Does anyone know of any sources online to learn more math/statistics?
Hey Everyone,
I'm not the greatest at math and would really like to get better at it. I'm looking for any online resources to study it over winter break. I'd prefer free resources, but would like to hear everyone's opinions. It would be great if there were resources that offer interactive questions, etc.
I majored in math but I was primarily self-taught so I hope this provides some help.
First off, math is very broad. There are plenty of fields within applied and pure mathematics, so it would help to narrow down what you're interested in first. Since you said stats as well, I'm going to assume you're looking more for the applied math side.
Make a list of the topics you'd like to study. Even applied math is very diverse. Some of the things under the umbrella are probability, combinatorics, differential equations, stochastic processes, stochastic calculus, etc. Now, you'll need to choose one of these topics, and find out what prerequisite math knowledge is needed to learn it. For example, if you wanted to study stochastic processes, you'd need to know probability, and to study anything beyond basic probability you'd need to know multivariable calculus. A great way to devise a plan of study and also understand the foundations you'll need to tackle courses is to go to a university's math department page, and download their degree requirements. This will let you know the suggested order of courses you'll follow, and also give you a sense of what constitutes a BA/BS in math.
Next, you have to find the right resources to learn your desired topic. This is more personal since different people learn differently. I'm a reader and don't have the patience to watch videos online, so I went for textbooks. You can find good books by searching Amazon by reviews, searching on Math Stack Exchange for recommended books, or just going off what the university courses recommend. Or, if you're a visual learner, you can use Khan Academy or the various Youtube teachers like PatrickJMT (they usually have the basics, and they teach them well). An alternate route is to use a site like MIT OpenCourseWare, where they upload former lectures. This is an amazing way to get an MIT classroom education for free in the comfort of your own home.
Finally - learning the material itself. You have to practice math to improve at it. Do textbook problems, download old exams from university sites, or grab some homework sets from MIT OCW. Work on them. Most importantly, focus on learning the material instead of grabbing the high score. You're not taking this for your grade, so do it right. And don't force yourself to do the trivial things by hand if you don't have to/don't want to. In real life, you're allowed to use WolframAlpha to solve an integral or use a TI-84 to do trig functions. Know what they are and how to do them, but after sophomore year of undergrad people don't waste time trying to solve tricky integrals (if you can, that's great though). Your goal is to be comfortable solving problems on a high level and not getting trapped up in the details.
That was a lot, but I hope you found it somewhat beneficial. Self-learning is a huge passion of mine and I completely believe you can get a top-notch education for free with the advent of the internet. Seeing people take advantage of this is one of my favorite things, no joke. If you have any questions, feel free to reach out.
With just a month, it'll be tough to learn a lot. I'd say to focus on stats, with a focus on regression analysis, and how to run tests in R/Pandas. A number of quant (and regular) HFs use stats and the data analysis packages I mentioned, and they are easy enough to pick up without a strong background in programming.
If you have more time afterwards, you could look into math. Unless you want to be a quantitative researcher, it's unlikely you'll need high-level math after probability, so I'd focus on a solid multivariable calculus base (multivariable derivatives and integrals), basic linear algebra (matrix operations), probability (conditional probability, Bayes', distributions, expected value), and discrete math/combinatorics (counting, permutations). Stats is more useful than math for the most part, regression, time series, other statistical methods. And finally, being able to make a computer do the heavy lifting is the glue, since you aren't going to whip out a pen and paper and simulate an execution algorithm 1000 times, so grab an introductory Python (and Pandas) book.
That's all stuff that will make you a stronger thinker and more comfortable solving problems. You might never even need any of it if you're trading certain products. Or maybe you'll find yourself writing Python scripts for most of your day. There's a lot up there, but pick and choose what interests you, and they're all related in some fashion so if you continue with it you'll undoubtedly run into everything on that list.