#5 overallClassic
18.06 Linear Algebra (Gilbert Strang)
MIT OpenCourseWare
78 recommenders · 76 threads · recommended in 18 years, 2009–2026 · score 126.7
MIT's undergraduate introductory linear algebra course taught by Gilbert Strang, covering matrices, vector spaces, eigenvalues, and the singular value decomposition, with video lectures, syllabus, and problem sets published through MIT OpenCourseWare.
Commenters call it the best linear algebra resource available, praising Strang's intuitive, unassuming lecturing style and how it clarifies concepts like the SVD and the four fundamental subspaces.
Recommendations by year
20062026
I really recommend Professor Gilbert Strang's linear algebra course and also would check out any Michael Penn videos, both on YouTube, but for linear algebra, the Strang/MIT course is the best resource anywhere that I know. The Gilbert Strang video series on linear algebra includes the 18.06 course, as well as an 18.06B or something like that where he goes into detail about the SVD and ML algorithms like gradient descent.
Generally if you're struggling with a math paper on the first or second page, no point in fighting it; gotta come back after you have the prerequisites. Nobody is born knowing this stuff, and also, all branches of math contain endless piles of really easy-to-describe but hopelessly difficult problems so never feel bad if you don't know how to solve a problem or even understand what you are reading. Just take your time, learn what you need, come back, a bit more hopefully makes sense, learn still more, and over time more things will become familiar.
Try these:
An interactive website https://seeing-theory.brown.edu that takes you through some of the most critical probabilities and statistics concepts.
Statistics 110: Probability
If you want a more advanced overview of Probabilities and Statistics, this course from Harvard University is an excellent introduction:
https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6...
This is MIT Course 18.06, taught by Professor Gilbert Strang.
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
One of the best linear algebra courses that you’ll ever find.
Essence of Calculus
This is Grant Sanderson’s excellent take on calculus:
https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...
Gilbert Strang's lectures on Linear Algebra [1]. Prof Strang is an amazing lecturer with a unassuming style. He's the expert on Linear Algebra and makes the topic so much approachable.
Ken Joy's lectures on Computer Graphics [2]. Prof Joy is another amazing lecturer, making the Computer Graphics topics seeming easy.
Stanford CS221 Learn AI (2019) by Percy Liang and Dorsa Sadigh. Both professors are great lecturers. Andrew Ng's ML class was great, but it was more academically tuned. CS221 is more on the practical side and is more updated as ML is progressing fast.
Micromouse 2021-2022 by UCLA [4]. It's a short series taught by graduate students and probably it's incomplete, but the content and teaching are amazing. I wish I had this kind of class when I was in school. The teaching and materials are very approachable and easy to understand. It shows how basic electronic components and basic circuitry work. It shows how to put them together and how to write simple programs to control the components. The end result is a robotic mouse that can traverse mazes with seemingly intelligence.
[1] https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D
[2] https://www.youtube.com/watch?v=01YSK5gIEYQ&list=PL_w_qWAQZt...
[3] https://www.youtube.com/watch?v=J8Eh7RqggsU&list=PLoROMvodv4...
[4] https://www.youtube.com/playlist?list=PLAWsHzw_h0iiz1EQEvQ9n...
Edit: added [4]
I did Strang's linear algebra course[0] (link goes to Youtube playlist of lectures) several years after graduating and recommend it highly. I was looking for refresher but I gained a deeper understanding of several important concepts; in particular it's fair to say I barely understood, or perhaps even misunderstood, SVD until Strang. If you're not sure if you need something like that, I suggest doing something like testing yourself on this video[1] or the MIT problem sets[2] it's easy to tell yourself that you "know" linear algebra when it would be closer to the truth to say that you used to know linear algebra, but can't answer even basic questions today. After Strang, Golub's book on Matrix Computations is also really incredible.[3]
[0]: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C...
[1]: https://www.youtube.com/watch?v=Cll03FUxjuk
[2]: https://ocw.mit.edu/courses/mathematics/18-650-statistics-fo...
[3]: https://www.amazon.com/Computations-Hopkins-Studies-Mathemat...
I will try to list resources in a linear fashion, in a way that one naturally adds onto the previous (in terms of knowledge)
[PREREQUISITES]
First things first, I assume you went to a highschool, so you don't have a need for a full pre-calculus course. This would assume you, at least intuitively, understand what a function is; you know what a polynomial is; what rational, imaginary, real and complex numbers are; you can solve any quadratic equation; you know the equation of a line (and of a circle) and you can find the point that intersects two lines; you know the perimiter, area and volume formulas for common geometrical shapes/bodies and you know trigonometry in a context of a triangle. Khan Academy website (or simple googling) is good to fill any gaps in this.
[BASICS]
You would obviously start with calculus. Jim Fowlers Calculus 1 is an excellent first start if you don't know anything about the topic. Calculus: Single Variable https://www.coursera.org/course/calcsing is the more advanced version which I would strongly suggest, as it requires very little prerequisites and goes into some deeper practical issues.
By far the best resource for Linear Algebra is the MIT course taught by Gilbert Strang http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr... If you prefer to learn through programming, https://www.coursera.org/course/matrix might be better for you, though this is a somewhat lightweight course.
[SECOND STEP]
After this point you'd might want to review single variable calculus though a more analytical approach on MIT OCW http://ocw.mit.edu/courses/mathematics/18-01sc-single-variab... as well as take your venture into multivariable calculus http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable...
Excellent book for single variable calculus (though in reality its a book in mathematical analysis) is Spivaks "Calculus" (depending on where you are, legally or illegally obtainable here http://libgen.org/ (as are the other books mentioned in this post)). A quick and dirty run through multivariable analysis is Spivaks "Calculus on Manifolds".
