6 ms·

Ask HN: Is there a website specialized in mathematics courses?

• henearkr 6y ago
  My own way to expand my knowledge was by going through textbooks and with a heavy support of Math StackExchange. Maths is a very written-oriented domain, but still if you are more a video-oriented learner you can probably find a lot on Youtube, and a lot of great researchers have videos there.
  • cmehdy 6y ago
    To add to this, "All the Math books you'll ever need"[0] compiles a fantastic list of books for all aspects of mathematics. [0] https://mathblog.com/mathematics-books/ https://mathblog.com/mathematics-books/
    • henearkr 6y ago
      Good one for a starting point! However the books I read are not in it lol...
• qz2 6y ago
  MIT OCW: https://ocw.mit.edu/courses/mathematics/ https://ocw.mit.edu/courses/mathematics/ I mostly fudge together what I need from that and Khan Academy when I’ve forgotten something fundamental.
• klunger 6y ago
  I am not sure what your "discrete math courses" were and if you have already taken these but, the Linear Algebra and Differential Equations courses on Kahn Academy are solid intros to the basics of those subjects.
  • dalleh 6y ago
    I just saw those course they look really well-structured and solid ones.
• moonbug 6y ago
  books are still a thing.
• errantspark 6y ago
  Khan Academy is great for this.
  • tasubotadas 6y ago
    Second this.
• Alexss 6y ago
  https://realnotcomplex.com/ https://realnotcomplex.com/ has a wide range of free textbooks and video courses collected
  • pthreads 6y ago
    Just found at least two books on topics of my interest and there are several more that I think I will read in the future. This is a good resource. Thank you!
• auroranil 6y ago
  https://tutorial.math.lamar.edu/ https://tutorial.math.lamar.edu/ is a good place to review continuous maths.
  • loufe 6y ago
    This site was a godsend in university maths. I also strongly recommend it.
• iflp 6y ago
  It's probably way easier to decide on a subject you want to learn more about, and find the most approachable textbook / lecture notes on e.g. StackExchange. It doesn't make sense to choose courses (or even subjects to learn) based on whether video lectures are available. I don't maintain a collection of these, but I can probably recommend * Stephen Abbott, Understanding Analysis, for mathematical analysis and a little bit of real analysis * David Williams, Probability with Martingales, for advanced probability * Dym and McKean, Fourier Series and Integrals Alternatively if you have a more cursory interest, you can probably check out Metacademy [1] which provides roadmaps to learning a variety of math (and ML) concepts. [1]: https://metacademy.org/browse https://metacademy.org/browse
  • dalleh 6y ago
    Although I am a bit interested in number theory, linear algebra and a bit of calculus and its applications, I still haven't fixed my mind on specific fields. Now from time to time I watch videos on popular math YouTube channels so I can see what I like most.
    • deleted 6y ago
      [deleted]
• BatteryMountain 6y ago
  Doing Khan Academy then 3Blue1Brown got me through many mental blocks when it came to math stuff. I used KA during university and it really helped me, but wish 3BlueBrown existed back then as it has even better visualizations - this was key for me to make math interesting and to see why certain levers exist in math and what happens when you pull them (how changing formula variable values changes outputs). https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
• sabas123 6y ago
  I would advice against resources like KA and 3B1brown. I'm a firm believer that you don't truly understand material unless you also understand a proof for it. Ane while those resources are AMAZING for simple intuition building, they aren't sufficient. Go pick up a book about proofs to develop mathematical maturity and then delve into some undergrad books for analysis (Abbott) or linear algera (Axler)
  • H8crilA 6y ago
    You're right, but a) those are effectively (small) lectures, b) practice does not preclude watching lectures.
  • indigochill 6y ago
    Perhaps another facet to this is that both KA and 3B1B are primarily video lectures, and it's common knowledge that simply listening to someone explain something performs poorly for learning relative to actually getting hands-on with the topic. KA is even trying to fill this gap. They've added interactive visualizations for some topics. I'd say the same is true for proofs. Simply reading a proof isn't the best if you want to understand/retain it. If you can "re-invent" the proof step by step (or in some contexts you might be able to translate steps between geometric and algebraic representations), then you have probably internalized it sufficiently.
    • posed 6y ago
      The more engagement with the topic, the better.
  • jordan_curve 6y ago
    Absolutely you should not use 3B1B as a replacement for reading a textbook and doing problems. However, I don’t think you that means you should skip watching 3B1B videos at all. In fact, Grant repeats quite often in his videos that they’re not a substitute for doing problems. I’d highly recommend watching the videos side by side with reading through Axler. They will help develop the right geometric intuition (which Axler does a decent job of, but books can only do so much as a medium). I believe the 3B1B videos can also be quite motivating, which in my experience is the most important factor when self studying.
