#44 overall
Essence of Linear Algebra
YouTube
10 recommenders · 9 threads · recommended in 5 years, 2017–2026 · score 12.8
A YouTube video series by Grant Sanderson (3Blue1Brown) that builds geometric, visual intuition for linear algebra concepts such as vectors, linear transformations, matrices, determinants, and dot and cross products.
Commenters call it second to none for visual intuition, say it made linear algebra click, and describe its insights as the kind they wish they had been given in college.
Mathematicsbeginnerfreevideo lectures#linear algebra#visualization#vectors#matrices#3blue1brown#sanderson
Recommendations by year
20062026
If anyone needs a longer tutorial, I strongly recommend 3b1b's series here: https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...
The visualizations made things click in a way my Linear 101 course didn't.
I strongly recommend 3blue1brown's intro to linear algebra[0] for quick intuitions, followed by Gilbert Strangs MIT Open Course[1][2] for (much) deeper detail. Strang is a genius, but Sanderson's graphics and intuitions can be helpful early on.
[0] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
[1] https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
[2] https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D
Good recommendations. In addition to the UT, MIT and Stanford courses you recommend above, for developing your visual intuition, 3Blue1Brown's Essence of Linear Algebra video series is second to none. [0]
Another good one is MathTheBeautiful [1] by MIT alum Pavel Grinfeld [2]. He approaches Linear Algebra from a geometric perspective as well, but with more emphasis on the mechanics of solving equations. He has a ton of videos organized into several courses, ranging from in-depth Intro to Linear Algebra courses to more advanced courses on PDEs and Tensor Calculus.
Esp note his video on Legendre polynomials [3] and Why {1,x,x²} Is a Terrible Basis: https://www.youtube.com/watch?v=pYoGYQOXqTk&index=14&list=PL....
Gilbert Strang was Greenfield's PhD advisor: https://dspace.mit.edu/handle/1721.1/29345. Pavel has a clear and precise teaching style like Strang, and he makes reference to Prof's Strang and his MIT course from time to time.
NB: Prof Strang has a new book Linear Algebra and Learning from Data that just went to press and will be available in print by mid Jan 2019. A few chapters are available online now, and the video lectures from the new MIT course should on YouTube in a few weeks. [4]
[0] Essence of Linear Video Series (3Blue1Brown): https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/pla...
[1] MathTheBeautiful https://www.youtube.com/watch?v=pYoGYQOXqTk&index=14&list=PL
[2] https://en.wikipedia.org/wiki/Pavel_Grinfeld
[3] https://en.wikipedia.org/wiki/Legendre_polynomials
[4] MIT Linear Algebra and Learning from Data (2018) http://math.mit.edu/~gs/learningfromdata/
I highly recommend these youtube videos by 3Blue1Brown https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x....
Each short lecture had a 'Why didn't they tell me that in college!' kind of insight. Transformations, determinants, dot products, cross products everything made sense in a visual way.
If you want to get better at geometry a very good start is brilliant.org. They have five great geometry course that's good for learning concepts visually and has some basic exercises, but not enough for drilling.
When it comes to exercises, brilliant.org is lacking in volume. Khan Academy is a great supplement for geometry, single and multivariable calculus although brilliant.org goes a bit further than Khan Academy with Linear Algebra, Group Theory and more.
Khan Academy also has a linear algebra course, but I found it to be kinda crap with no exercises. For linear algebra it's better go with brilliant and 3blue1brown's linear algebra videos, then a good continuation would be Linear algebra done right by Sheldon Axler and also fast.ai's free online course Computational Linear Algebra for Coders.
“Introduction to Linear Algebra” by Gilbert Strang is the book. Recommend getting a used older edition as not much has changed.
His course at MIT is legendary, completely available online https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010...
And there’s so much good linear algebra stuff on YouTube from 3brown1blue.
If you can do one thing now, watch this Veritasium video to disprove the myth that you’re a visual learner: https://youtu.be/rhgwIhB58PA.