Another exellent book (that covers both single and multivar analysis) is Walter Rudins "Principles of Mathematical Analysis" (commonly referred to as "baby rudin" by mathematicians), though be warned, this is an advanced book. The author wont cradle you with superfluous explanations and you may encounter many examples of "magical math" (you are presented with a difficult problem and the solution is a clever idea that somebody magically pulled out of their ass in a strike of pure genius, making you feel like you would have never thought of it yourself and you should probably give up math forever. (Obviously don't, this is common in mathematics. Through time proofs get perfected until they reach a very elegant form, and are only presented that way, obscuring the decades/centuries of work that went into the making of that solution))
At this point you have all the necessery knowledge to start studying Differential Equations http://ocw.mit.edu/courses/mathematics/18-03sc-differential-...
Alternativelly you can go into Probability and Statistics https://www.coursera.org/course/biostats https://www.coursera.org/course/biostats2
[FURTHER MATH]
If you have gone through the above, you already have all the knowledge you need to study the areas you mentioned in your post. However, if you are interested in further mathematics you can go through the following:
The actual first principles of mathematics are prepositional and first order logic. It would, however, (imo) not be natural to start your study of maths with it. Good resource is https://www.coursera.org/course/intrologic and possibly https://class.stanford.edu/courses/Philosophy/LPL/2014/about
For Abstract algebra and Complex analysis (two separate subjects) you could go through Saylors courses http://www.saylor.org/majors/mathematics/ (sorry, I didn't study these in english).
You would also want to find some resource to study Galois theory which would be a nice bridge between algebra and number theory. For number theory I recommend the book by G. H. Hardy
At some point in life you'd also want to go through Partial Differential Equations, and perhaps Numerical Analysis. I guess check them out on Saylor http://www.saylor.org/majors/mathematics/
Topology by Munkres (its a book)
Rudin's Functional Analysis (this is the "big/adult rudin")
Hatcher's Algebraic Topology
[LIFE AFTER MATH]
It is, I guess, natural for mathematicians to branch out into:
[Computer/Data Science]
There are, literally, hundreds of courses on edX, Coursera and Udacity so take your pick. These are some of my favorites:
Artificial Intelligence https://www.edx.org/course/artificial-intelligence-uc-berkel...
Machine Learning https://www.coursera.org/course/ml
The 2+2 Princeton and Stanford Algorithms classes on Coursera
Discrete Optimization https://www.coursera.org/course/optimization
Convex Optimization https://itunes.apple.com/itunes-u/convex-optimization-ee364a... https://itunes.apple.com/us/course/convex-optimization-ii/id...
[Physics]
http://theoreticalminimum.com/courses
http://ocw.mit.edu/courses/physics/
Expanding on my previous comment (https://news.ycombinator.com/item?id=8444705), here are some excellent, tried-and-tested resources to help you learn the fundamentals.
1. Probability and stats: For probability, work through John Tsitsiklis's MIT OCW course 6.041. There is also an archived version of the course available on EDX. Norman Matloff's book (http://heather.cs.ucdavis.edu/~matloff/132/PLN/ProbStatBook....) approaches stats from a CS practitioner's point of view (lots of sample simulation code in R), and has intuitive explanations of many different statistical concepts. For Hypothesis testing, checkout the courses Mathematical Biostatistics - 1 and 2 on Coursera.
2. Linear Algebra: Gilbert Strang's OCW lectures / course notes is hands down the best resource. But depending on your mathematical background, the lectures can be a bit long-winded.
3. Programming proficiency: For algorithms, Robert Sedgewick's algorithms course on Coursera has excellent videos. His textbook is very well written too. I really like his style of writing actual working code for each algorithm he describes (in contrast to say, CLRS): i find his code samples rather elegant and worthy of study. For learning object orientation and design patterns, the best way is to write large programs and read the book "Head First Design Patterns" as you do so.
The aim is to develop an ability to think with a statistical / algorithmic lens. Many real world phenomena are stochastic in nature. Modelling them by simulation and measuring and drawing confidence intervals around your measurements must become second nature. When confronted with an image / text processing problem, representing you data as vectors and manipulating them must be natural. While writing large programs, being aware of design considerations such as preferring composition must come naturally to you. Of course, you should be able to always recognize when a computation is O(n^2) vs O(n log(n)) vs O(2^n).
Once you are done with that, all you need to do is work through Andrew Ng's Machine Learning course and compete in a few Kaggle competitions / build some ML related side projects. Congratulations, you are now a data scientist good enough to work at most places in the tech industry!;)
While in university I took linear algebra and didn't understand much of it, especially on a deeper level. Then I stumbled upon Gilbert Strang's linear algebra lectures and watched them... After watching his explanations I got all of it and actually understood things at a much higher level. It was a sweet revelation and today I find linear algebra beautiful. I highly recommend watching his linear algebra lectures: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
Edit: I also find linear algebra to be useful and much more important for programming/CS than calculus, especially for implementing various ranking algorithms (e.g. Google's PageRank algorithm is mostly rooted in linear algebra).
not sure about its specific applications to quantum mechanics, but I worked through MIT OpenCourseWare's Linear Algebra class (taught by Gilbert Strang) and I thought it was amazing. The lectures are very very good.
Ok, boy, I'm also reviewing LinAlg textbooks as we speak. Coming in with a similar interest for ML / AI.
I've done math on KA academy up to linear algebra, with other resources / textbooks / et al. depending on the topic.
People will recommend 3B1B, Strang (MIT OCW Lin Alg lessons). For me the 3B1B is too "intuitionist" for a first serious pass, and Strang can be wonderful but then go off on a tangent during a lecture that I can't follow, it's a staple resource that I use alongside others.
LADR4e is also nice but I can't follow the proofs there sadly (yet). There is also 'Linear Algebra done wrong', as well as the Hefferon book, which all end up being proof-y quite quickly. They seem like they'll be good for a second / third pass at a linear algebra.
