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Reddit mentions of Introduction to Linear Algebra

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Reddit mentions: 18

We found 18 Reddit mentions of Introduction to Linear Algebra. Here are the top ones.

Introduction to Linear Algebra
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Found 18 comments on Introduction to Linear Algebra:

u/skier_scott · 5 pointsr/math

As everyone else is saying, Gilbert Strang's book. He also has a [great course][1] on MIT's OCW.

[1]:http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm

u/Aeschylus_ · 4 pointsr/Physics

You're English is great.

I'd like to reemphasize /u/Plaetean's great suggestion of learning the math. That's so important and will make your later career much easier. Khan Academy seems to go all through differential equations. All of the more advanced topics they have differential and integral calculus of the single variable, multivariable calculus, ordinary differential equations, and linear algebra are very useful in physics.

As to textbooks that cover that material I've heard Div, Grad, Curl for multivariable/vector calculus is good, as is Strang for linear algebra. Purcell an introductory E&M text also has an excellent discussion of the curl.

As for introductory physics I love Purcell's E&M. I'd recommend the third edition to you as although it uses SI units, which personally I dislike, it has far more problems than the second, and crucially has many solutions to them included, which makes it much better for self study. As for Mechanics there are a million possible textbooks, and online sources. I'll let someone else recommend that.

u/Second_Foundationeer · 2 pointsr/Physics

I think the book I used was by Gilbert Strang. He also has some video lectures, apparently. However, I think most of my real understanding of linear algebra (after being introduced to the formalism) came from some combination of upper division classes (classical mechanics, mathematical methods, linear algebra in the math dept). Maybe quantum mechanics was when I just got used to it..

I think I'd suggest complex analysis if you've already been introduced to the basic formalism of linear algebra because you have to use linear algebra a shit ton in quantum mechanics so you'll get good at it just from sheer exposure, imo.

u/user0183849184 · 2 pointsr/gamedev

I realized as I was writing this reply, I'm not sure if you're interested in a general linear algebra reference material recommendation, or more of a computer graphics math recommendation. My reply is all about general linear algebra, but I don't think matrix decompositions or eigensolvers are used in real-time computer graphics (but what do I know lol), so probably just focusing on the transformations chapter in Mathematics for 3D Game Programming and Computer Graphics would be good. If it feels like you're just memorizing stuff, I think that's normal, but keep rereading the material and do examples by hand! If you really understand how projection matrices work, then the transformations should make more sense and seem less like magic.

I took Linear Algebra last semester and we used http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716, I would highly recommend it. Along with that book, I would recommend watching these video lectures, http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/, given by the author of the book. I've never watched MIT's video lectures until I watched these in preparation for an interview, because I always thought they would be dumb, but they're actually really great! I will say that I used the pause button furiously because the lectures are very dense and I had to think about what he was saying!

In my opinion, the most important topics to focus on would be the definition of a vector space, the four fundamental subspaces, how the four fundamental subspaces relate to the fundamental theorem of linear algebra, all the matrix decompositions in that book, pivot variables and special solutions...I just realized I'm basically listing all of the chapters in the book, but I really do think they are all very important! The one thing you might not want to focus on is the chapter on incidence matrices. However, in my class, we went over PageRank in detail and I think it was very interesting!

u/bobbyj_chard · 2 pointsr/MachineLearning

| $350 on amazon

wat? the newest edition (2009) of his undergrad book is available for about 70 dollars, which is probably a steal.

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716/ref=sr_1_1?ie=UTF8&qid=1459450518&sr=8-1&keywords=gilbert+strang

u/IjonTichy85 · 2 pointsr/compsci

Hi,
do you want to become a computer scientist or a programmer? That's the question you have to ask yourself. Just recently someone asked about some self-study courses in cs and I compiled a list of courses that focuses on the theoretical basics (roughly the first year of a bachelor class). Maybe it's helpful to you so I'm gonna copy&paste it here for you:



I think before you start you should ask yourself what you want to learn. If you're into programming or want to become a sysadmin you can learn everything you need without taking classes.

If you're interested in the theory of cs, here are a few starting points:

Introduction to Automata Theory, Languages, and Computation

The book you should buy

MIT: Introduction to Algorithms

The book you should buy


Computer Architecture<- The intro alone makes it worth watching!

The book you should buy

Linear Algebra

The book you should buy <-Only scratches on the surface but is a good starting point. Also it's extremely informal for a math book. The MIT-channel offers many more courses and are a great for autodidactic studying.

