributions of Daniel Hausman on the topic. To me, he has written THE book (although it is a bit outdated) on the philosophy of economics. Albeit I am an economist myself, I think philosophers have the right answer to your question. I'll try to give a very short synthesis, although it is not easy, given that the book itself is not. There might be errors.

• So, first on what is a law?
  
  >Scientific laws are not prescriptive laws dictating how things ought to be, but true expressions of regularities. [...] What makes laws difficult to understand is that they are not just regularities, for there are also true generalizations that appear to be "accidental". [...] Laws are supported by, incorporated in, or derivable from accepted scientific theories (Berofsky 1971).
  
  
• Are law necessary for science?
  
  Not really, for Hausman. Although laws and causation are strictly connected, you don't need the first to discuss the second and viceversa. Also, in the definition of "laws" above, the part on their distance from "accidental generalization" is pretty important for epistemologists. And this difference is difficult to establish in economics. For example stylized facts, although they are very consistent, as discussed by , are very far from being laws.
  
  
• Are there laws in economics? what type? and do we care?
  
  There is at least one, which is demand's law (or 2, with supply's law). We could increase the number, under sufficient ceteris paribus statements. The problem is that 1) discussing an empirical counterfactual to all this ceteris paribus statement is usually impossible and 2) some of the "disturbing elements" are unspecified. This lead to a problem of "inexact generalization" (using Hausman's words). However, whether something is a law or not is, as others have stated, not super important in economics, because we don't want to test laws but theories. And the relationship between laws and theories is very complicated. It will suffice to say that laws can help in establishing theories. Having to cope only with inexact generalization do not hinder the formation of theories.
  
  Hausman also says (about microeconomics):
  
  >The behavioral postulates of microeconomics do not have the same status as fundamental natural laws. They are inexact and economists regard many as no more than useful first approximations, which theorists are free to supersede or reject in particular investigations. Some of the "laws," such as those of utility theory, diminishing marginal rates of substitution, and diminishing returns, are more central than others, and what makes some bit of theoretical work a part of economics is a commitment only to some disjunction of these "laws" and in particular to the more central ones. [he thinks in particular to the law that states that market are or will quickly go to equilibrium, my note]
  
  The absence of unmovable laws is not "fatal" to economics as a science, but it characterizes it. How economists have, more or less consciously, coped with the problem is one of the main topics of the book and the inspiration for its title.

There are lots of good "popular press" books. Why Nations Fail is boring and deeply flawed, but is ultimately a must-read. Deaton's Great Escape is fine. For a micro approach you can't do any better than the magnificent Banerjee and Duflo.

You might enjoy leafing through some growth textbooks as well. I'd recommend Jones and Vollrath. Vollrath also has an (infrequently updated) blog that I like.

Freakonomics (and sequel) are entertaining, but they don't actually explain economics--they try to use economics to explain other things. In doing so, they explain a few economic concepts, but that was never their goal.

If you want some enjoyable reading that actually aims to teach econ, I highly recommend naked economics. It is well written, easy to understand, and a number of elite undergrad econ classes use it as a companion to a "real" textbook (like Mankiw) because it does a really good job building intuition. Covers micro and macro, and I might not have majored in econ had I not read it in my intro class.

You can get older editions super cheap on amazon...I can't say what the differences are, but they probably all cover the basics. What you'd miss out on by using an older edition is probably refined explanation of the financial crisis (which might be worth the extra few bucks).

That may be true. Thanks for the comment. After reading the wikipedia page on MMT and going down a few rabbit holes, I'm still a bit fuzzy about what you mean. Could you explain?

I'm a real beginner in understanding economics and just picked up this book: https://www.amazon.com/Binary-Economics-The-New-Paradigm/dp/0761813217 which is clearly a perspective from the outskirts of the profession--I mean, the basic premise is, "we need to rethink things."

Just taking the 30,000-foot view here, how does MMT relate to the basic idea of binary economics? How would MMT reflect on this general notion:

>As an economic theory, binary economics holds that broad-based capital acquisition on market principles has a potent (but presently untapped) distributive relationship to growth that is independent of productivity gains and governmental strategies to redistribute or regulate demand.