Side note - for a second or a third pass in LA it seems there is such a thing as 'abstract linear algebra' as a subject and the texbooks there don't seem that much harder to follow than the "basic" linear algebra ones designated for a second pass.
I've gotten off to the most of a start with ROB101 textbook (https://github.com/michiganrobotics/rob101/blob/main/Fall%20...), up until linear dependence / independence, along the MIT Strang lectures. ROB101 is nice as it deals with the coding aspect of it all, and I can follow in my head as I am used to the coding aspect of ML / AI.
I also have a couple obscure eastern european math texbook(s) for practice assignments.
Most lately I have been reviewing this course / book - https://www.math.ucdavis.edu/~linear/ (which has cool notes at https://www.math.ucdavis.edu/~linear/old), and getting a lot of mileage from https://math.berkeley.edu/~arash/54/notes/.
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/
A lot of it depends on what exactly you want to do (in|with) tech. Plenty of developers get by with high-school algebra. At the more extreme end, if you want to write software for weather forecasting or other fields using numerical computation, simulation, etc., then you probably need a background roughly equivalent to a degree in maths. And there's a lot of "in between" those extremes.
For my money though, I'd say a good starting point would be:
1. Calculus through Calc III (as the Calculus sequence is typically structured in American universities)
2. Linear Algebra
3. Differential Equations
4. Probability Theory
5. Statistics
Sidebar: if you specifically want to work with cryptography / cryptanalysis, you probably want to study number theory, abstract algebra, and probably a bunch of other stuff that I don't know anything about. :-)
Resources? Hmm... there's a whole world of stuff out there, and plenty of previous HN threads discussing various books, blogs, courses, videos, etc. But you could do worse than using Khan Academy, and the ProfessorLeonard channel on Youtube. Other good Youtube channels include Michael Penn, 3blue1brown, blackpenredpen, Organic Chemistry Tutor, MathMajor (which is still Michael Penn - he has two channels), NancyPi, and MIT's OCW stuff (Gilbert Strang in particular has great video lectures on Calculus and Linear Algebra).
Also note that if you're self-studying (as opposed to taking a class at university) then it mostly doesn't matter what edition of books you use. And you can find used copies of older editions of maths books for pretty much every topic imaginable for pretty cheap. Search on Alibris and then sort by "Price - Low to High" and you'll usually be able to find a book on your topic for $2.00 - $5.00 or so. If you prefer ebooks there are legitimately available free books on most subjects again, and there's always the pirate e-book sites if you want to go that route.
Khan academy will teach you all of pre-k, high-school, pre-calc, calculus and infinite series pretty well. mathsisfun.com is a great resource if that's ever lacking. High school physics on khan is good to give you a practical application of the concepts if they seem too abstract.
I found Strang's youtube lectures the best for linear algebra along with 'vector maths for 3d graphic'. Khan's linear algebra course seems like more a collection of practical things you can do with linear algebra rather than a coherent cource but it's still a great resource.
Khan academy's multi-variable calculus is good enough to give you a reasonable grasp, but I'd call it a good complement rather than sole resource.
I've tended to go through the cycle of watching the lectures, then doing the exercises, going forward, going back after a few months to ensure I understand the whys and not just the hows, and then writing my own notes. Machine Learning et al is a great practical application of all this maths.
Because the people best placed to assess a candidate for a role are those who know the duties of that role in detail. Much of what's taught at university has marginal benefits beyond a core, much smaller, cirriculum.
Take something fairly complex like game development, say. Now: do some linear algebra, geometry, programming, etc. assessment in a wholistic way. Maybe a quick quiz for initial filter, then a hackathon with applicants (or w/e).
People filtered by the quiz can be directed to the now many resources for self-study (you can easily do an entire degree via MIT lectures, etc. -- i know i did, i barely attended lectures and just watched stanford/MIT classes; gilbert strang's LA course several times).
If you really want to be a game dev, and can't self-study after a failed attempt and a year or so of reflection then go to university. Now you know it's for you, that it really will help, etc. They're providing a service you actually need.
Strang's OCW lectures on linear algebra are excellent. From a distance, he truly seems like a professor that was at least as interested in educating the next generation as he was making his own discoveries.
I personally consider Linear algebra to be foundational in AI/ML. Intro to Linear algebra, Gilbert Strang. And his free course on MIT OCW is fantastic too.
While having strong mathematical foundation is useful, I think developing intuition is even more important. For this, I recommend Andrew Ng's coursera courses first before you dive too deep.
Don't read books, take classes instead - Khan Academy, MIT 18.01, 18.02, 18.06, Harvard Stat100 etc.
I believe I used this back in the day when preparing the LA course at uni, A First Course in Linear Algebra: http://linear.ups.edu/download.html .
Also I'm sure it's been mentioned here already, but the MIT Linear Algebra course by Gilbert Strang was absolutely phenomenal. Really made it click for me.
Just chiming in to say that you can dive directly into Strang's Youtube lecture series, without a book or anything else; like, an immediate next step you could take if you wanted to is just to pull up his first lecture right now and watch it. (I mostly watched him at 2.5x speed).
“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.
I’ve been watching the 18.06SC linear algebra course on MIT OpenCourseWare (taught by Gilbert Strang) and it’s really great - one of the best courses I’ve ever seen. I’ve just started the follow-up course that covers applications.
Agree, I said starting point assuming that he has some basic knowledge as he is struggling so he must know something.
For more advanced linear algebra I would recommend the class from Prof. Gilbert at MIT.
https://youtube.com/playlist?list=PLE7DDD91010BC51F8
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
What is your recommendation?
Take university classes - it's the same material, you just won't get any academic credits. MIT Opencourseware has Single Variable Calculus (18.01), Multivariable Calculus (18.02) and Linear Algebra (18.06). That's plenty of material to get started with. Watch the lectures, follow along with the textbook, do the exercises.