Everything I've posted requires no or only minimal previous education.
You should think of this as a starting point. Maybe you'll find lessons or books you'll prefer. That's fine! Make your own choices. If you've understood everything in these lessons, you just need to take a programming class (or just learn it by doing), a class on formal logic and some more advanced math classes and you will have developed a good understanding of the basics of cs. The materials I've posted roughly cover the first year of studying cs. I wish I could tell you were you can find some more math/logic books but I'm german and always used german books for math because they usually follow a more formal approach (which isn't necessarily a good thing).
I really recommend learning these thing BEFORE starting to learn the 'useful' parts of CS like sql,xml, design pattern etc.
Another great book that will broaden your understanding is this Bertrand Russell: Introduction to mathematical philosophy
If you've understood the theory, the rest will seam 'logical' and you'll know why some things are the way they are. Your working environment will keep changing and 20 years from now, we will be using different tools and different languages, but the theory won't change. If you've once made the effort to understand the basics, it will be a lot easier for you to switch to the next 'big thing' once you're required to do so.

One more thing: PLEASE, don't become one of those people who need to tell everyone how useless a university is and that they know everything they need just because they've been working with python for a year or two. Of course you won't need 95% of the basics unless you're planning on staying in academia and if you've worked instead of studying, you will have a head start, but if someone is proud of NOT having learned something, that always makes me want to leave this planet, you know...

EDIT: almost forgot about this: use Unix, use Unix, and I can't emphasize this enough: USE UNIX! Building your own linux from scratch is something every computerscientist should have done at least once in his life. It's the only way to really learn how a modern operating system works. Also try to avoid apple/microsoft products, since they're usually closed source and don't give you the chance to learn how they work.

u/cr3bits · 2 pointsr/math

You might also want to search for your question on MSE. One advice that I recall is to consider Gilbert Strang's book Introduction to Linear Algebra along with his videos on OCW. He has an offbeat style both in his book and in his videos that might be unappealing to some people but the reason is that he really tries to make his students understand rather than remember. Also note that his target audience is typically engineers so proofs are present in his book but not the emphasis of his course.

u/crowsmen · 1 pointr/learnmath

> don't think that there is a logical progression to approaching mathematics

Well, this might be true of the field as a whole, but def not true when it comes to learning basic undergrad level math after calc 1, as the OP asked about. There are optimized paths to gaining mathematical maturity and sufficient background knowledge to read papers and more advanced texts.

> Go to the mathematics section of a library, yank any book off the shelf, and go to town.

I would definitely NOT do this, unless you have a lot of time to kill. I would, based on recommendations, pick good texts on linear algebra and differential equations and focus on those. I mean focus because it is easy in mathematics to gloss over difficulties.

My recommendation, since you are self-studying, is to pick up Gil Strang's linear algebra book (go for an older edition) and look up his video lectures on linear algebra. That's a solid place to start. I'd say that course could be done, with hard work, in a summer. For a differential equations book, I'm not exactly sure. I would seek out something with some solid applications in it, like maybe this: http://amzn.com/0387978941

That is more than a summer's worth of work.

Sorry, agelobear, to be such a contrarian.

u/dp01n0m1903 · 1 pointr/math

Yes, -5/9 is a typo, just as you say.

By the way, the lecturer in the MIT video is Gilbert Strang, and his textbook, Introduction to Linear Algebra is the text that he uses for the course. I'm not really familiar with that book, but I believe that it has a pretty good reputation. See for example, this recent reddit thread, where Strang is mentioned several times.

u/BallsJunior · 1 pointr/learnmath

To piggy back off of danielsmw's answer...

> Fourier analysis is used in pretty much every single branch of physics ever, seriously.

I would phrase this as, "partial differential equations (PDE) are used in pretty much every single branch of physics," and Fourier analysis helps solve and analyze PDEs. For instance, it explains how the heat equation works by damping higher frequencies more quickly than the lower frequencies in the temperature profile. In fact Fourier invented his techniques for exactly this reason. It also explains the uncertainty principle in quantum mechanics. I would say that the subject is most developed in this area (but maybe that's because I know most about this area). Any basic PDE book will describe how to use Fourier analysis to solve linear constant coefficient problems on the real line or an interval. In fact many calculus textbooks have a chapter on this topic. Or you could Google "fourier analysis PDE". An undergraduate level PDE course may use Strauss' textbook whereas for an introductory graduate course I used Folland's book which covers Sobolev spaces.

If you wanted to study Fourier analysis without applying it to PDEs, I would suggest Stein and Shakarchi or Grafakos' two volume set. Stein's book is approachable, though you may want to read his real analysis text simultaneously. The second book is more heavy-duty. Stein shows a lot of the connections to complex analysis, i.e. the Paley-Wiener theorems.