After getting sick of the repetitive bitching on economic-related blogs about "the free market" and the varying impacts of the new tax law, I found this quote where the binary economics guy acknowledges those gripes and in the same breath actually seems to be proposing a solution:

>So close to breakdown is our myth-ridden, over-inflated, labor-strife-torn, craftsmanship-atrophied, debt-burdened, bureaucratized boondoggle economy, that steps to broaden the capital ownership base must be given priority over every other aspect of economic reform if we are to recapture the American innocence that once made the United States the epitome of a good society.

Don't know exactly whether the "solution" has any merit, or whether there are some other practical roadblocks to getting where the theory says we should go. Like is binary economics something that's been intentionally discarded by hard-minded economists as wild-eyed ravings, or if there are aspects of these ideas that are just implausible non-starters politically, or if there are core pieces of its analysis that are just off/misguided?

I'd probably need a few years of studying economics to grasp the answers, but someone like you might know a few shortcuts...stuff to read and concepts to digest.

Anyway, I found this article which seems to boil it all down pretty well. But without a solid foundation in economics, it's hard to tell which aspects of this analysis are hogwash, myopic, profound or whatever. As a person with more depth of understanding, how would you parse this?

Thanks in advance for any thoughts.

​

​

The text likely refers to the first welfare theorem in general equilibrium theory, which states that a competitive equilibrium is a Pareto efficient allocation. On one hand, this is often considered a formalization of the invisible hand argument. On the other hand, the model in which the theorem holds abstracts away from a lot of real-world issues that may lead to suboptimal market outcomes. The best way to think about it, IMO, is as a theoretical benchmark that allows us to better understand properties of markets, not as an actual policy-relevant result.

A classic reference is Debreu's Theory of Value. More modern treatments can be found in graduale-level microeconomics texts, such as the one by Mas-Collel, Whinston & Green. There are also several lecture notes online, for example these by J. Levin are quite short and accessible.

So the thing to remember that alot of the different things that you talk about, such as the general use of maths, came from the hard sciences first and were transferred over to economics. Thus I don't think that there is much mathematics that economics can teach to the hard sciences in terms of mathematical techniques and analysis. Use of game theory in evolutionary biology might be the exception. And much of convex optimization was probably inspired by economics, though I'm not sure.

What economics potentially can transfer over is certain economics concepts. For example, the concept of a market might be useful in explaining certain biological interactions. I came across this paper looking at gut microbes:

https://www.pnas.org/content/111/4/1237

Perhaps you might be interested in some areas where economics needs to account for natural systems, like ecological economics or the economics of climate change.

There also is looking at how economic forces shape how science is conducted. I came across that idea in this book:

https://www.amazon.co.uk/Economics-Shapes-Science-Paula-Stephan/dp/0674088166/ref=sr_1_1?keywords=how+economics+shapes+science&qid=1565834193&s=gateway&sr=8-1

Otherwise, that's all I know in my limited knowledge of how economics interacts with science. I'm sure there's plenty more.

In general, Peterson is not reliable. He tends to cherry pick, selectively omit, or outright distort, the 'facts' he cites. For the case of the Pareto Principle, which is often stated as "20% of the population will own 80% of the wealth", this is only true for certain parameters of the Pareto distribution. In reality, human societies are diverse; some societies have a high concentration of wealth and income, while other societies have much lower concentrations. As you correctly surmised, much has to do with the institutions that exist in the society. As Acemoglu and Robinson argue, when the elite control the government, they set up institutions that enriches the elite while dispossessing the majority of the people. A strong government that strives to restrain the exploitative tendencies of the elites will enable the majority of the people to reap the economic benefits of their work and will lead to faster economic growth and a more equal society.

I tried to watch some videos of his, but it's very hard to follow him. Take this 2,5 years old video:

• first come five and a half minutes of nonsense - a lot of financial terms thrown around but not one coherent point.
  