If you're concerned that you don't have some of the prerequisites like high school algebra or trigonometry, Khan Academy have a pre-calculus course - start there.
I switched to data science from an unrelated field and had to do a lot self-study like this to catch up on my math.
IMO 3B1B's course for linear algebra is not good for Learning linear algebra, but it is great for Augmenting your geometric intuition. I don't believe his course ever claims any different.
I'd recommend instead Gilbert Strang, who teaches a full and well reputed course over at MIT.
https://www.youtube.com/watch?v=Cx5Z-OslNWE&list=PLUl4u3cNGP...
- MIT 18.06 - https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... - The lectures and the textbook for the course are a default recommendation.
- Linear Algebra Done Right - This is a textbook, there are also youtube videos from the author - https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS...
- Khan Academy - https://www.khanacademy.org/math/linear-algebra - Also a good place to start, very accessible, missing some of the more advanced material.
- 3blue1brown - https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... - These videos are good but they're more of a nice overview than a way to learn.
I know that you've decided to take a gap year but my advice for next steps is actually to take undergraduate courses in single variable calculus, multivariable calculus, linear algebra and probability theory. All four of these are available online for free (course names: MIT 18.01, 18.02, 18.06, Harvard Stat110).
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
Gilbert Strang's linalg lectures on MIT OCW are amazing.
You can not really appreciate the beauty of machine learning without the maths behind it. I don't know what your maths background is but if I had to recommend, a good understandig of Linear Algebra makes all the difference when you read ML papers. I would storngly recommend Gilbert Strang's two courses on Linear Algebra [1] and Matrix Methods[2].
Everything else that mostly cares about application is easy to find on the internet (see the r/MachineLearning subreddit).
[1] https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... [2] https://ocw.mit.edu/courses/mathematics/18-065-matrix-method...
Oh yeah Gilbert Strang's original course is amazing , https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
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.
Try Gilbert Strang's course at MIT, it's publicly available in video format, and starts from basic principles.
This course was a godsend for me.
Before I dropped out of FSU, I managed to rope myself into two math classes (Complex Variables and Game Theory), both of which had a strict requirement of Linear Algebra, which I hadn't taken.
I was a bit panicked because it was a bit too late to sign up for anything else, and so I binged through this MIT course, and learned just enough to get permission from both the professors to still let me take the classes. It definitely would have been better to have taken linear algebra directly, but having this as a resource was super valuable.
I haven't watched the 1999 version (the one linked) of this class, but I have watched Gilbert Strang's newer lectures on this subject and they were absolutely wonderful. The book is great as well.
Don't watch these just because it's from MIT, watch them just because of Strang!
Strang is an excellent teacher and this an effective course for coming up to speed in Linear Algebra fundamentals.
I watched every lecture and did most of the homeworks a couple of summers ago in preparation for taking grad ML courses at Carnegie Mellon (10-601 Intro and 10-605 Scalable ML). The foundations that I built from Strang's course were essential to my success later.
I’ve watched Gilbert Strang’s Linear Algebra videos:
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
Highly recommended.
Does he have videos that go with his calculus book?
https://www.freetechbooks.com/calculus-t1345.html
Gilbert Strang's Linear Algebra course is often recommended, but I also recommend a set of lectures on YouTube from Technion with Aviv Censor: https://www.youtube.com/watch?v=aefKXYYXT6I&list=PLW3u28VuDA... since it's very beginner friendly and there's a lot of step-by-step explanation.
Start small. I would look at Stat 110 from Harvard, Strang's OCW lectures, and the intro calculus MIT course.
When you're done with that, it'll be easy to see where you want to go next.
Those are all linear algebra concepts, I would suggest Gilbert Strang's series of lectures which can be found on YouTube. They should be fairly accessible without prerequisites.
Execution of a determinant. [0]
Always love it when a professor can bring in some comic relief in the midst of a very heavy math topic. The students seem to enjoy it. I am self-teaching myself background math for preparing me to the likes of PRML-Bishop, and I wholeheartedly recommend his Linear algebra course available on MIT Courseware[1] coupled with his book[2]
[0] https://www.youtube.com/watch?v=amv58LCqCMI [1] https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... [2] https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-S...
The Linear Algebra OCW is great if you do all the exercise and read the book as you study. For Calculus it's not so great, though the ODE course is fine.
This kind of courses from UPenn are really good if you need to refresh single variable, though I did an older version were all the courses were given together than I can't find in the current Coursera: https://www.coursera.org/learn/single-variable-calculus
I agree, Strang's Linear Algebra course is excellent. I worked through the entire course in March/April this year.
I just completed my final exam at CMU in their graduate intro to ML class (10-601). Having gone through the LA course was essential to my success. But equally important (if not more) to ML is a solid foundation in probability.
His linear algebra video lectures from 1999 are fantastic: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
I used them ~2006 when I was college. Someone I know who just graduated this year in mechanical engineering also found and used them independently from me.
In my social circles, we've always talked about Gilbert Strang as the best math professor who never actually worked at the university we went to.
Forever grateful to this man. 18.06 is my all time favorite online course, it's hard to beleive it was recorded so many years ago.
search for the LA course by "maththebeautiful" on YouTube. Also check out Gilbert Strang's MIT lectures.
I just realized there's a deep connection among your recommendations...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 I've heard him reference Prof's Strang's courses before but didn't make the connection. Good trees produce good fruit. The small world graph and the truth of that never ceases to amaze. Good trees, good stuff.
His videos on linear algebra are excellent, but they are not a complete resource. If you want a comprehensive resource, search for the LA course by "maththebeautiful" on YouTube. Also check out Gilbert Strang's MIT lectures.
The video lectures of Prof. Gilbert Strang’s linear algebra class at MIT are very good: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
He's an amazing teacher and conveys a lot of intuition + makes even complicated ideas look straightforward.
