Recently, I've noticed my quantitative abilities slipping. I want to refresh myself on probability, statistics, linear algebra, and maybe calculus?<p>Piggybacking on the thread below, I'd be curious to hear any new sites/apps/books/practices the HN community recommends. This is more of a mental exercise than an application towards a particular problem. Thanks in advance!<p>https://news.ycombinator.com/item?id=3569761
Here are some excellent YouTube playlists for the subjects you mentioned. I have used and can vouch for the high quality of all of them:<p>Linear Algebra: <a href="https://www.youtube.com/playlist?list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv" rel="nofollow">https://www.youtube.com/playlist?list=PLlXfTHzgMRUKXD88IdzS1...</a><p>Probability: <a href="https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo" rel="nofollow">https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB...</a><p>Calculus: <a href="https://www.youtube.com/user/professorleonard57/playlists" rel="nofollow">https://www.youtube.com/user/professorleonard57/playlists</a><p>Be sure to work through problems and not just watch lectures, because otherwise you'll forget the content. For example, the linear algebra course has a companion site with problems, and the professor of the probability course wrote an excellent book with problems.
Few days ago HN user post a Calculus Made Easy as a pdf[0] book, I found that much interesting.<p>[0]. <a href="https://news.ycombinator.com/item?id=14161876" rel="nofollow">https://news.ycombinator.com/item?id=14161876</a>
I am the main developer of the MathPiper computer algebra system (<a href="http://mathpiper.org" rel="nofollow">http://mathpiper.org</a>). I found that a great way to improve one's understanding of math is to learn how a computer algebra system works. I would be happy to teach the fundamentals of a CAS to anyone who is interested.
I'd love to have enough time to read everything about homotopy type theory / category theory / number theory / cryptography. Heck I'd even want to read the complete Art of Computer Programming from beginning to end. It's so hard to balance this with being productive. Life is too short.
For Algebra, if you need certain subjects in depth or need to take a test to assess your skills, try Khan Academy [1]. Also, Khan covers trigonometry and geometry. For Calculus, MIT did a series called Calculus Revisited which covers calc 1,2,3.[2] Calculus Revisited was designed for professionals who needed a refresher or first crash course. It's from 1968-72 but I thought they were great.<p>[1] <a href="https://khanacademy.org" rel="nofollow">https://khanacademy.org</a>
[2] <a href="https://ocw.mit.edu/resources/#Mathematics" rel="nofollow">https://ocw.mit.edu/resources/#Mathematics</a>
Install Anaconda. Start playing with open science data sets. Gain superpowers. Solve big problems. Good luck!<p><a href="https://www.continuum.io/downloads" rel="nofollow">https://www.continuum.io/downloads</a>
Even mental exercises could use a purpose. What are you interested in? Try to keep an end goal in mind. If you want to learn more about machine learning, it might be an idea to start with a mathematical preliminaries chapter in a typical machine learning textbook and look up difficult topics in a probability/statistics textbook. If you want to learn more about databases, perhaps you could pick up a book on relational algebra, and explore it in the context of abstract algebra. There are many ways to get the job done.
I asked this question on reddit a few days ago!<p>My basis was I wanted something like Charles Petzold's "Code" from 1995 which is the BEST way to understand computers.<p>The recommended book by far was..."Mathematics: From the Birth of Numbers".<p>See here: <a href="https://www.reddit.com/r/math/comments/673yxa/best_book_for_understanding_math_at_a_deep/?st=J2TTEFP6&sh=9ec1def2" rel="nofollow">https://www.reddit.com/r/math/comments/673yxa/best_book_for_...</a>
Same boat. I was just going through boxes in my garage and came upon my old college math textbooks and some old exams/homework assignments. It was like gibberish.<p>My plan was just to take a textbook and see if I can just relearn. Probably are better options out there, but I'm clueless.<p>Probably will start with either linear algebra or maybe set theory?<p>Happy to hear other ideas of how people would do this. For me, there's no practical application. I just used to love this stuff and hate how much I've forgotten.
When I was preparing to apply to grad school ~4 years out of undergrad I spent a lot of time working through the various Math modules on Khan Academy and found it very helpful for getting me back up to speed on the basics. They have some higher-level math content on there too now, I believe.
3Blue1Brown's videos are of a great quality. <a href="https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw" rel="nofollow">https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw</a>