* Subscribe to Beast Academy, and do the interesting problems (puzzle and challenge ones). Cost is $15/month, and you should be able to do this fast, so it shouldn't be too high
* Sign up for Alcumus. This is free. Set it to easy. Try problems in each section, and use this to identify gaps. If you find a gap, do a deep dive to address it. If you can't solve a problem independently, solve it using online resources (but put in the wrong answer / give up -- you don't want the ITS thinking you could do it).
* Watch videos on 3B1B, and sign up for Brilliant. Take a few courses.
* This will sound silly, but do sinerider, nandgame, and the fun Khan Academy courses (Advanced JavaScript and Pixar-in-a-Box), and things like this. Math is broad, and those give helpful exposure to a broader range of topics.
https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
https://artofproblemsolving.com/alcumus/
Since you mentioned ML, I assume you'll need linear algebra (LA). I hated it for a long time since the notation abstracts away too many things. You can look at an equation involving matrices, but you cannot imagine how it would be coded. Unlike calculus where numerical approximations and code implementations are relatively obvious.
But I eventually needed to learn it as I have to code something not in Python/Matlab/etc as part of an app and would like to postpone using LA libraries unless absolutely needed for performance. What helped me get the grips on LA is Jeff Chasnov's lectures on youtube and Mike Cohen's book. I would also recommend 3blue1brown for appreciation, if he happens to cover the topic you wish to dive into.
I'm many years older than you, by the way.
I took linear algebra through a community college and had one of those rare, really awesome CC instructors. He had spent most of his career at Cray and later Raytheon and then semi-retired as a community college instructor. He took time to make really great interactive Jupyter notebooks. That combined with 3 brown 1 blue videos really made linear algebra click for me.
My only regret is that I took the class as a six week short course. I think my recall would be better if I had taken the full semester. We covered all the material, but missed out on the longer spaced repetition. Linear Algebra was by far my favorite pure math course, I hope to revisit it soon. Maybe Strang's lectures are the way to do that.
I quickly audited all the courses a few months ago, I find OSSU to be much easier to grasp than teachyourselfcs.com because it doesn't always use modern day MOOC's which makes learning things way quicker
You can learn things by a book sure. But if you go on a udemy or coursea or whatever course, there's always Q/A comments with other people working on the same course and that insight is extremely invaluable so this is why I prefer OSSU over teachyourselfcs.com. I prefer MOOC's because there's also some level of accountability as well, you can go for the certificates too but I don't really care too much about them.
OSSU does have way too many topics just pick 80% of them and you should be okay, depending on what your weaknesses are.
Some course overlap in both so you should focus on those first and foremost. These include things like nand2tetris, 3blue1brown's linear algebra, data structures & algorithms (various choices, sedgewick, skienna, etc).
Do your homework on reddit threads as well before picking one or the other.
I like OSSU because it also tells you what the prereqs are clearly as well.
Currently doing nand2tetris because I have a lack of hardware knowledge and the course is fantastic. Also doing a lot of math courses so I can do mathmatical proofs much easier to understand why one algorithm is better than another, or how to derive it based on whoever invented it etc. I prefer a traditional book for math though, but everything else I prefer MOOC's.
Start here: https://youtu.be/F_Riqjdh2oM
You don't need to know quantum theory necessarily, but you will need to know some maths. Specifically linear algebra.
There are a few youtube courses on linear algebra
For a casual set of video: - https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...
For a more formal approach:
- https://youtube.com/playlist?list=PL49CF3715CB9EF31D
And the corresponding open courseware
- https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010...
Linear algebra done right comes highly recommended
- https://linear.axler.net/
I've never been to high school or college. The last school grade I completed with 7th -- or really just 6th. I can go into that in more detail if you like but there's a lot of personal drama that is irrelevant.
I will say that math is one of those things that you don't need to go to school to learn if you are persistent and passionate enough to learn on your own. There are tons of ways to learn.
First is to determine where you are. For that I highly recommend taking some of Khan Academy's free math courses. They start at the very basics. You will get bored of those.