Currently enjoying the 2017 lectures (and I bought the text) for McElreath's bayesian stats course:
http://xcelab.net/rm/statistical-rethinking/
Strang's MIT OCW Linear Algebra is pretty good. Probably also needs the textbook.
John Tsitsiklis' MITx edx Probability intro course is probably the best course I've taken anywhere and better than anything I did in person at university. I didn't buy the text for this one though I probably should.
Robert Sapolsky's Human Behavioral Biology Stanford lectures are well worth watching. https://www.youtube.com/playlist?list=PL848F2368C90DDC3D
This is kind of a masters degree course i created for myself to get knowledge of Machine Learning from bottoms up
First, you need a strong mathematical base. Otherwise, you can copy paste an algorithm or use an API but you will not get any idea of what is happening inside Following concepts are very essential
1) Linear Algebra (MIT https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... ) 2) Probability (Harvard https://www.youtube.com/watch?v=KbB0FjPg0mw )
Get some basic grasp of machine learning. Get a good intuition of basic concepts
1) Andrew Ng coursera course (https://www.coursera.org/learn/machine-learning)
2) Tom Mitchell book (https://www.amazon.com/Machine-Learning-Tom-M-Mitchell/dp/00...)
Both the above course and book are super easy to follow. You will get a good idea of basic concepts but they lack in depth. Now you should move to more intense books and courses
You can get more in-depth knowledge of Machine learning from following sources
1)Nando machine learning course ( https://www.youtube.com/watch?v=w2OtwL5T1ow)
2)Bishops book (https://www.amazon.in/Pattern-Recognition-Learning-Informati...)
Especially Bishops book is really deep and covers almost all basic concepts.
Now for recent advances in Deep learning. I will suggest two brilliant courses from Stanford
1) Vision ( https://www.youtube.com/watch?v=NfnWJUyUJYU )
2) NLP ( https://www.youtube.com/watch?v=OQQ-W_63UgQ)
The Vision course by Karparthy can be a very good introduction to Deep learning. Also, the mother book for deep learning ( http://www.deeplearningbook.org/ )is good
Start with Strang's MIT OCW Linear Algebra course: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...
You really only need to know arithmetic to get started.
Use Anki to create flash-cards so that you learn faster and don't forget.
https://apps.ankiweb.net/
Also, manual calculation is fundamentally how you learn mathematics. Following along is a first step, but is not good enough to learn the material. You need to do the calculations and run into problems, so you can re-create the knowledge in your brain.
EDIT> Take Coursera's Learning How to Learn Course. It sounds flaky, but will accelerate all of your other learning, and help with procrastination as well.
https://www.coursera.org/learn/learning-how-to-learn
For anyone who wants to learn linear algebra, I highly recommend Gilbert Strang's book and course from MIT: https://www.youtube.com/watch?v=ZK3O402wf1c.
I'd also heartily recommend Gilbert Strang's Linear Algebra video lectures (OCW MIT). They seem to have the same goal--to develop a very strong geometric intuition.
Check out Gilbert Strang's Linear Algebra course[0]. Material is of superior quality.
[0] https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algeb...
There are many excellent courses available online if you wished to take a look.
See MIT OCW Scholar's Linear Algebra offering: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algeb...
Take a look at the final exam and see if it seems like something you've seen. If not, I strongly urge you to consider studying the subject.
A book that shows linear algebra's applications at a more advanced level is Strang's Computational Science and Engineering: http://math.mit.edu/~gs/cse/
Recently I have taken it upon myself to gain a basic understanding of philosophy and linear algebra. I found this primer book (http://www.qcc.cuny.edu/SocialSciences/ppecorino/INTRO_TEXT/...) and I try to read it when I have some free time.
For linear algebra, I have been watching this MIT OpenCourseWare lecture series taught by Gilbert Strang: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algeb...
MITOCW is a great place for anyone looking to expand on their current knowledge base and an alternative for those seeking to take a course that they did not have the opportunity to take in college.
Strang's text is also great, and you can take the course via MIT OCW Scholar from the man himself.
For those wanting a more mathematical perspective (versus engineering/applied science), there's Axler's Linear Algebra Done Right.
For the programmers in the audience, another fun and illuminating (and cheap!) text is Klein's Coding the Matrix.
For Calculus check Coursera - the Ohio State course if you really don't know absolutelly anything, then do the Penn State course(s) Calculus in a Single Variable
For Linear Algebra check Gilbert Strang's course on MIT OCW
For Probability/Statistics either John Tsitsiklis' course on MIT OCW (or even better on edX when it re-runs) or Harvard's Statistics 110: Probability course on youtube
The level of multivar calculus you'll need is really minimal, just google these terms "partial derivative", "total derivative", "differentials and integrals commute" ("Symmetry of second derivatives", "Fubini's theorem") or take the vector calculus course from MIT OCW
I have worked a bit with Strang and I love the intiution that his lectures provide but I did not finish the full course :)
I initially wanted to suggest Linear Algebra from Foundation to Frontiers [1] as it had an accompanying book [2] from Edx, but I had no experience in that, so checked up a bit online and outside their course website, they had not so good reviews [3]. So I am providing the links for you to decide yourself. Another answer on quora [4] suggests Coding the Matrix from Coursera, which is supposed to be rigorous in algorithms with excellent assignments in real world applications. So may be that is your cup of tea.
[1] https://www.edx.org/course/linear-algebra-foundations-fronti...
[2] http://ulaff.net/
[3] https://www.quora.com/Which-online-course-for-linear-algebra...
[4] https://www.quora.com/If-linear-algebra-is-so-important-for-...
If you are interested in this stuff, check out Strang's Linear algebra course lectures (mit opencourseware iirc).
