I wan to learn Linear Algebra - any interactive resources?

>be me >be bad at maths >have no maths >adult >no math teacher Anyone know a site or program that'll teach me linear algebra? I think this will be the most germane math topic for someone as math deaf, and programming rich as me. I'll also take suggestions on good books.

This is the book I used to teach myself linear algebra and it was written with autodidacts in mind. I think it's pretty good

https://hn.algolia.com/?query=linear%20algebra&sort=byPopularity&prefix&page=0&dateRange=all&type=story

>>4125 Interactive resources to teach linear algebra include, The following website: immersive linear algebra http://immersivemath.com/ila/index.html The following textbook that uses MathCad (for an open source alternate to MathCad that is MathCad compatiable try Smath Studio ) Interactive Linear Algebra A Laboratory Course Using Mathcad https://www.math.upenn.edu/~gjporter/ila/ Some interactive Ipython notebooks based on the material covered in MIT Open Courseware Linear Algebra class can be found at https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06 and the other supporting materials can be found at https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm Also see https://github.com/fastai/numerical-linear-algebra and http://www.fast.ai/2017/07/17/num-lin-alg/, which uses interactive Jupyter notebooks and videos you can watch. Also see http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/ For Terrence Tao's Linear Algebra notes. In addition please find attached several linear algebra textbooks, I have found useful in learning linear algebra.

linear algebra is really just formalizing and generalizing the algebra you learned in high school. You're right that it's the best kind of math for programmers to learn, except for maybe basic proof methods.

>>4137 It has some obvious practical applications. My ability to do graphics programming was hampered by my misunderstanding of vector addition / dot products and search What math comes next? I'm thinking calculus so I can finally understand how the Fourier transform works under the hood.

>>4138 look into the formal analysis of algorithms.

>>4127 This is the book. Those were the answers.

>>4135 I learned LA with that Strang book. It's pretty good. >>4138 Calc+Differential Equations will give you the fourier transform, but it's kind of high level compared to linear algebra. At a more basic level, you'll get sequences and series. They're good to know. Discrete mathematics is the other area commonly recommended to CS types. Most textbooks will start you off with boolean logic. Eventually you'll get to finite fields, which will give you crypto. If you know linear algebra and discrete, you could probably teach yourself undergrad abstract algebra (or at least group theory). You'll need to be good at reading and understanding proofs. There aren't a ton of direct applications in CS, but it will let you understand "what's really going on" in the first two subjects.

Id check out the mit course on youtube, and follow along with one of the books in this thread. Ive got a couple books from the gentoomans library that ill throw up here, not sure if theyre any good though.

>>4176

>>4125 >be me Thank god we cleared that up.

>>4125 This series of youtube vids was pretty good: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

>>4169 Not op or anyone you replied to, but just wanna say thanks! I'm doing a discrete mathematics course with Grimaldi's "Discrete And Combinatorial Mathematics" and its pretty straight up theoretical, but this pdf that you linked will help me clear up some stuff. Thanks!

>>4135 good stuff

>>4137 >linear algebra is really just formalizing and generalizing the algebra you learned in high school maybe basic linear algebra. higher level stuff like null spaces, projections, etc can go farther.

Khan is still the original online teacher-who-can-actually-teach, and he started with math. https://www.khanacademy.org/math/linear-algebra

>>4137 Care to specify which part of highschool algebra the Jordan normal form generalizes? Or the polar decomposition? Or tensor spaces?

>>7165 Seconding this op, yt videos a generally bad for learning stuff, but this guys videos are very high quality

>>4125

here

>>8290 I used this to freshen up on some other math stuff, its good

This is a very good book for learning linear algebra although it doesn't take the standard approach, it gets the job done well.

>>4125 A trick that I often use to learn higher school topics is going to an university website, look for a professor in the topic of choice and search for the books used in lessons. It works.

