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• Hull's Derivatives is the bible
  
• Stigum's Money Market is a legitimately enjoyable read and taught me SO MUCH
  
• Fabozzi's Fixed Income Handbook is a good general overview of the FI market. (More widely known than, but not as good as Stigum's.)
  
• I don't know where your programming skills are, but try to model out anything that you find interesting in the books above using Jupyter. This will help a great deal with internalizing what's happening mechanically underneath the concepts you're learning.
  
• How I Became A Quant for easy train/bed reading.
  
• Mandlebrot for a dose of realism. Models are always wrong.
  
• The Medium of Contingency for a glimpse into the mind of a practitioner. It's... weird.
  
• Cliff's blog because he's humble (and also my idol). His chapter in How I Became A Quant is the best, imo.
  
  disclaimer: Not a quant, never went to school for it nor worked in finance. I just like reading. This list is more than enough for the summer, but let me know if you want material focused on anything in particular. (Structured products, history, etc.)

I have a similar academic background as you (math / econ) and am a largely self-taught quant. For books, I recommend Active Portfolio Management and Quantitative Equity Portfolio Management. I also recommend academic papers to get a feel for the empirical side in addition to theory that you will read in the books. Great papers to start with are Fama / French (1992) and Avellaneda / Lee (2008). As mentioned, Quantopian is also great for the user forum and pre-baked back-testing engine. You would also find a lot of value in building your own simple back-testing engine in python or matlab or whatever. I wrote mine in python.

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Don't feel intimidated. When I first picked up academic papers, I understood 10% of it on first read. Now, I'm able to breeze through many of them, depending on how esoteric the math / symbology is. Feel free to message me any specific questions you need and I can try to point you in the right direction.

The programming languages really depend a lot. If you're looking to work in low-latency, more than likely, you'll want to have pretty much expert knowledge in C++. Many other firms use Java, Python, or Matlab to develop their strategies.

What I've found is knowing either Python or R is really useful as well for those really quick calculations/ideas.

As for math, knowing linear algebra and probability (extends to stochastic calculus) is a must in any case at all. Having a reasonable knowledge in Calculus is also really helpful. Most of the intense math lie in the derivative markets. If you're working with pure equities, you can usually get away with a lesser knowledge of math in favor of better technical skills (i.e. market microstructure).

There's a lot you can read, but to start off, I would say Dan Stephanica's financial engineering book is a must if you're going into derivatives:
http://www.amazon.com/Mathematics-Financial-Engineering-Advanced-Background

If you're looking into DMA, I highly recommend Algorithmic Trading and DMA:
http://www.amazon.com/Algorithmic-Trading-DMA-introduction-strategies/dp/0956399207

What you'll notice going into the field is that you can't be just an expert in one thing: you need to be well-rounded and an expert in several topics.

A book from 2005:

Quantitative Finance for Physicists: An Introduction. Anatoly B. Schmidt. ISBN 0-12-088464

I don't know anything about the book or author but the title stuck in my mind and it seems like it might be appropriate for you. Good luck!

"Y'all"? Ha you remind me of my friend from da South.

Anyway, getting fixated on a specific journal will not be effective, especially when you are not familiar with the fundamentals. I suggest reading some introductory texts (Hull, Baxter). Then maybe you can move on to Wilmott magazine (school library might have it). Then perhaps you will know enough to search for relevant papers on http://www.ssrn.com/en/.


Hope that helps.

Hey man, I interviewed a couple of months ago at a trading firm in Chicago for an Analyst/Quant role. Aside from the one the other user mentioned, this one was super helpful for me too!

Heard on the Street. The classic.

https://www.amazon.co.uk/Heard-Street-Quantitative-Questions-Interviews/dp/0994103867

Very good luck.

What kinda strategies?
There is Fama-French and a few hundreds of other factors, some of which probably work if done right (though maybe not quite in this market).
There is all the microstructure literature like e.g. https://scholar.google.com/citations?user=-ggKCCAAAAAJ&hl=en&oi=ao about LOB and order flow imbalances predicting short-term price moves.
There is the new fashionable ML stuff
https://www.amazon.com/Advances-Financial-Machine-Learning-Marcos-ebook/dp/B079KLDW21
There are all sorts of standard books on various topics, like this list

https://www.quantstart.com/articles/Quantitative-Finance-Reading-List

And some of them might even be somewhat relevant to the actual quant work.
But ultimately, as with a lot of data science, it's about data not the models. If you read a decent time series and a decent ML book it should be more than enough to start interviewing at quant funds (or to start working and developing models).

There are tonnes of 'Inverview Questions' books out there. This one is probably the best known.

I haven't read this, but it may be of interest to you.

I'm assuming that the classics are O'Hara's market microstructure theory and Hasbrouck's Empirical Market Microstructure.

You could take a look at High-frequency Trading
, a compilation of relatively recent papers (chapters are available online somewhere, don't pay for it). I thought that the chapter by Michael Kearns and Yuriy Nevmyvaka "Machine Learning for Market Microstructure
and High Frequency Trading" was interesting, though not very useful from a practical perspective.

I also found this book to be interesting: https://www.amazon.com/Financial-Markets-Trading-Introduction-Microstructure/dp/0470924128.

Otherwise, I would just pay attention to recent papers posted to SSRN and Arxiv

https://www.amazon.com/gp/aw/d/0979757649/ref=mp_s_a_1_10?ie=UTF8&qid=1474590120&sr=8-10&pi=AC_SX236_SY340_FMwebp_QL65&keywords=quant

This one is good IMO

I kinda liked Joshi's book, "The Concepts and Practice of Mathematical Finance" link

Edit: Article with several books on c++

not free but heres a book.

Here's a list of resources I've been collecting. Note that quantitative finance is a broad term, so different people will be doing very different things, and have different opinions about them. The work can range anywhere from high frequency trading strategies to macro global trends.

Quantitative Trading Summaries:

A summary of quantative trading

Max Dama - On Automated Trading

Cliff Asness - A Brief and Biased Survey of Quantitative Investing

Mark Joshi - On Becoming a quant

Becoming a quant for a programmer

Interview Prep:

Jane Street - Probability and Markets

Heard On The Street

Brainteaser section of On Automated Trading


Sites:

Wilmott

Nuclear Phynance

Blogs:

Math Investor

Investment Idiocy - Systematic Trading

Meanderful - HFT stuff

Jane Street Blog

Jane Street Youtube

Papers From funds:

AQR

Two Sigma