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Immersive Linear Algebra – A free interactive online book
- snake117 11y agoI was thinking of working in a lab that does research in the field of computational biology. However, I never took a linear algebra course before so I always felt like it would be a waste to make an attempt. I did a quick skim and this looks very promising. If I can comprehend this, then maybe I will be of some use in the lab. Thanks for sharing :)
- krat0sprakhar 11y agoThis is actually pretty cool! I spent the last few weeks going through Gibert Strang's popular OCW course[0] & I'm sure this would serve as a great companion. I can't wait for the chapter on Eigenvalues to be published as that is something I don't yet grasp intuitively. Great work and thanks for making this free and accessible! [0] http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
- RockyMcNuts 11y agoshoutout to LAFF as well - https://www.edx.org/course/linear-algebra-foundations-frontiers-utaustinx-ut-5-03x https://www.edx.org/course/linear-algebra-foundations-fronti... - http://www.ulaff.net/ http://www.ulaff.net/ might be good for you if you're motivated by a deadline, graded progress, some Matlab/Octave implementation, and certificate of accomplishment, vs. self-paced Strang (AFAIK).
- generic_user 11y ago+1 LAFF is great
- krat0sprakhar 11y agoHad no clue about this course! Thanks a lot for the recommendation!
- krohling 11y agoThis looks amazing and well timed as I've been attempting to learn Linear Algebra on the side. However, everything after Vector Products is "coming soon". I will definitely use this once it's all there, which i hope is soon. Heck I'd be willing to pay for it if it were ready now.
- nstart 11y agoSlow to load (possibly due to HN traffic), but once it does, it seems like it's got the makings of a great learning tool. Waiting for matrix chapter since that's where I stopped learning Linear algebra on both my past two attempts (Gilbert Strang made my mind explode as I tried to comprehend past 4 dimensions. And then I just got lazy). Really want to pick this up because without linear algebra it's easy to get lost in all the major streams of Machine Learning. At least that's what I felt when I tried to skip linear algebra and move on to ML. Sigh. I sometimes wish I paid more attention to my studies while I was in school instead of goofing off and playing card games :'(
- jjangsangy 11y agoCool, well doesn't work on my mobile device, but I'll definitely check this again later since I need to review more Maths before going back to uni
- Scottopherson 11y agoThis looks awesome. The popup-help's are a little jarring though since there's no indication as to which words will trigger a popup. Also: "Oh come on, you should know what a vector, v, is by now. Check out Chapter 2, for crying out loud." seems kind of harsh to say to the reader while they're reading the first sentence of Chapter 2..
- cokernel 11y ago"Kind of harsh" is an understatement. Insulting the reader like this is not acceptable. Mathematics is already difficult enough to learn by its very nature. Authors, you don't need to help make it more difficult. We already have a hard enough time convincing people that they can learn something this difficult.
- immersivemath 11y agoThanks for the feedback. We have removed the popup for "vector".
- nicklaf 11y agoSimilar project, but for multi-variable calculus: http://mathinsight.org/thread/multivar http://mathinsight.org/thread/multivar
- generic_user 11y agoIs this available in an off-line bundle? I am becoming increasing wary of online books/training/applications that can not be read locally. If I am going to take the time to read through a full book (possibly weeks of reading) I want to be able to use/reference it in 5 years like my paper books. most of the value of a good math book is that years after reading it you can use it as a reference to look things up you will inevitably forget.
- thaumasiotes 11y agoWhile I don't disagree with your comment, I think once you've learned this material you could reasonably look it up in a different book. Put another way, going through this course might greatly increase the value (to you personally) of having any other linear algebra text available. It's not necessary to look things up in the same textbook you learned them from.
- generic_user 11y agoThis issue has come up with MOOCS also. If you look at the MOOC sites they offer there class content including videos as downloads. Even tho most of the MOOCS are introductory courses and you probably would need to get a good book to go along with them lots of people were requesting downloads of the content. There is a variety of reasons why people want off-line bundles. Its just something I have gotten use to with this sort of content.