>>4125 3 Blue 1 Brown's videos are great for getting an intuitive grasp of the subject to get started. https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

I tutored a lot of people who were bad at math. It sounds like you're going about this the wrong way. You need to start at the point where you went off the rails. For a lot of the students I encountered, that point was fractions. The other thing I can tell you is that if you try to learn math by memorization, you will never be "good at math." For example, don't memorize a formula like length x width = area. Draw it on a grid. Understand why that works. Then without any algebra at all, you can draw and understand why (x^2) -1 = (x -1)(x + 1)

>>13757 >Then without any algebra at all, you can draw and understand why (x^2) -1 = (x -1)(x + 1) Explain what you mean, your equation seems to work, but I can't see how it can be intuitional.

>>13836 it actually does take some algebra, but it is really easy to see why. When you plot the function, you'll notice that it crosses the x-axis at two spots, meaning that the function becomes 0. Call them x1 and x2. So, if we assume that the function can be factored into equations like (x-n) , one of the factors must be 0 when x = x1, and another must be zero when x = x2. An equation (x1 - n) = 0 iff x1 = n, so any factorable polynomial factors into its roots.

>>13836

>>13836 >>13844 ORZ

>>13485 Thank you for posting that Lain >>13836 You can see, no matter how large you draw the square, that >>13845 applies. You can move the row either direction, it's the same result. You can do this sort of algebra with children's blocks. I would use the same visualizations to teach fractions. Instead of trying to make a student memorize formulas, I would explain it as pieces of pizza. To be good at math, you only need to understand it in concrete terms. Once you understand it this way, you don't need to memorize formulas, because you can derive the formula on the spot. I would suggest, if you don't understand a math concept, you try to visualize it. Or search it. "Visualize the Pythagorean Theorem" for instance, https://tapintoteenminds.com/pythagorean-theorem-part2/

well you certainly shouldn't pirate MATLAB. Nosiree don't do that.

>>4125 A lot of the books have already been mentioned in this thread, but there's a good discussion on methodology (how to study/where to begin) in this hackernews thread: "Ask HN: How to self-study mathematics from the undergrad through graduate level?" https://news.ycombinator.com/item?id=18939913

>>4137 Perhaps you meant Abstract Algebra?

>>16010 no, linear structures are actually very rich. It's hard to say anything general about groups because they are not as well behaved as vector spaces.

Friedberg's book about Linear Algebra is very good. A general algebra course, but very good even for Linear Algebra is Artin's book called Algebra. A classic. Google for undergraduate 1st year Linear Algebra exam subjects for practice. But I would rather use exercise books because let's be honest, the level in universities is getting lower and lower, even Ivy League. Books have very high quality and challenging exercises. A suggestion, from a programmer's perspective: Use a computer algebra system alongside your study of LA. I recommend Wolfram Mathematica IF you have access to it, if not, Jupyter is very good too, and if you're a CLI guy, ipython with sympy is really good too. You will want to visualise the effect of linear transformations on matrices interactively, especially when studying endomorphism reduction and quadratic forms if you will look into it too, and generally anything finite-dimension. Good luck. Come ask here if you need anything...

http://cow.math.temple.edu/

>>4125 I read through Ivan Savov's book "No Bullshit Guide to Linear Algebra" which I enjoyed a lot. It only covers the basics but it has some pretty interesting sections for applications. It was good for a fool CS major like myself. Pic related is the book preview.

>>4169 This 100% Discrete Mathematics was my gateway into the world of math.

>>19335 It's less than 1/3 of my univ one semester introduction to algebra on first year on computer science course.

>>19355 >Not "Concrete Mathematics" by Donald Knuth, Oren Patashnik, Ronald L. Graham

>>19374 for whatever reason i rarely see the knuth book used in math department discrete classes, but i do see it come up pretty often in CS department discrete classes (or whatever they call it). i've never read it so idk why.