A field not covered by danielsmw is that of electrical engineering/signal processing. Whereas in PDEs we're attempting to solve an equation using Fourier analysis, here the focus is on modifying a signal. Think about the equalizer on a stereo. How does your computer take the stream of numbers representing the sound and remove or dampen high frequencies? Digital signal processing tells us how to decompose the sound using Fourier analysis, modify the frequencies and re-synthesize the result. These techniques can be applied to images or, with a change of perspective, can be used in data analysis. We're on a computer so we want to do things quickly which leads to the Fast Fourier Transform. You can understand this topic without knowing any calculus/analysis but simply through linear algebra. You can find an approachable treatment in Strang's textbook.

If you know some abstract algebra, topology and analysis, you can study Pontryagin duality as danielsmw notes. Sometimes this field is called abstract harmonic analysis, where the word abstract means we're no longer discussing the real line or an interval but any locally compact abelian group. An introductory reference here would be Katznelson. If you drop the word abelian, this leads to representation theory. To understand this, you really need to learn your abstract/linear algebra.

Random links which may spark your interest:

u/skytomorrownow · 1 pointr/compsci

I think for a rigorous treatment of linear algebra you'd want something like Strang's class book:

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716

For me, what was great about this book was that it approached linear algebra via practical applications, and those applications were more relevant to computer science than pure mathematics, or electrical engineering like you find in older books. It's more about modern applications of LA. It's great for after you've studied the topic at a basic level. It's a great synthesis of the material.

It's a little loose, so if you have some basic chops, it's fantastic.

u/ProceduralDeath · 1 pointr/mathbooks

Strang's book looks nice, and I noticed he has accompanying lectures which is good. I found this version, which is more or less in my price range but appears a bit outdated. https://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716

u/acetv · 1 pointr/math

Differential geometry track. I'll try to link to where a preview is available. Books are listed in something like an order of perceived difficulty. Check Amazon for reviews.

Calculus

Thompson, Calculus Made Easy. Probably a good first text, well suited for self-study but doesn't cover as much as the next two and the problems are generally much simpler. Legally available for free online.

Stewart, Calculus. Really common in college courses, a great book overall. I should also note that there is a "Stewart lite" called Calculus: Early Transcendentals, but you're better off with regular Stewart. Huh, it looks like there's a new series called Calculus: Concepts and Contexts which may be a good substitute for regular Stewart. Dunno.

Spivak, Calculus. More difficult, probably better than Stewart in some sense.

Linear Algebra

Poole, Linear Algebra. I haven't read this one but it has great reviews so I might as well include it.

Strang, Introduction to Linear Algebra. I think the Amazon reviews summarize how I feel about this book. Good for self-study.

Differential Geometry

Pressley, Elementary Differential Geometry. Great text covering curves and surfaces. Used this one in my undergrad course.

Do Carmo, Differential Geometry of Curves and Surfaces. Probably better left for a second course, but this one is the standard (for good reason).

Lee, Riemannian Manifolds: An Introduction to Curvature. After you've got a grasp on two and three dimensions, take a look at this. A great text on differential geometry on manifolds of arbitrary dimension.

------

Start with calculus, studying all the single-variable stuff. After that, you can either switch to linera algebra before doing multivariable calculus or do multivariable calculus before doing linear algebra. I'd probably stick with calculus. Pay attention to what you learn about vectors along the way. When you're ready, jump into differential geometry.

Hopefully someone can give you a good track for the other geometric subjects.

u/GhostOfDonar · 1 pointr/math

I recommmend the math video lectures at the MIT [1]. Single variable calculus is 39 lectures at about 50 minutes each [2]. Go through the first ones and you'll have not only a refresher but also a head start. While you are about it, don't miss out Prof. Gilbert Strang's video lectures on Linear Algebra [3], that man is phenomenal (he teaches based on one of his own books [4].)

Resources:
1,
2,
3,
4.

u/ekg123 · 1 pointr/learnmath

> To be honest, I do still think that step 2 is a bit suspect. The inverse of [;AA;]is [;(AA)^{-1};] . Saying that it's [;A^{-1}A^{-1};] seems to be skipping over something.

I realized how right you are when you say this after I reread the chapter on Inverse Matrices in my book. I am using Introduction to Linear Algebra by Gilbert Strang btw. I'm following his course on MIT OCW.

The book saids: If [;A;] and [;B;] are invertible then so is [;AB;]. The inverse of a product [;AB;] is [;(AB)^{-1}=B^{-1}A^{-1};].