He goes through SVD and FFT in terms of matrices. Really illuminating course.
The possibility of deep NLP suggest that there are tremendous opportunities for building a personal assistant. For Deep NLP, I would suggest course CS224D at Stanford on YouTube (going on now but also delivered last year: https://www.youtube.com/watch?v=kZteabVD8sU
For Deep NLP, you will need to be solid on linear algebra and machine learning. For introduction to machine learning, check out Andrew Ng at Coursera: https://www.coursera.org/learn/machine-learning and my favorite talks on Linear Algebra are the ones done by Gilbert Strang: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
For web crawling, there are plenty of open source libraries. If you are not familiar with it, check out the Common Crawl: http://commoncrawl.org/ This is a great source of data to crawl.
If you focus solely on NLP and data from the Common Crawl (or even Wikipedia), then you will see where you stand as the smoke clears and you feel comfortable with the state of the art techniques.
Ignore all the naysayers. The good news is that it has never been easier to get started in deep NLP. Once you have the experience of training a model and seeing how well it works, you can decide on the next steps. Perhaps, you will find a niche that is not well-served that you can go after as a first step of a personal assistant.
Good luck.
A couple of friends recommended these:- (Not sure if they are relevant though for deep learning specifically)
1) http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... 2) https://www.khanacademy.org/math/linear-algebra/vectors_and_...
If anyone knows anything else (relevant to deep learning) could you please share :)
Sure, a couple things.
(I'm assuming you're comfortable with multivariable calculus.)
Andrew Ng's coursera course is good.
PRML (pattern recognition and machine learning) by bishop is good, and has a useful introduction to probability theory.
You also want a good grounding in linear algebra. Strang is basically the authority on linear: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
You want a strong grounding in probability theory and statistics. (This is the basic language and intuition of the entire field.) I don't have as many preferences here (although its the most important); someone in this thread pointed to a course on statistical learning @ stanford that's good.
A good understanding of optimization is helpful. Here's a link that leads to a useful MOOC for that: http://stanford.edu/~boyd/cvxbook/
there's a lot of other stuff (markov decision processes, gaussian processes, monte carlo methods come to mind) that is useful that I'm not pointing to, but if you've hit the other stuff here then you'll probably be able to find out those things.
If you're into it, https://www.coursera.org/course/pgm is good but not vital.
You may want to know about reinforcement learning. This answer does better than I can: https://www.quora.com/What-are-the-best-books-about-reinforc...
Deep learning seems popular these days :) (http://www.deeplearningbook.org/)
Otherwise, it depends on the domain.
For NLP, there's a great stanford course on deep learning + NLP (http://cs224d.stanford.edu/syllabus.html), but there's a ton of domain knowledge for most NLP work (and a lot of it really centers around data preparation).
For speech, theoretical computer science matters (weighted finite state transducers, formal languages, etc.)
For vision, again, stanford: (http://cs231n.stanford.edu/syllabus.html)
For other applications, well, ask someone else? :)
Also:
arxiv.org/list/cs.CL/recent arxiv.org/list/cs.NE/recent arxiv.org/list/cs.LG/recent arxiv.org/list/cs.AI/recent
EDIT: unfortunately, there's also a lot of practitioner's dark art; I picked a lot up as a research assistant, and then my first year in industry felt like being strapped to a rocket.
Dr. Strang's linear algebra course is absolutely amazing: http://web.mit.edu/18.06/www/videos.shtml
https://en.wikipedia.org/wiki/Gilbert_Strang
I can highly recommend Gilbert Strang's Linear Algebra course, available as video lecture series [1]
[1] http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
For linear algebra check out Prof. Gilbert Strand's course on MIT OCW. He's great at explaining the material and the course resources are comprehensive.
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
If you want more, I can definitely recommend the video lectures from MIT's linear algebra course by Prof Gilbert Strang:
http://web.mit.edu/18.06/www/videos.shtml
I know it's not related to this but if anyone has not watched the Linear Algebra lectures by Gilbert Strang of MIT. They are definitely worth a look as a strong foundation in Linear Algebra never hurt anyone. (http://web.mit.edu/18.06/www/videos.shtml)
Also available on iTunes U.
His lectures are wonderful! In college I skipped my regular Linear Algebra lectures, and used the time slot in my schedule to watch his MIT lectures instead.
I ended up scoring one of the highest grades in the class.
I really can't agree with this strongly enough. I had enough Calculus and Differential Equations courses to kill a horse in college (Chemistry major) and I've never used that knowledge once in my entire programming career. But I find uses for linear algebra and matrices in coding all the time. Thank god Strang's excellent course is available online for free.
One approach to getting a list of topics is to look at the degree requirements for a couple of universities. I'm wrapping up a similar project, and here's what I included, along with some resources I used:
* Algorithms (CLRS, Skiena)
* Databases (db-class.org, any text by C.J. Date)
* Probability, Statistics, and Combinatorics
* Programming Languages (I liked Grossman's course on Coursera)
* Linear Algebra (http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...)
* Natural Language Processing (Coursera has several courses)
* Machine Learning/Information Retrieval/Data Mining (I used a couple books, Mining Massive Datasets and Data-Intensive Text Processing with MapReduce being the two I'd recommend)
* Networking (Coursera has a good course)
* Operating Systems (https://www.youtube.com/watch?v=XgQo4JkN4Bw&list=PL62A66DDD3...)
* Distributed Systems (I read Tanenbaum's book)
* Computability
This is what was recommended to me:
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
For Linear Algebra, I'd humbly suggest Gilbert Strang's Introduction to Linear Algebra. This is the companion book to the lectures here: http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...
I'm currently going back and learning linear algebra from the excellent MIT OCW course [1]. I somehow didn't have to learn linear in the course of a CS degree at a big state school. Focusing solely on learning this one subject has allowed me to get the subject at a much deeper level than learning enough to pass a test.