- 70seconds 11y ago70 seconds to load a chapter? That's a terrible benchmark for even for some of the heaviest websites out there! This may not be a popular opinion but I (and many ordinary readers like me) see that link as a website. Not a book. It feels heavy and overwhelming to see a large number of 3D diagrams and visual depictions on just one web-page. Having to scroll down to read the full chapter with all that animation and "motion" is probably a bad move too. Given that this is supposed to come off like a book you can probably ditch the scroll. Ideally, you'd want to give away few concepts in small easy-to-understand chunks with just 1 or 2 figures per page. And let the reader flip/click over to the next section like it happens with an ibook or kindle book or even a real physical book. IMHO the idea of ripping apart a book at its spine and forcing the loose design of websites over it is a complete no-go for avid book readers. Especially for the mobile and tablet users (probably even for the desktop users!, why else would everyone insist to download PDF, ePub or other artifacts?). But I'm sure that a section of developers over here wouldn't agree with my opinion. So take it all with a pinch of salt. Also just the place where I'd let the designers take over.
- sudo_bang_bang 11y agoI never studied math in college, in fact I barely studied math in high school. It was always daunting to try to parse the notation and figure out how the abstract symbols corresponded to some piece of reality. When I became a self-taught developer I found my math skills continuously lacking. I started teaching myself on Khan Academy and really picking it up a lot better because of the simplicity of the language and the good examples. I finally realized I learned math best visually. Interactive lessons like these are great. There are things that can be improved about this book (load times and enhanced interactivity) but all in all this a great resource for people that learn best visually. I'll come back to this soon in my future self-education.
- wingerlang 11y agoWhat exactly do you do when you need math skills in developing? What do you develop with it? Some specific examples? I've done math while developing 3D stuff, physics simulation and a lot of things - yet I never felt like my math skill mattered that much. And I really dislike theoretical math like in school.
- EvanKelly 11y agoMath is certainly not for everyone, but I actually found that once I started diving into pure math (NOT what was taught in my school's math curriculum) it was a whole new world. Did your school actually teach pure math? I bet a lot of programmer types had similar frustrations to the computationally intensive version of math taught in many high schools when they knew that these processes could simply be automated.
- devin 11y agoThis. I had the same experience. By the time I realized this, I was sufficiently jaded that it made devoting my own time to learning it sting more than a little.
- wingerlang 11y agoI don't even know what pure math is to be honest. The courses I specifically lost interest in was linear algebra, discrete mathematic and statistic-something. I did however use linear algebra just after while writing a simple collision/physics engine prototype and found that to be very fun.
- jesicamila 11y agoIs this available in an off-line bundle?
- immersivemath 11y agoAt this time, it is not available as an off-line bundle.
- cptvideo2 11y agoI'm sure that this a wonderful book, but please note the error right off the bat in equation 1.3 The tangent of the angle in question is b/a NOT a/b as stated. Probably a good idea to keep an sharp eye on the math as you go along in this thing.
- immersivemath 11y agoThanks for the catch! The site has now been updated.
- deleted 11y ago[deleted]
- immersivemath 11y agoSend me your name to immersivemath@gmail.com and we will add you to the acknowledgements section!
- cptvideo2 11y agoThat's o.k. I'm usually the one making boo-boos like that. Glad we caught it.
- cabinpark 11y agoI always see linear algebra on HN and many people comment on how they never understood the subject. This makes me ask: what exactly is it that people don't get about linear algebra? What makes it appear to be a difficult subject? As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA courses that involve linear algebra, it is good to know where the problems are.
- wodenokoto 11y agoWhat it is, I think was my major problem. Matrix multiplication, ranks etc. are some of the most random seeming operations you can tell a student to memories.
- dalke 11y agoMy view is that the people who get to matrix algebra didn't have problem understanding the random seeming operation of previous math courses. Consider the existence of the "FOIL" mnemonic for multiplying two binomials (https://en.wikipedia.org/wiki/FOIL_method https://en.wikipedia.org/wiki/FOIL_method ), or SOH-CAH-TOA, where it was easier for me to just remember the definitions than the acronym. I think those are hints that some people consider those to be 'random seeming'. When I took algebra, I remember being tripped by all the new vocabulary. Why do mathematicians say something is "Abelian" instead of 'commutative'? Why is it important to have terms like "group", "ring", and "vector space"? Sure, I learned the definitions, but at that level they were 'random seeming'.
- ashishb4u 11y agoI think it's mostly because mathematics is taught as is with little or no attention to practical applications of the theory. For instance, till date, I could not see how eigen values/vectors are useful.