• then the actual "next trick" of the federal reserve that has been promised in the title - a massive dilution of the dollar by "money printing" by the end of 2015 which never materialized
  
• followed by another 5 minutes aimless ramblings on "backdoor quantitative easing", "market volatility" and his options trading
  
  He really likes to talk about options trading a lot which is a strange combination with his anti-fed rants. It's also pretty bad, it looks like he saw this Khan Academy series and tried to summarize it without understanding the implications very well. He seems to think options are just a lucrative way of betting your money.
  
  Speaking of that, he also seems to have written a black jack strategy guide.
  
  When you consider all that together with the fact that his videos look like he made them in his parents' basement, and you should get a good picture of him.
  
  edit: Also have a look at who wrote the 6 five-star reviews of his book

A PhD program with professors who study MD teaching a MD course while funding your life in order to give you free time to study MD is probably the best resource available.

Maybe this book? https://www.amazon.com/Game-Theory-Introduction-Steven-Tadelis/dp/0691129088?ref_=Oct_BSellerC_13922_6&pf_rd_p=69cae946-7b1e-5471-ad6b-68cb8cd88dee&pf_rd_s=merchandised-search-6&pf_rd_t=101&pf_rd_i=13922&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=MSFW9P1T62G0KQXBDGPK&pf_rd_r=MSFW9P1T62G0KQXBDGPK&pf_rd_p=69cae946-7b1e-5471-ad6b-68cb8cd88dee

Same as the other post, absolutely. In fact, I would say it's even more valuable with the rise of AI. If you were to ask about Computer Science then it's a whole different ballgame....

Economics is a toolkit for critical thinking. The book Prediction Machines ( https://www.amazon.com/Prediction-Machines-Economics-Artificial-Intelligence/dp/1633695670 ) tries to understand how AI will impact the future. A
central idea in their book is that as the cost of computing and prediction decrease (AI, cloud, quantum computing), the skills that are required to work with them and understand when/how/why AI should be used goes up (critical/big picture thinking). I am 100% not biased (cough cough) but I can't think of a better degree for that kind of skill set.

Now, I will say, that as an economist in tech, my programming skills are below average. And at first this made me frustrated and want to learn Python (puke). I quickly realized that there is scope for economists to code, but our comparative advantage is in thinking through casual mechanisms and laying out intricate models of behavior/the world that an ML program would skip over. I can't tell you how many times in high-levels meetings I hear people say "I love the way your mind works through these problems." Anybody can code nowadays, focus on what separates you from the pack.

I'd recommend a growth textbook, like Weil's Economic Growth or Jones and Vollrath's Introduction to Economic Growth.

If you want something different than recessions, you could look at growth theory and / or development economics. Acemoglu and Robinson have a good pop book on the institutional view.

Try: https://www.amazon.com/Modern-Principles-Economics-Tyler-Cowen/dp/1429202270

and: https://www.mruniversity.com/

Also, ask your professors - although they will lean to the heavily academic side, it will prepare you for their classes. Of course, asking them will show interest in the subject, too. Which might help you stand out a little more, once the courses start.

There are plenty of books named "Money, Banking and Financial Markets" and pretty much they teach the same. I used Pearson version by Mishkin and it was well explained and demonstrated with lots of real-life examples
https://www.amazon.com/Economics-Money-Banking-Financial-Markets/dp/0134733827/ref=sr_1_4?crid=2ARPQ35QRKU2&keywords=money%2C+banking+and+financial+markets&qid=1565963646&s=books&sprefix=money%2C+banking+and%2Cstripbooks%2C127&sr=1-4

Mishkin's textbook is probably the best place to start. It will give you an overview and a foundation.

If you want a solid foundation I would start with something like This starting at chapter 29.

I would recommend Acemoglu and Robinson's book Why Nations Fail on this topic. Expands on the other answers already given.

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.

For graduate (at quals-level) courses my undergrad institution used Mas-Colell, Whinston, and Green's Microeconomic Theory and Ljungqvist and Sargent's Recursive Macroeconomic Theory.