So, before I went through with step two, I would have to have proved that [;A;] is indeed invertible.

>Their proof is basically complete. You could add the step from A2B to (AA)B which is equivalent to A(AB) due to the associativity from matrix multiplication and then refer to the definition of invertibility to say that A(AB) = I means that AB is the inverse of A. So you can make it a bit more wordy (and perhaps more clear), but the basic ingredients are all there.

I will write up the new proof right here, in its entirety. Please let me know what you think and what I need to fix and/or add.

Theorem: if [;B;] is the inverse of [;A^2;], then [;AB;] is the inverse of A.

Proof: Assume [;B;] is the inverse of [;A^2;]

  1. Since [;B;] is the inverse of [;A^2;], we can say that [;A^2B=I;]

  2. We can write [;A^2B=I;] as [;(AA)B=I;]

  3. We can rewrite [;(AA)B=I;] as [;A(AB)=I;] because of the associative property of matrix multiplication.

  4. Therefore, by the definition of matrix invertibility, since [;A(AB)=I;], [;AB;]is indeed the inverse of [;A;].

    Q.E.D.

    Do I have to include anything about the proof being correct for a right-inverse and a left-inverse?

    > That's a great initiative! Probably means you're already ahead of the curve. Even if you get a step (arguably) wrong, you're still practicing with writing up proofs, which is good. Your write-up looks good to me, except for the questionability of step 2. In step 3 (and possibly others) you might also want to mention what you are doing exactly. You say "therefore", but it might be slightly clearer if you explicitly mention that you're using your assumption. You can also number everything (including the assumption), and then put "combining statement 0 and 2" to the right (where you can also go into a bit more detail: e.g. "using associativity of multiplication on statement 4").

    I haven't began my studies at university yet, but I sure am glad that I exposed myself to proofs before taking an actual discrete math class. I think that very few people get exposed to proof writing in the U.S. public school system. I've completed all of the Khan Academy math courses, and the MIT OCW Math for CS course is still very difficult. I basically want to develop a very strong foundation in proof writing, and all the core courses I will take as a CS major now, and then I will hopefully have an easier time with my schoolwork once I begin in the fall. Hopefully this prior knowledge will keep my GPA high too. I really appreciate all the constructive criticism about my proof. I will try to make them as detailed as possible from now on.
u/roninsysop · 1 pointr/learnmath

I find Gilbert Strang's Introduction to Linear Algebra quite accessible, and seems to be aimed towards the practical (numerical) side of things. His video lectures are also quite good, IMHO.

u/ood_lambda · 1 pointr/AskEngineers

I don't, but I'm in the minority of the field. It definitely required a lot of catch-up in my first couple years. If you want to try and break in I can make some suggestions for self-teaching.

Linear Algebra is the backbone of all numerical modeling. I can make two suggestions to start with:

  • I was very impressed with Jim Hefferon's book. It's part of an open courseware project so is available for free here (along with full solutions) but for $13 used I'd rather just have the book.

  • The Gilbert Strang course on MIT Open Courseware is very good as well. I didn't like his book as well, but the video lectures are excellent as supplemental material for when I had questions from Hefferon.

    As for the actual FEA/CFD implementations:

  • Numerical Heat Transfer and Fluid Flow ($22, used) seems to the standard reference for fluid flow. I'm relatively new to CFD so can't comment on it, but it seems to pop up constantly in any discussion of models or development.

  • Finite Element Procedures, ($28, used) and the associated Open Courseware site. The solid mechanics (FEA) is very well done, again, haven't looked much at the fluids side.

  • 12 steps to Navier Stokes. If you're interested in Fluids, start here. It's an excellent introduction and you can have a basic 2D Navier Stokes solver implemented in 48 hours.

    Note that none of these will actually teach you the the software side, but most commercial packages have very good tutorials available. These all teach the math behind what the solver is doing. You don't need to be an expert in it but should have a basic idea of what is going on.

    Also, OpenFoam is a surprisingly good open source CFD package with a strong community. I'd try and use it to supplement your existing work if possible, which will give you experience and make future positions easier. Play with this while you're learning the theory, don't approach it as "read books for two years, then try and run a simulation".
u/INTEGRVL · 0 pointsr/matheducation

Introduction to Linear Algebra by Serge Lang.

http://www.amazon.com/Introduction-Linear-Algebra-Serge-Lang/dp/3540780602

Or Introduction to Linear Algebra by Gilbert Strang

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716

I have not used the Strang book, but I here it is all right for non-mathematicians.