Aspiring Quant

Set up an account with Interactive Brokers. Use their API. Write some basic quant algos to get your feet wet (like VWAP, Bollinger Bands, etc.). Use Python.. it's what many quants use.

Get 25K together (FINRA minimum) and TRUST YOUR ALGOS WITH YOUR REAL MONEY. Paper trading is ok for test, but you need to feel the heat when the market moves against you. That experience is worth its weight in gold. I can't stress this enough... you won't learn if you don't have skin in the game. How can you expect a hedge fund to trust their money with your algo if you don't trust it yourself??? A quant needs an education... and he has to pay for it.

Also, read the two referenced books.

That's what I did to get into the hedge fund community.

http://interactivebrokers.github.io/tws-api/
Thank you, this looks great
 
...I want to get some experience in quant trading but I have no idea where to start.

I'm also a math grad, and cut my teeth as a quant research/support at an HFT outfit about 12 years ago. My advice is that you start with a bit of industry research; talk to people in the field, look for internships, do whatever you can to find out the quant related skill shortages that are or will be in demand then focus on learning things in those areas.

Blindly backtesting, optimizing ("machine learning" lol) historical data isn't going to get you anywhere. Too many guys are doing that, and most fund upper management guys (I'm 1 of those) know it doesn't add much value.
 
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