But after that... I would say to take some things in your life and determine how to apply math. Create your own questions and try to answer them.
When I was 26 I was at the tail end of a janitorial job. I had applied (and learned) math to determine how much cleaning stock would likely be in use each week. Sometimes the math was "wrong" in so much as cleaning stock would be used more frequently or less frequently depending on what events there were that week. But it was a good exercise.
I'd also been writing some software on the side. Software and math are like two peas in a pod. A lot of people will tell you that you don't need to learn math to write software and they might be right for certain kinds of software. But even if you don't need math for software, it will certainly help. I now write software to fly drones and geometry is one of the core requirements.
Beyond the basics are Khan Academy there are plenty (!) of youtube videos from mathematicians who describe some of the simple [0] and more complex [1] concepts. Those have also been handy to me. All you need to do is search one math term that involves what you think you want to learn. A lot of the videos will include links to other videos that are prerequisites. Almost all of them will mention math words that will be new to you and if you search for those math terms you are likely you find other useful information.
Ten years ago I would have recommended that you search Google. Now? Don't do that. Google is full of trash and shit that want to take your money. Use Wikipedia, youtube, and reddit.
I've found 3blue1brown's lessons [0] [1] to be quite insightful for myself and have successfully used knowledge learned from his videos.
[0]: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
[1]: https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVl...
For context I studied physics for about 2 years in university, before I switched to maths with the intention of returning with better mathematical foundations.
That being said let's start with the maths you will need to be comfortable with:
- Complex Numbers (e^(i*theta))
- Linear Algebra (Matrix Multiplication, Basis of a vector space, Finding Eigenvalues)
- Calculus and some Differential Equations (Taylor Expansions, Solving DEs)
- Probability, Expectation values and Distributions
That's probably what you'll need to dive into textbooks. For a deeper understanding, it would help to know these (worry about these later):
- Analysis (My math major friends say that functional analysis is required later on)
- Hamiltonian Mechanics (QM is littered with Hamiltonians)
- Group theory (if you want to get into Particle Physics)
I'd also recommend having a good grasp on classical mechanics because quantum mechanics builds on it. On my todo list is to review this using:
- The Feynman Lectures on Physics, Volume I available at https://feynmanlectures.caltech.edu/I_toc.html
- Structure and Interpretation of Classical Mechanics by Sussman and Wisdom available at https://mitpress-request.mit.edu/sites/default/files/titles/...
As for books, at uni we used:
- Quantum Mechanics by McIntyre, Manogue and Tate during 2nd year
- A Modern Approach to Quantum Mechanics by Townsend during 3rd year
They generally do a good job covering the material and explain things well.
As for other resources, I haven't read these but they are generally recommended:
- Introduction to Quantum Mechanics by David Griffiths (I liked the author's writing style in his EM book)
- The Feynman Lectures on Physics, Volume III available at https://feynmanlectures.caltech.edu/III_toc.html
- Quantum Computing Since Democritus by Scott Aaronson (I was recommended this for understanding why complex numbers are used in QM)
Some other miscellaneous resources:
- http://www.staff.science.uu.nl/~gadda001/goodtheorist/primar...
- https://www.youtube.com/3blue1brown (The essence of Linear Algebra series is excellent)
- https://ocw.mit.edu/index.htm (In case you want to watch lectures)
- https://physicstravelguide.com/
All of this is at an undergraduate level. It's probably best to grab one of the books and start running through, consulting the others when you want another explanation.
Let me know if you have any further questions. QM is damn cool dude, I hope you have a fun time delving into it.
It's interesting how content discovery has remained ad-hoc despite the arrival of ed-tech platforms like Coursera or EdX. People still prefer to ask for best books, courses, podcasts, cheatsheets on Slack/Discord/Twitter etc.
I think this has to do with the conflict of interest. Any platform that creates its own educational content, necessarily becomes bad at content _curation_. For ex, 3Blue1Brown has amazing series on linear algebra and calculus but we don't find Coursera pointing to it.