• ben_w 6y ago
  I’m working through the entirety of brilliant.org right now; some of its courses are specifically maths, and the skill level goes from introductory courses all the way up to maths-degree level topics.
  • bvm 6y ago
    How is it? I've seen it peddled by a lot of youtubers that I like.
    • hastingo 6y ago
      My take: it's good but has some drawbacks. The biggest one for me is that the questions are mostly multiple choice. You don't have to show your work or reason through the problem, so it's easy to mentally cheat and say "eh I think it's this one." This isn't so much a fault of Brilliant as a limitation of the smartphone/web technologies vs. pen and paper. I've been having some success with a blend of Brilliant, books, and application (using what I learn to read some physics). I don't think using it on its own will probably be enough though if you want to be able to apply or know the topics deeply.
    • ben_w 6y ago
      There’s a lot of good content, and the explanations (both before and optionally after you answer a question) are usually pretty good. It’s not perfect, but it is pretty good — the single largest change I would make is “more practice examples for any particular topic”.
• app4soft 6y ago
  > part of the major was just a couple of calculus and discrete math courses On Coursera[0] there are a lot of courses on math[1], including on discrete math[2]. [0] https://en.wikipedia.org/wiki/Coursera https://en.wikipedia.org/wiki/Coursera [1] https://www.coursera.org/courses?query=mathematics https://www.coursera.org/courses?query=mathematics [2] https://www.coursera.org/courses?query=discrete%20mathematics https://www.coursera.org/courses?query=discrete%20mathematic...
  • conformist 6y ago
    Coursera and MIT OCW are both great. I would also add edx: https://www.edx.org https://www.edx.org
• rorykoehler 6y ago
  I had the best results from mit ocw https://ocw.mit.edu/index.htm https://ocw.mit.edu/index.htm
• saivan 6y ago
  I'm making youtube videos https://www.youtube.com/channel/UCafIamqsRUHoRT4496jgvMQ https://www.youtube.com/channel/UCafIamqsRUHoRT4496jgvMQ And I'm also working on a website that has a fair bit of the foundations: https://treena.org/ https://treena.org/ Admittedly, we don't have a huge amount of the higher stuff yet. But we are making our way through steadily :) Hopefully it's of some help to you
  • tuxxy 6y ago
    This looks really neat. I noticed a typo on https://tuition.treena.org/ https://tuition.treena.org/ "Enrol Now" should be "Enroll Now" :)
    • saivan 6y ago
      Oh awesome, thanks for picking that up, will fix asap :P
    • y7 6y ago
      Enrol is the preferred spelling outside North America. https://grammarist.com/spelling/enrol-enroll/ https://grammarist.com/spelling/enrol-enroll/
  • andreygrehov 6y ago
    Very well done! I like your animations. What software/hardware do you use to make it?
• chrisweekly 6y ago
  Slight tangent given it's not all about "courses" per se, but my all-time favorite math-related website -- https://betterexplained.com https://betterexplained.com -- is remarkably good at aiding in the development of intuition and deep understanding. Enjoy!
• smukherjee19 6y ago
  I heard this from a senior colleague of mine that he's been working through the book "How to prove it: A Structured Approach"[1] that show how to prove things in mathematics, and has quite good exercises. Perhaps a hands-on approach such as solving the exercises while working through this book will prove beneficial and is complimentary to watching, say, KA or 3B1B. [1]: https://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/1108439535/ https://www.amazon.com/How-Prove-Structured-Daniel-Velleman/...
  • jeffreyrogers 6y ago
    I think that book is better once you're already fairly comfortable with proofs. I tried to read it early on in my mathematics studies and couldn't understand it. Until you've done a number of proofs and start to see commonalities between them (e.g. proof by contradiction, induction, etc.) you don't have the mental scaffolding to learn more systematic approaches to proofs. I realize the book attempts to teach these techniques, but in my opinion it is hard to motivate these until someone has actually needed to use them to solve problems they're interested in.
• posed 6y ago
  Personal opinion: Mathematics should be learned with a piece of paper, a pencil and a sheet full of problems.
  • saivan 6y ago
    I agree with you 100%! But a good resource is never a bad thing :)
  • intotheabyss 6y ago
    Live on the edge and use a pen
• joeblau 6y ago
  This is one I’ve heard a lot on the Data Skeptic podcast. Great for math and science. https://brilliant.org/ https://brilliant.org/
  • tmhrtly 6y ago
    Has anyone here used it and could comment on its efficacy for people with say, good high school + some college courses knowledge of maths looking to grow? I've seen more than enough adverts for it on youtube but would love to hear thoughts from someone not being paid to hawk it!
