HN Theater @HNTheaterMonth

It depends on who wants to hire you. For the top jobs, this is for sure not enough.

I always tell people to please make sure they know all the contents from here https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C... (Gilbert Strang's Linear Algebra course) before they make any claims about being a data scientist. I bet I can teach a monkey to open a CSV in pandas and call .fit() in sklearn. But do the people really understand the underlying assumptions. Most self-proclaimed data scientists don't I am sure.

I still have a hard time calling myself a data scientist. And I am three years into a relevant PhD. The more I study, the less I feel I truly know.

Love Gilbert Strang's original linear algebra lectures on YouTube [1]. They were a huge help while I took the course.

In my opinion, he takes great care to motivate each topic and express his train of thought when working through problems.

[1] https://m.youtube.com/watch?v=ZK3O402wf1c

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...

⬐ colmvp

I like Strang and have worked through some of his books but when I was first learning Linear Algebra, I preferred learning from Dr. Aviv Censor's videos on YouTube[0] from when he was teaching at Technion. It's a few dozen videos where he spends a lot of time going through each component of an introductory course on Linear Algebra.

[0]: https://www.youtube.com/watch?v=aefKXYYXT6I&list=PLW3u28VuDA...

⬐ hyperpallium

/aside As someone who's also refreshing maths: What's the point of investing in studying hard, if I end up forgetting? Is there some aspect of maths I should focus on, that is an enduring investment?

My feelings is that getting an intuitive understanding is key, so that it becomes part of myself... but I find proofs don't give me this (they show me that it is true, but not why it is that it is true - if that makes sense). Derivations seem important, because then I can re-derive when I forget (though, I must recall the "tricks" of the derivation, and also know the operations used). General skills can persist, if they get ongoing exercise (e.g. methodicalness, care with definitions, close reading, organization to cope with complex and multi-layered problems).

Finally - and awfully - I now think mathematics is like a language, not so much in the sense of communication, but by being full of special cases, exceptions, "abuse of notation". Becoming fluent in a language takes much practice, and may be impossible without special talent. But once achieved, is never fully forgotten, and quickly regained.

⬐ Eldandan

The payoff is indeed learning the intuition, but also learning how to prove things and learning how to learn math. The content itself is only as important as whatever field you're in, or whatever application you're studying that requires that specific mathematics. But the "thinking like a mathematician" and knowing how to learn new math is the valuable skill you'll gain.

⬐ the_svd_doctor

Another great "intermediate" textbook (in my opinion) is Trefethen's Numerical Linear Algebra [1]. Much more readable than Golub's I would say, which is more like a reference than a textbook.

[1]: https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefet...

⬐ dxbydt

This is actually the best book of the lot.

⬐ laserson

Strongly agree. This was actually the text book when I took numerical methods at MIT. As far as math texts go, it is definitely a joy to read.

⬐ laserson

Strang just published a new book called "Linear Algebra and Learning From Data" [1] which I only just started but find to be quite enjoyable so far. It's simultaneously conversational but also quite terse (similar to "All of Statistics"). There are many advanced and very contemporary applications covered in the book, with a focus towards machine learning.

[1]: https://www.amazon.com/Linear-Algebra-Learning-Gilbert-Stran...

⬐ tomjakubowski

I love Strang's conversational style. If you've ever heard him give a lecture, you hear him when reading his textbooks.

⬐ whymauri

Absolutely this!

"Now this is a matrix you wouldn't want to meet in a dark alley!" - Gil

⬐ bookofjoe

Q&A with Strang: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3060226/

⬐ throwawaymath

Golub's Matrix Computations is definitely a gold standard, but I wouldn't characterize it as something you read so much as reference :)

⬐ hamburglar1

When taking Lin Alg in undergrad, I attended the first 3 classes. My friend then showed me the youtube series from Strang; I never went to class again and learned it all.

⬐ derangedHorse

I partially credit Strang for getting me an A in Linear Algebra. His lectures and the book from David C Lay that I thought was pretty good.

⬐ derangedHorse

The PSET posted is for Statistics for Applications. I was wondering why it looked so different from when I went through it a couple years ago haha

⬐ wittedhaddock

So grateful something mentioned this man. Strang is just amazing. When I first moved to Cambridge, his corresponding book was a relatively expensive prospect, and I was rather serious about 18.06, so ascertaining its book was very important to me. He was gracious enough to gift me a copy that I still have and cherish to this day. Some real moments of thrilling discovery happened for me, it was exhilarating, though trite as they may be! Like in implementing a program for general inversion of any MxN matrix, one would typically perform the Gaussian elimination (going down) and then the Jordan (going back up) and finally divide by the scalars in the pivot columns. But, as it turns out, it's a much simpler program if you do Gauss elimination, literally rotate all matrices by 180 degrees, do Gauss elimination again, then rotate everything back, and then address the non-unit pivot columns. src: https://github.com/wittedhaddock/AlgebraicCircumscriptions/b...