- cousin_it 11y agoOne nice application is that the eigenvectors of a stochastic matrix correspond to stationary states of the Markov chain. That leads naturally to a conversation about PageRank, which is super useful because it made billions of dollars for some people. Then you could talk about the use of eigenvectors for principal component analysis in data science, which is making a lot of money for other people right now. If these examples are not useful, then I don't know what is.
- thyrsus 11y agoAt some point, I'm hoping to get enough of this to solve this problem: you've taken a picture of, say, the Mona Lisa in its rectangular frame, but because of crowds you weren't in line with dead center, instead you were 5 meters back, 1 meter high, and 2 meters to the side, and not even pointed at the center. Your photo now contains some quadrangle that is a projection of the rectangle. I'd like to tag the four corners and have an algorithm map the photo to its original rectangle - I intuit there's enough information in the photo and the four tagged points, given that the original is actually a rectangle.
- tiglionabbit 11y agoThis exact application appears in the Coding the Matrix class on Coursera. http://codingthematrix.com/ http://codingthematrix.com/
- mcintyre1994 11y agoDefinitely doable - see the various scanner apps in your app store of choice. They work really well.
- gjm11 11y agoA word of warning about solutions to this problem. The "easy" version states it this way: the mapping you want takes (x,y) to ((ax+by+c)/(gx+hy+i),(dx+ey+f)/(gx+hy+i)) for some a,b,c,d,e,f,g,h,i -- a general "projective transformation". If you decide ahead of time exactly what rectangle you want to map to, you have 8 constraints on a..i (two coordinates for each of four corners) and one irrelevant degree of freedom (if you multiply all of a..i by the same constant, nothing changes) so you have "exactly enough" information to find those parameters. So you solve the equations and you're done. This works, provided your measured positions are perfectly accurate, but it isn't the best you can do. The reason is that a single projection actually has one degree of freedom less than a general projective transformation. (Three parameters to say where your camera is located. Three to say how it's rotated. One scaling factor. Total is 7 rather than 8.) This means that there's an extra (slightly hairy) constraint on the parameters a..i, which turns out to mean that the aspect ratio of the rectangle you're mapping to is determined for you. Imposing that constraint will give you (1) more information -- you won't have to know ahead of time what aspect ratio you have -- and (2) a more accurately estimated transformation. You can find more details of this stuff in, e.g., this PDF document: http://people.csail.mit.edu/bkph/articles/Harmful.pdf http://people.csail.mit.edu/bkph/articles/Harmful.pdf .
- jimhefferon 11y agoNot Free? That's fine, but I couldn't see a statement of that. If so, I wonder how they plan to do DRM.
- immersivemath 11y agoThis service is free of charge!
- jimhefferon 11y agoAre you involved with the project? If so, thank you. What is the license?
- Voltbishop 11y agoReally great site. It's clean, look forward to seeing the complete interactive book.
- something123 11y agoIn terms of programming and linear algebra - please consult someone who is actually knowledgeable about the subject if you're implementing it in code. Linear algebra without error analysis is very dangerous. Many many things are theoretically useful, but can't be used in practice. You can't calculate determinants, you can't count unique eigen values, you can't use certain decompositions. Unfortunately this isn't really topic you can do a quick tutorial on and start writing new algorithms
- memming 11y agoand also don't compute the inverse if you don't have to!
- neovive 11y agoFrom a technical aspect, this is an excellent implementation of MathJax.
- wehadfun 11y agoTo bad that teachers rarely have the freedom to teach using tools of their choosing
- adam12 11y agoThis is the first time I've ever heard someone say algebra with a hard g sound. https://www.youtube.com/watch?v=TIcSnsmitHw https://www.youtube.com/watch?v=TIcSnsmitHw
- mrcactu5 11y agoAre there any ways to contribute?
- orange_county 11y agoThanks for this! I am currently taking linear algebra with Serge Lang's book and I feel that this is a good addition to my studies. When do you expect to have the other chapters done?
- shurane 11y agoDoes anyone know if there's source code or a github page associated with this? It would be nice to submit fixes to errors, typos and maybe make suggestions. For starters, there might be a way to do away with the loading screen for shorter pages.
- immersivemath 11y agoAt this moment there is no github available, but bugs reports are welcome at immersivemath@gmail.com!