I'm hoping to move on to statistics, which I slept through because I was an immature shit-head my sophomore year.
Then a review multivariable and diff-eq, and the end goal is to do the full Stanford Machine Learning class, taught by Andrew Ng [2]. I also really want to tackle "Underactuated Robotics", which is another MIT OCW course.[3]
[1] http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...
[2] http://see.stanford.edu/see/courseinfo.aspx?coll=348ca38a-3a...
[3] http://ocw.mit.edu/courses/electrical-engineering-and-comput...
I'd recommend downloading some lectures. I struggled with Linear Algebra before downloading Strang's MIT lectures, and I didn't understand the Dragon Book before following Coursera's Automata Theory course.
Depends on what you want to learn about, a degree in astrophysics or aeronautial engineering prepares you for many different possible jobs. I'm in a somewhat similar situation, maybe this will help:
(DISCLAIMER: I am not an aerospace engineer by training)
Calculus:
You'll definitely need to be very comfortable with single variable calculus and vector calculus up to partial derivatives, vector calculus integrals (Green, Stokes, Gauss) will definitely help. I wouldn't learn that from a book, try MIT's OCW, there is a calculus course covering all that. Learn the basic about ODEs, and be comfortable around PDE notation.
Linear Algebra:
In some sub-disciplines such as control and signal processing you'll also need to be very comfortable with linear algebra, so that all those matrices and stuff don't get in the way when learning modern control/DSP. I definitely recommend Prof. Strang's course in OCW for this. Try to at least be comfortable with simple ODEs before starting it. Linear algebra also helps a lot with Physics.
To get more into lineal algebra maybe you can read Linear Algebra Done Right if you want to learn more about Hilbert Spaces, and then maybe Shilov for tensors... those two books should be optional...
Software:
You don't need to be fast or maybe even know how to solve complex integrals in pen and paper. Try to complement learning calculus, differential equations and linear algebra with learning Matlab/Simulink and Mathematica. I can't even find a word to emphasize how much Matlab/Simulink is used in aerospace engineering...
Dynamics:
Learn classical mechanics, lots of it. Be confortable with rigid body dynamics in 3D. This is the best reading guide I know about, oriented to game development, but also useful for simulation and control: http://chrishecker.com/Physics_references Code simulators, visualizations, etc... Know what rotation, nutation and precession are, when and how they happen, etc...
From that list I have read a little of Goldstein and some Symon. If you find this books too hard, don't follow the guide but instead jump directly to the Feynman lectures (if you want to read) or Physics I from OCW (Prof. Lewin course, really really good).
Physics II from OCW can also help, maybe.
Space:
Once you are not scared with simple problems from all the previous subjects and can solve them, and can understand complex ones you should have no trouble following the first chapters (about dynamics, orbital and attitude maneuvering, etc) of some classical but real space books, for example:
SMAD by Wertz, a really classical book for space engineering courses. You should really be able to read it cover to cover but its not a very specific book and more oriented torwards missions management. Sometimes it gets boring because of it lack of details. http://www.amazon.com/Introduction-Space-Dynamics-Aeronautic... http://www.amazon.com/Spacecraft-Dynamics-Control-Practical-... http://www.amazon.com/Modern-Spacecraft-Dynamics-Control-Mar...
You can also browse here: http://astrobooks.com/ and see if you find something particularly interesting. I really would like to recommend a more engaging approach and less boring books, but this is the best that I can come up with now.
After you can comfortably read the first chapters of those space books you should really choose what to focus into. Dynamics, Simulation, Finite Element Analysis, Mechanics/Thermal engineering, Signal Processing, Control... then learn the basics of that discipline and then try to apply it to space exploration or spacecraft design. Each of this disciplines would need their own reply and reading list I guess... some require more physics than rigid body dynamics, like fluid dynamics or thermodynamics, electromagnetism, etc...
Also, as usual, try to have fun but still be disciplined about reading/learning.
I think you are talking about a different thing than I do. I have nothing against demanding some rigour in reasoning very early on in mathematics courses, what I am concerned about is the purely formal presentation of mathematical concepts, especially those that were first discovered by studying physical or geometrical situation and which naturally arise in such contexts. For example, is the formal epsilon-delta definition of a limit the best way to begin a calculus course? Yes, this is logically one of the basic building blocks of the theory, but what value does it have pedagogically for a beginning student? It is known that learning happens to a large degree via associating new concepts with ones already known, what can such a definition be associated with? This is carried out to extremes some times, I've seen introductory calculus books replacing sentences in natural language with formal-logic apparatus like quantifiers etc. and advertising it as some great pedagogical improvement.
Those are in my opinion excellent examples of courses developing intuition without sacrificing rigour:
http://ocw.mit.edu/resources/res-18-006-calculus-revisited-s...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
I also love the books by Richard Courant for how they manage to explain the concepts in crystal-clear English writing, present both the applications and the theory, building up the rigour gradually.
I find that at a practical level, linear algebra and probability/stochastic processes are the most valuable and heavily used topics in machine learning. For Linear algebra, i'd recommend Gilbert Strang's book+his MIT OCW lectures. Check out Papoulis's text for probability. It is very dense, and packs in lots of insight per page.
Subject: Linear Algebra Recommendation: Introduction to Linear Algebra by Gilbert Strang Reason: Strang presents the subject so clearly and intuitively that you feel like an expert on the subject after reading each chapter. It is by the far the best textbook I have encountered. He is also an excellent teacher and offers the lecture notes to the corresponding MIT class online.
Book: http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edi...
Lecture: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
I highly recommend the MIT 18.06 open course on linear algebra - the lectures are first rate. I've been going through this as a refresher, in prep for the Stanford machine learning class.
Link to the course: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
Link to the YouTube videos of the lectures: http://www.youtube.com/watch?v=ZK3O402wf1c&feature=resul...