⬐ dxbydt

> general inversion of any MxN matrix

??! is there such a thing ? only nonsingular square matrices can be inverted. a general mxn matrix may have a “left inverse” or a “right inverse”, but i don’t think your code is computing that.

⬐ wittedhaddock

You're 100% correct, the algo only handles square matrices! Typo. So, disclaimer, where m === n :) thanks!

⬐ olooney

https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse

⬐ throw20102010

There is such a thing as a generalized inverse, in which you can invert non-square or non-full rank matrices and the generalized inverse meets many (but not all) of the properties of an inverse. The tough part is that the agreed upon set of properties does not create a unique solution for a generalized inverse like it does for the inverse, so there are multiple possibilities when someone says generalized inverse. However, the most popular is probably the Moore-Penrose inverse: https://en.wikipedia.org/wiki/Moore–Penrose_inverse

⬐ wittedhaddock

thank you very much for this !!

Gilbert Strang's Linear Algebra course from MIT, available on youtube (3 million views!), and his textbook of the same name are awesome. What a great teacher.

https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101...

Like Gilbert Strang? https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C...

Does your degree program not include at least one Linear Algebra class? Or are you just trying to get a head start?

In either case, you might find this course[1] and accompanying videos[2] useful.

Also, of course, is 3blue1brown[3] on Youtube.

And then there are the Gilbert Strange lectures[4] on Youtube.

[1]: http://codingthematrix.com/

[2]: https://cs.brown.edu/video/channels/coding-matrix-fall-2014/

[3]: http://www.3blue1brown.com/essence-of-linear-algebra-page/

[4]: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C...

⬐ mindcrime

And then there are the Gilbert Strange lectures[4] on Youtube.

That should be "Gilbert Strang". Derp.

⬐ biggb

It doesn't. It assumes at this level you have already taken linear algebra. My undergrad advisors recommended I take number theory and more logical / theory based courses - unfortunately.

I'm just trying to not fall behind haha, not necessarily a head start.

Thanks for the reply though, I appreciate it.

I've mentioned this on HN before but I think its still relevant to people interested in learning ML who feel they are behind on the math. If, like me, you can't sit thru lots of pages of mathematics text and instead prefer that a human explains it to you via videos that you can replay, here is a list of courses that take you from basic algebra and pre-calculus math all the way to the concepts you need to understand the principles behind the most advanced ML algorithms. All explained by very energetic people who are experts in their fields, and starting from the very basics.

This covers calculus, linear algebra, probability, statistics, convex optimization and a math for ML course thrown in for the HN audience:

(The first two are "MOOCs" recorded in the 1970s! probably the first ever recorded MOOC, even before the internet, and the lecturer is absolute gold)

Calculus Revisited: Single Variable Calculus | MIT https://ocw.mit.edu/resources/res-18-006-calculus-revisited-....

Calculus Revisited: Multivariable Calculus | MIT https://ocw.mit.edu/resources/res-18-007-calculus-revisited-....

Complex Variables, Differential Equations, and Linear Algebra | MIT https://ocw.mit.edu/resources/res-18-008-calculus-revisited-....

Linear Algebra | MIT - https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101....

Introduction to Linear Dynamical Systems |Stanford https://see.stanford.edu/Course/EE263

Probability | Harvard https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6....

Intermediate Statistics | CMU https://www.youtube.com/playlist?list=PLcW8xNfZoh7eI7KSWneVW....

Convex Optimization I | Stanford https://see.stanford.edu/Course/EE364A

Math Background for ML | CMU https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW....

⬐ nagarc

Many of the links are not working

⬐ thomanq

Links as per the original comment [0]

Calculus Revisited: Single Variable Calculus | MIT https://ocw.mit.edu/resources/res-18-006-calculus-revisited-...

Calculus Revisited: Multivariable Calculus | MIT https://ocw.mit.edu/resources/res-18-007-calculus-revisited-...

Complex Variables, Differential Equations, and Linear Algebra | MIT https://ocw.mit.edu/resources/res-18-008-calculus-revisited-...

Linear Algebra | MIT - https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101...

Introduction to Linear Dynamical Systems |Stanford https://see.stanford.edu/Course/EE263

Probability | Harvard https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6...