>>19376 Of all the reasons there might be for this, I think the strongest would be that it doesn't have the Theorem-Proof format of math books, instead it shows techniques to solve some problems, mostly related to analysis of algorithms.

>>19381 >it doesn't have the Theorem-Proof format of math books oh i see. yes, that would certainly be the reason. proofs are pretty indispensable for pure math studies. as an aside, is concrete mathematics worth reading for someone who already knows all of the topics from an undergrad maths perspective but is trying to expand their self-taught CS knowledge (i.e. me)? i've heard it recommended very highly but i never bothered with it because i figured it would all be review.

>>19392 There's only one way to know. But seriously, you can read the first chapter which is quite light and see if it fits your needs, you may be able to skip around (for example, the second chapter on sums you probably already know, though the section on 'finite calculus' may be interesting to read). I don't know exactly what you know, for all I know you could have a strong theoretical basis but little by way of actual computation skills. The book generally shows techniques for finding results to concrete problems. On the other hand you might want to check out SICP instead. May be closer to your needs. Or both. CM uses mathematical notation you amy be at home with while sicp uses a programming language. Do as I do, skip around, read bits that catch your eye, see if the book's for you. And have fun.

>>19409 thanks, that sounds like good advice.

I'm doing linear algebra on my soykafty curriculum, so far we've done a crash course by Zkolter, some geometric lectures by Wildberger where he teaches you to become 3blue1brown yourself, and finally programming linear algebra in Python from CS053 at Brown University using the book 'Coding the Matrix' you can get for free on library genesis or buy for $30 https://learnaifromscratch.github.io/math.html A future course is Gilbert Strang's 'Linear Algebra with deep learning' he has on OCW I think it's 18.065 https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/video-lectures/ If you go on Stellar you can get the latest lectures but they haven't changed much, any of you anons can learn this there's nothing impossible about learning a few rulesets then just applying them.

For programmers: https://jeremykun.com/2011/06/19/linear-algebra-a-primer/ To programmers: did learning linear alg/mathematics at large improve your ability to make fun things? Is it worth it?

>>19520 3blue1brown warms my heart. My soykafty linear algebra curriculum was so fuarrrking soykaf I feel I totally wasted my time. For starters, it's cut in half for some retarded reason. The introduction is taught as a tangential topic in what's essentially a multivariable calculus course. The other part, more CS-related, taught a YEAR LATER, was basically a fuarrrking survey on methods to factorize matrices and their stability. Kinda cool but the professor just couldn't care less about proofs so there was really not much to it. Also Octave gives me a headache. I have been trying to get into it again and really learn what was that actually about, but wageslaving drains the soul out of me. I want capitalism to stop lains

>>19523 i'm a math major that learned programming so idk if im the best person to answer your question, but i will say knowing math made learning programming very easy. the hardest part for me was learning hardware stuff like how CPU architectures work, but I just took a couple CS/EE classes to fill in that gap. i'd say since you're coming at it from the other direction: CS knowledge but limited math, it depends on what you want to do. linear algebra is indispensable if you want to do anything with 3d graphics, and will eventually become necessary if you get into high performance/vectorized code (or really anything that involves a GPU). if you get into machine learning you'll need linear algebra of course, but also some vector calc and statistics (statistics mostly just so you can read ML papers. i personally find the statistics jargon to be an annoying holdover from more empirical scientific fields, but most papers frame everything in terms of distributions and optimizing expected values). i'm going to assume you already have a good understanding of basic logic and set theory. if you don't then definitely start there. it doesn't have to be formal mathematical logic; an engineering book on digital logic design is good enough and may even be more useful. discrete math is good to know but the benefits are less direct. it'll mostly just help you understand math papers and lay the groundwork for formal analysis of algorithms and things like cryptography, for which you will also need some number theory and basic abstract algebra.

>>4137 Discretre math is more important

>>4125 MIT has a great OCW library and even courses on Youtube, they are not as complicated as some might think think