• impendia 6y ago
  I am a math professor. In my observation, there is a huge amount of material available on the web, but it isn't very centralized -- especially at the upper levels. My advice would be to get a book on any topic which interests you, read through it, and do a significant number of the exercises. You might try Epp's Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive to buy new, but just buy older editions. Resources like Khan Academy and 3blue1brown are also fantastic, and I have shared some of these with my students. I'd recommend using these as a supplement; if you rely on them solely then you'll develop vague intuition but not much else. Also, with the pandemic, there are a huge number of traditional university courses that have moved online, and you could probably enroll in one for not too much money. Check the RateMyProfessor reviews -- you want a mix of positive reviews claiming the prof inspired them, and negative reviews complaining that work was expected. I have a RateMyProfessor review which complains bitterly that "homework is graded for accuracy and not completion". :)
  • wcarss 6y ago
    With many books, I'm not sure how to verify that I'm actually doing the exercises properly. In the (simple!) maths I took, my misunderstandings often led me to do exercises incorrectly, but to think I'd done them right, or to have half a proof and no idea what insight I was missing. Even when solutions were provided (which was rare!), the path connecting the dots could be foggy. "What made them think to introduce this lemma?" kind of questions. I often needed discussion with others to help figure out my misconceptions and correct them -- so... big ask, but do you have any further suggestions on how to replace talking with a TA, or with a smart group of upper-year friends?
    • impendia 6y ago
      Very good question. This is difficult. One way to do this is to participate on Math Stack Exchange: https://math.stackexchange.com/ https://math.stackexchange.com/ I'd recommend not only asking, but also answering others' questions. It's not the same as having a group of people that you regularly talk to, but it's something. You could also hire a graduate student tutor. For example, here is a list of math grad students at the University of Wisconsin willing to do this: https://www.math.wisc.edu/tutors https://www.math.wisc.edu/tutors An hour every two weeks would go a long way.
• rramadass 6y ago
  I suggest spending less time with online lectures/videos etc. and more time with actual Books. The online stuff should be an adjunct to your study of books. Also it is best if you look at books dealing with a survey of all the relevant topics required for Science/Engineering before delving into specialized ones. To that end, i can recommend the following; Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences by Jordan and Smith - This book is really accessible. Mathematical Methods for Physics and Engineering: A Comprehensive Guide by Riley, Hobson, Bence - A more advanced coverage of topics than the one above. Mathematics for Physicists: Introductory Concepts and Methods by Altland and Delft - The coverage is excellent but somewhat challenging to read.
• swiley 6y ago
  As much as I really hate to say it, youtube seems to have the best collection of recorded math lectures I can find anywhere. OCW has quite a few but only the ones from MIT. One of my professors only uploaded to youtube (and I think he was doing this without the administration knowing, they were generally hostile to recorded lectures and the official policy was that recordings of lectures should never be shared to non students for some reason.) Besides that good math books are usually very cheap. I would highly recommend those over a website.
• laichzeit0 6y ago
  I'd like more math professors to make recordings of their courses. E.g. here is a pure gem [1]. This is a recording of a real analysis course from Rudin's principles of mathematical analysis (aka Baby Rudin aka the architect of many beginning mathematics students' misery). Anyone that's worked through this book knows the world of pain you're about to enter. I'd love if there was a similar recording for say, Charles Pugh's real mathematical analysis. I mean he's still alive, dunno if he still lectures from his book, but why not record one of those? It would be game changing for those who self-study. Here's another request: Terrence Tao does a recording of a measure theory course. Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle. [1] https://www.youtube.com/watch?v=ab41LEw9oiI&list=PLun8-Z_lTkC6qJF1sVh3_Hx7aL6FPd0IN&index=1 https://www.youtube.com/watch?v=ab41LEw9oiI&list=PLun8-Z_lTk...
  • TrackerFF 6y ago
    > Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle. Sorry, but what? You'd be hard pressed to find any single person, in the past 10 years, that has ushered more people into STEM by providing a solid fundamental education, than Salman Khan. I understand that you're wanting more rigorous math, on a higher-level, but still - to blow off KA, 3B1, etc. as a waste of time sounds more ignorant than anything. Of the millions and millions that have seen these those guys, I'm sure a certain % have gotten their "Aha!" moments there, which have helped them tackle on much more comprehensive topics / fields. edit: Just to clarify, I do not think these vids are any replacement for a solid book, just in the way I do not think lectures or tutorials are a replacement. But they can be fantastic aids for your learning. Interactive websites are IMO vastly more efficient at conveying information, compared to static pages (like books, for example).