Intermediate Statistics | CMU https://www.youtube.com/playlist?list=PLcW8xNfZoh7eI7KSWneVW...

Convex Optimization I | Stanford https://see.stanford.edu/Course/EE364A

Math Background for ML | CMU https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW...

[0] https://news.ycombinator.com/item?id=14581962

⬐ nagarc

Thank you

⬐ vecter

These are great resources, but the ultimate approach is wrong. In order to truly learn math, you must be willing to invest the time and "sit through lots of pages of mathematics text" and also do a ton of problems, many of which will take hours and some which will require days of thinking.

I you aren't willing to invest the energy and effort to do that, all the video watching won't do anything for you. It will get you 5% of the way at best. The true learning comes from staring at a problem for hours, trying 100 dead ends, and then finally having an insight two days later while taking a shower that suddenly make that intractable problem seem trivial.

⬐ mindcrime

These are great resources, but the ultimate approach is wrong. In order to truly learn math, you must be willing to invest the time and "sit through lots of pages of mathematics text" and also do a ton of problems, many of which will take hours and some which will require days of thinking.

These things aren't mutually exclusive. I don't know about anybody else, but I'd rather watch a video of a human explaining the subject, then sit down with a textbook and start working through problems.

⬐ vecter

Of course they're not, but OP kind of implied that it wasn't necessary to read a lot of pages of mathematics when he said

> you can't sit thru lots of pages of mathematics text

Even if you watch those videos, you still need to sit through lots of pages of mathematics if you want to master the subject.

Also Gilbert Strang's lectures: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C...

If you find it easier to keep at it and learn from lecture videos instead of from textbooks, here's a math curriculum of lecture videos I've curated. This covers calculus, linear algebra, probability, statistics, convex optimization and a math for ML course thrown in for the HN audience:

Calculus Revisited: Single Variable Calculus | MIT https://ocw.mit.edu/resources/res-18-006-calculus-revisited-...

Calculus Revisited: Multivariable Calculus | MIT https://ocw.mit.edu/resources/res-18-007-calculus-revisited-...

Complex Variables, Differential Equations, and Linear Algebra | MIT https://ocw.mit.edu/resources/res-18-008-calculus-revisited-...

Linear Algebra | MIT - https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101...

Introduction to Linear Dynamical Systems |Stanford https://see.stanford.edu/Course/EE263

Probability | Harvard https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6...

Intermediate Statistics | CMU https://www.youtube.com/playlist?list=PLcW8xNfZoh7eI7KSWneVW...

Convex Optimization I | Stanford https://see.stanford.edu/Course/EE364A

Math Background for ML | CMU https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW...

⬐ hayden592

This looks awesome. Thanks

⬐ koopuluri

This is great. Thank you!

⬐ None

None

⬐ None

None

⬐ None

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⬐ FlyingLawnmower

Thank you for collecting these resources together!

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.

Linear Algebra by Gilbert Strang, MIT https://www.youtube.com/watch?v=ZK3O402wf1c

Probability by Joe Blitzstein, Harvard http://projects.iq.harvard.edu/stat110/youtube

⬐ hackernewsacct

Excellent, thanks for you recommendation!

⬐ aswanson

Gilbert Strang is an excellent lecturer and teacher. He, along with Andrew Ng, are amongst the best.

Gilbert Strang's linear algebra

https://www.youtube.com/watch?v=ZK3O402wf1c

Walter Lewin's Classical Mechanics

https://www.youtube.com/watch?v=Uo28HOrhipc

for the content and the delivery

Useful list. I would recommend adding one more resource for linear algebra/machine learning:

I absolutely enjoyed learning Linear Algebra from these beautiful lectures by Prof. Gilbert Strang (MIT): https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD9101...

Seriously, I gained a new found appreciation for Linear algebra after going through these lectures. You should go over some of these lectures even if you already know linear algebra - it might give you insights you never had before (it did, for me). Absolute must-watch if you are into machine learning or related areas.

Ah but the beauty is that you can read for pleasure knowing that you won't have an exam at the end and trying to work out what your professor thinks is important.

If you want to enjoy linear algebra without the pressure of doing any, I can heartily recommend MIT's open coursewear videos featruring Gilbert Strang

http://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD91010...

In fact all the MIT stuff I have tried is fun to watch

I don't understand this. Most of my teachers use blackboards and it's really annoying to follow a presentation like that, you have to wait for the person to write, you have no slides later on to support your notes, and since you have no slides online you have to write everything they write, so you can't even listen properly to the talk.

And some stuff are just clearer on slides... I don't really see a lot of benefits in whiteboard-only lectures. Combination of whiteboard and slides are best.