Start with the MIT linear algebra course (18.06) by Gilbert Strang and Stanford course on linear dynamical systems (EE263) by Stephen Boyd. Then move on to Boyd's course on convex optimization (EE364). Lectures for all of these are on youtube.
Do not try to read any books on "machine learning" (most of which are a total mess) before you have this background or you will just end up hopelessly confused.
I would actually suggest another set of MIT courses that I think are more relevant:
Linear Algebra http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
Probability and Statistics http://ocw.mit.edu/courses/electrical-engineering-and-comput...
and finally
Machine Learning http://courses.csail.mit.edu/6.867/
There is a site http://openstudy.com/ where you can get into contact with other people taking the courses at OCW.
I wanted to work through the 18.06 calculus course anyway, so having that with enhanced material is great news to me.
Yes, the book is great as well, it's written in a very friendly tone.
These lectures were recorded long ago (1999), recent lectures (on calculus and another course) by Strang have higher video quality.
I have experienced mono audio on some too, you might be able to fix it with your video player though. ( If you are watching on iPhone/iPad, there is a mono setting in settings-accessibility btw.)
Check out http://www-math.mit.edu/~gs/ for the other lectures by Strang. Also in this paper: "too much calculus" http://www-math.mit.edu/~gs/papers/essay.pdf he discusses why linear algebra should be emphasized more (and calculus less) in the digital age.
I'm not sure how to pass the clearly understandable Khan academy style test, but Gilbert Strang of MIT has a series of 35 excellent lectures on Linear Algebra, starting here http://www.youtube.com/watch?v=ZK3O402wf1c
iTunes U has some amazing lectures. Gilbert Strang (MIT) has some video lectures (MIT OCW) on linear algebra. They are a bit dull, but they are pretty decent.
I also recommend academicearth.org.
If you are near a university, take a class "mathematical physics". These kind of classes usually cover a lot of undergraduate material in a semester and are offered by many physics department. They usually use "Mathematical Methods" by Boas as a text.
Try this (lectures from the man himself):
http://academicearth.org/courses/linear-algebra
The SVD connects the four fundamental subspaces of a linear system. I was fortunate to receive this great insight from one of Strang's lectures. I highly recommend you watch one of his videos online on this particular topic.
This post doesn't do full justice to the beauty of the SVD. Intuitively, you are trying to compute a transformation that diagonalizes the covariance matrix of the data. Computing the covariance has two problems: 1) this is a O(n^2) operation and 2) can lead to big numerical errors for really small values in the matrix.
By creative use of elementary matrix operations, the SVD gives you the transformation on the original matrix. If you are interested in just the first few singular vectors, certain math libraries also support an economical mode that does just this.
Learn some linear algebra. Literally every how'd-they-do-that-technique from OCR to PageRank is based on putting data in to a matrix and extracting some eigenvectors.
I took LA in college, but my professor was no where near as good and on topic in relation to computer algorithms as this guy: http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Cours...
Oh, check out R. There are a lot of free papers and example code showing say, how principal component analysis on a dataset of migratory geese can be used to explain so and so, along with generating some pretty pictures.
It's a really nice bit of OSS!
I think I got to chapter 6 of deep learning(deeplearningbook.org) before I ran out of steam. I went non-traditional as a Chem then physics-pre med major before grad school in comp sci so my linear algebra is piecemeal from quantum physics and math methods in physics. I really wish I took linear algebra before going through my cs grad school, but now I"m almost tempted to do Gilbert Strang's course on OCW to brush up on it. Linear algebra is the key to this stuff--well some tensor analysis as well, which, in my case, Dr. Houston snuck into math methods using Einstein notation. Yes, I did the Tensor Flow examples with the MNIST data, which was neat. I'm going to try the Coursera course as suggested by this article. I have links to Strang's linear algebra as well as a Drexel University course on Tensors on my page (https://hackereducation.wordpress.com/hacker-education-conte...)
One problem is the definition of a MOOC. What is it? (not the acronym, we all know that, I'm talking about the meaning).
1) Is it training? Competing with brick and mortar vo-techs and stackexchange and frankly just plain ole google?
2) Is it education? Competing with textbooks (paper and ebook) and brick and mortar college/univ and projecteuler and zillions of something-koan projects?
3) Is it socialization which is why everything gets deleted after it "ends"? Competing with a zillion internet social-type sites and facebook and G+ groups and even this site?
4) Is it presentation and puttin on an interesting show? Competing with MIT OCW videos and Kahn Academy?
5) Is it just signalling and raising awareness and showing off your hip-ness? Competing with the big social media sites, awareness ribbons (I want to buy a Chinese made $5 colored magnetic ribbon sticker to attach to my car to "raise awareness" of functional programming, either that or a colored bracelet, can anyone on HN help?)
6) Is it just a fad? Competing with "fill in the blank of memes".
For most existing products its possible to improve almost all areas, but if one product is optimizing area "X" above its possible someone reviewing with a focus on area "Y" is not going to be very happy. So you need to meta-mod review the reviewers or have some manner of tagging or something to indicate (the reviewers opinion of) whats good.
Above I was not trying to express an opinion, just trying to list the problem space, but I'll try an opinion based on some experience. If you want to optimize for #2 above in basic college math (calc, linear alg, etc) I claim you can't do better than MIT OCW's videos of Strang's classes (probably downloaded from archive.org?). But if you're trying to optimize for #4 above, then those videos are barely passable on a technical level (like if you can't read the blackboard at an overcompressed video level, why even release at that compression level? And some of the sound/mic needs work although its usable) and if you're trying to optimize for #3 above they're truly an epic fail not even really trying.
Another opinion, if you want to optimize for #4 it would be hard to beat most TED talks. Obviously done by pro-level video and audio crew on a good (from a technical standpoint) set.