    • dtornabene 6y ago
      Err, uh, where do you get the idea that Khan academy "has ushered more people into STEM than any single person"? Seriously. I don't even know how you would measure something that.
• Arun2009 6y ago
  If you are in India, NPTEL courses are a possibility, but I've heard that it can be a hit or a miss depending on the lecturer. You get to write regular assignments, and a proctored exam for a certificate.
• artagnon 6y ago
  I've self-taught myself undergraduate-level Mathematics, and am currently enrolled in an advanced Masters program specialized in higher category theory at Université de Paris. Here are some thoughts: First, the amount I learnt on a day-to-day basis from self-studying in my free time pales in comparison to the amount I learnt from a structured course ending with an exam, in which you have to commit to studying 2~4 hours of math every single day. Second, classroom lectures mainly act as a structured table-of-contents for working through various textbooks. The problem sheets they distribute in the tutorials are very helpful, as is the discussion of problems that some students might have got stuck in. Graduate-level math textbooks are fantastic, and the authors have poured 10+ years of their lives writing them. No online course with cute interactive video can substitute them. Having said that, there are some video lectures that can act as good motivation for studying a subject. For instance, Wildberger's lectures on algebraic topology (find them on YouTube) are a great starting point for the subject. You first have to decide on what you want to learn, by looking through various fields, and narrow your scope. Mathematics is a huge discipline, and you have to decide what you like, and work through the prerequisites in a disciplined manner. I cannot emphasize the importance of working through exercises enough. All mathematics textbooks have exercises at the end of each section, a subset of which you must work through. Having said all this, you might find the following site interesting: it contains a lot of unpolished notes from studying various math textbooks, but it requires a lot more work to be useful to a larger audience. Look through it, and pick something you like. On request, I might find the time to add some material. https://artagnon.com https://artagnon.com
  • jkmcf 6y ago
    How long did you self study? Total years and average hours per day? Merci!
    • artagnon 6y ago
      I started in late 2016. Initially, it was just during the weekends. I was a regular at the local coffee shop near my place in Boston: I'd go in with my iPad and some sheets of paper, spend 4~5 hours studying, while constantly consuming coffee. Then, I found a friend who had done a Bachelors in math, and we'd visit the local community college 3~4 times a week, and discuss general math and GRE problems on the blackboard for a couple of hours after work: it was a lot of fun. In mid-2017, I moved to California and spent ~2 hours a day studying by myself, while maintaining a day job writing Haskell and Coq. Then, in late-2019, I quit my job and moved to India to study mathematics full-time (read: 4~6 hours every single day). I started meeting a professor at the local university once a week to discuss my solutions to problems in Miles Reid. We worked through Reid together. I also audited a course in algebraic topology at the university, simultaneously. In mid-2019, I moved to Paris to continue studying part-time (1~2 hours a day) while working on a Coq project. After some shuffles, I found a professor I really liked, and we started working together. He wrote me the primary recommendation for the Masters program. I hope the elaboration was more useful than two numbers.
• rbtprograms 6y ago
  I'm in the same boat as you and I just started taking classes at my local community college/university. Options are affordable and lots of online offerings.
• 21eleven 6y ago
  Is there something like leetcode.com but for math?
  • posed 6y ago
    https://projecteuler.net/ https://projecteuler.net/
• strangattractor 6y ago
  You may try https://mitpress.mit.edu/books/street-fighting-mathematics https://mitpress.mit.edu/books/street-fighting-mathematics. It is free. If you like learning math by programming https://greenteapress.com/wp/think-complexity-2e/ https://greenteapress.com/wp/think-complexity-2e/ also free.
  • strangattractor 6y ago
    I forgot https://ocw.mit.edu/index.htm https://ocw.mit.edu/index.htm Mit Open Courseware also free.
• redwoolf 6y ago
  What sort of mathematics ought one to study if interested in designing programming languages?
• stakkur 6y ago
  I highly recommend http://schoolyourself.org/ http://schoolyourself.org/ over just about anything else (Khan Academy, etc.) It's free, and has a great interactive user experience. Algebra through Calculus.
• isaacaderogba 6y ago
  As an alternative to getting a textbook, I would strongly recommend Krista King's maths courses. They're available through Udemy or her personal website [1][2]. Each section has a 1) written explanation, 2) video explanation with an exercise walkthrough and a 3) set of exercises. Each exercise also has a well-written walkthrough in case you can't solve them. I've been working through them part-time for 4 months now, and it's honestly the first time that maths has clicked for me (I've found that most books tend to skip concepts which leave me lost). [1] https://www.udemy.com/user/kristaking/ https://www.udemy.com/user/kristaking/ [2] https://www.kristakingmath.com/ https://www.kristakingmath.com/