I can still think of some great people who don't use slides but it's rare and a few people do it well (Gilbert Strang comes to my mind[1]).

[1]: https://www.youtube.com/watch?v=ZK3O402wf1c

⬐ snotrockets

You don't need slides to support your notes. There are two kind of classes: those that bring you up to speed; all the stuff there is found in textbooks or review papers.

And those that present wholly new ideas (research seminars, conferences,) where you can just read the paper or the preprint for details.

The only time I've seen something on the board that I really had to copy down to keep an copy of was exercises and their solutions.

⬐ baby

if your teacher has a textbook that he follows okay, but here in France most teachers don't and you have to copy everything they write. And even if they have a course online, they will waste so much time just writing it...

⬐ Crito

I find that blackboard oriented lectures are much more conducive to audience/lecturer communication because during blackboard oriented lectures going off the rails is seamlessly natural, while that could not be further from the case with powerpoint oriented lectures.

Overhead projector lectures are the best of both worlds. You can make pre-prepared foils but modify them on the fly, and create new ones on the fly as naturally as you can write on a blackboard.

The MIT ones taught by Strang, my new favorite professor. http://www.youtube.com/watch?v=ZK3O402wf1c

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...

⬐ achompas

The course is taught by Gilbert Strang, who has written an excellent introductory textbook on the subject:

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...

⬐ colanderman

Strang has another great book, Linear Algebra and its Applications: http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St... Everything I know about linear algebra I learned from this book.

⬐ seanharnett

Seconded. I'm an applied math PhD student (optimization) and I use linear algebra constantly. This book taught me everything.

⬐ m0nastic

Thirded. We used an earlier edition at my school for Linear Algebra, and in spite of having a Professor who was retiring at the end of the class (complete with "I'm getting too old for this shit" demeanor), the book was approachable enough for us to get by.

⬐ cop359

A slightly more advance books which I love is: Matrix Analysis and Applied Linear Algebra by Carl Meyer. http://www.amazon.com/gp/product/0898714540

You can find a free PDF version online.

I like it more then Strang because it's a lot more concise, covers some more advanced topics and unlike Strang everything is said very accurately. I think Strang's rather hand-wavy way of explaining things starts faltering when he talks about more advance topics.

I would read Strang and listen to his lectures to get a good feel for Linear Algebra (to build up the intuition), and if you feel like you want more then pick up Meyer's book

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

⬐ bugsy

I agree with you. Lee should donate the $5000 to Strang and be done with it. If they are not to his satisfaction, it is up to him to specify what he doesn't like about these world class lectures from a renowned expert teacher.

⬐ bosie

"(and passes the "clearly understandable", Khan academy style, 10 minute video lecture)"

it definitely doesn't pass the 10 minute video lecture requirement though. Strang talks about SVD for almost 45 minutes.

⬐ weaksauce

Here are all the other videos and assignments + solutions:

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

⬐ ludwigvan

Absolutely. Strang makes it seem really easy, perfect lecturer.

The lectures are available on iTunes University too.

You may find his style slow though, I used to watch his lectures at about 1.5x speed using Quicktime (opt+ff). You can use vlc too on Windows.

⬐ jackfoxy

I'm a little slower, 1.4x on VLC.

⬐ johnwatson11218

I am watching those lectures as well. I ordered the previous edition of the textbook to follow along with. One thing that really irked me was that the quality of the audio in some of the lectures was spotty. I had to turn the audio up all the way in my headphones and then it seemed to only come in on one side. I know it is a minor detail but when I think about the high quality feeds dedicated to celebrity gossip it gets a little bit depressing.

I clicked into some of the other courses and was disappointed to see that video lectures weren't available for all the courses. We really need to get to a point where all the math, comp sci, etc is available in high quality format. Another thing we need is redundancy. I think G. Strang is an excellent lecturer but we need variety for different learning styles. Still I am impressed with what MIT is doing and hope to see more of this in the future.

⬐ ludwigvan

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.

⬐ johnwatson11218

yea I caught that point about too much calculus. I studied math as an undergrad - 3 semesters of calc, 2 real analysis, 2 more of topology and have not used any of it as a programer. I did linear algebra and discrete math but it was not enough to really make a difference. It seems like history is more at play here than anything else. For 300+ years they have been polishing up that continuous math track and it was what all the scientists and engineers found useful.

I also think this is the reason everybody uses doubles and floats for doing financial apps. It makes so much more sense to use integers and talk about "how many" pennies one has rather than "how much" money one has. Floats and doubles were designed to estimate continuous quantities not exact figures.