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Free Linear Algebra textbook
- axegon_ 6y agoAt a glance, I don't see anything I haven't studied in high school and university. However, the fact that people are writing such books and offering them for free is absolutely astonishing. For that reason alone I'm purchasing the hard copy, people like that deserve the support! Amazing!
- giu 6y agoHe also has published the answers to the exercises, which is freaking awesome: http://joshua.smcvt.edu/linearalgebra/jhanswer.pdf http://joshua.smcvt.edu/linearalgebra/jhanswer.pdf
- acalzycalzy 6y agoI don’t like how advanced math has always butchered the Greek letters μ is pronounced Me not Mew
- jaygray0919 6y agothat's a joke, right?
- stormdennis 6y agoHaitch or aitch, zed or zee.
- Joker_vD 6y agoIt's "AR-sh" and "zet", obviously (also, in French "i" and "j" rhyme, "ee" and "gee", it's very neat).
- 867-5309 6y agono, it's a yolk
- SamBam 6y agoI don't think it's meant to be a joke, but I don't think it's right either, in English. In modern Greek, the top poster is correct, μ IS pronounced "Me" or [Mi] (spelled as μι). Here is a YouTube video of a Greek person going through the alphabet, linked to μ. [1] However, in English this was never used, at least not recently, and its not a "mathematicians" thing. English pronunciation of Greek letters was fixed around the 16th century (see [2] for a tiny bit of history) and was an attempt to use the classical Greek pronunciations, though probably not a very successful one. If you're going to complain about μ, then hopefully you also complain about π, which in modern Greek is pronounced like "pee," not "pie," and so would make π-day very different... 1. https://youtu.be/P85PXR6deIw?t=214 https://youtu.be/P85PXR6deIw?t=214 2. https://en.wikipedia.org/wiki/Pronunciation_of_Ancient_Greek_in_teaching#England https://en.wikipedia.org/wiki/Pronunciation_of_Ancient_Greek...
- jacobolus 6y agoI was told that some of these pronunciations have changed over time, and the English versions are an attempt to approximate the pronunciation from ~2000 years ago, because some parts of the Christian bible were written in Greek. I don’t know much about it though.
- Tainnor 6y agoThe New Testament was originally written in Greek.
- commandlinefan 6y agoMost modern translations of the old testament are based primarily on the Septuagint translation which was also written in (Koine) Greek.
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- jimhefferon 6y agoEverybody that I know pronounces it this way, but I could be wrong. If you could send me a bug report with evidence, I'd change it. I have long thought about a web site that contains mathematical pronounciations. A person could click to hear a native German speaker say Entscheidungsproblem, for example. I've never seen one, although I have seen a book online along those lines (written by a blind mathematician?).
- Joker_vD 6y agoOn the topic of pronunciation, say, "beta", "eta", "zeta" — is the first vowel actually pronounced as "ei" in English, instead of just "e" (as in "bed")? "Mew" and "new" are actually a good approximation for the ancient Greek letter names: actual sound was of course "y", "i Graeca", but it's close enough, the blending of initial "j" with following "u" produces a reduced "y".
- ogogmad 6y agoIn BrE, "beta" is pronounced /bi:tə/ ("bee-ta"). In AmE, it's pronounced /beɪtə/ ("bay-ta").
- enriquto 6y ago> μ is pronounced Me not Mew Ouch! I always say "Moo"...
- artagnon 6y agoI'm not too fond of the example-driven approach. The student will certainly be able to multiply simple matrices and compute determinants in some simple cases, but will not be able to answer fundamental questions like "what can I put in a matrix?", or "what is a vector field?" (the author gives 10 "rules" with no structure, so it's impossible for the student to memorize them). The author throws around `R` everywhere, but all his examples use `Z`. For a book on linear _algebra_, there is very little algebraic rigor in the book. The standard textbook for learning linear algebra at the undergraduate level is Hoffman and Kunz, which is far better. In short, this is a poor textbook.
- jsinai 6y agoMy first course in linear algebra was extremely formal with very little practical examples or visual intuition. It’s easy not to appreciate just how much intuition can go a long way in helping us understand a concept, even if the intuition is formally “fuzzy”. I used Hefferon’s Linear Algebra to plug the gaps in my intuitive and practical knowledge, and was all the better for it. People have different reasons and approaches for learning, and in the linear algebra landscape Hefferon is a worthy addition. (edit: just like one of the commenters below I bought the hard copy a few years ago to show my support and thanks for the free edition.)
- solinent 6y agoIn my experience teaching my friends and colleagues there are two ends of the learning spectrum--you can learn by example first or by theory first, or both, but the former is by far the lion's share of the population. I've taught people where there's absolutely no way I can teach them a generalization unless it's rote--however they can get domain-specific knowledge and beat me over the head in their domain and teach me something about my generalization as well that I might have been missing. The best way for me to teach calculus to most people is to walk around a room explaining concepts like velocity, speed, acceleration, and position. However, I personally would never learn it this way--I prefer Spivak, during my read through I learned more than I could ever learn in a class. It's also my belief that most people aren't like me in the sense that they learn from example first. However, most people I know are like me so it's hard to realize how needed a textbook like this is and how huge it could be for the regular person to learn something like this.
- enriquto 6y agoI'm not exactly the target for this book, but since I love so much this distribution model (freely downloadable latex/pdf plus print-on-demand) I just ordered a printed copy!
- mwigdahl 6y agoJust ordered one myself and looking forward to working through it!
- josrod 6y agoThank you, this is a great resource. Looks like there's additional material for independent learners and even some Youtube video lectures: https://hefferon.net/linearalgebra/independent-study.html https://hefferon.net/linearalgebra/independent-study.html
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- hnthwaccount 6y agoThis is amazing for self-learners. Free textbook, free lecture videos, free solutions. I bought a hard copy of this book when I first came across this resource. This is really outstanding because most textbooks do not contain full solutions and it can be difficult for self-learners without access to universities, tutors, peers to debug errors or check their work. If such a student ever got stuck, then it could be hard to move forward. One solution is to use sites like Math Stack Exchange, but I can imagine it would be tedious to do multiple proofs every chapter and type every single one of them up for someone to check. Some would argue that if your solution is correct then you should be able to rigorously justify each step and you should “know” in the end of its right. Beginners often don’t have the mathematical maturity developed to do this yet and even experts make mistakes in their proofs. If you had a question, then I could see scenarios where the question would be closed on sites like MSE for being duplicates or some odd thing that didn’t satisfy some sort of rule somewhere. These are more barriers for the self-learners that those in classrooms don’t necessary face and textbooks are typically written for those that access to professors. I think more math textbooks should be written this way.
- radmuzom 6y agoI logged into post the same comment - instead up-voted yours. While online courses are often good, I hate the idea of learning math by answering multiple choice questions. The fact that this provides the complete proofs as answers will help one to check their own thought process (assuming they don't cheat and look at the solution without putting in any effort).
- skohan 6y agoWorking with linear algebra has been one of the most valuable skill-sets to develop as a programmer. It's not relevant to a lot of domains, but for dealing with real or simulated 3D spaces it is like a super-power.
- mettamage 6y agoI feel awkward for asking this. Are there programmers that deal with real or simulated 3D spaces without knowing any linear algebra? How? Euler angles (including gimbal lock) all the way?
- SamBam 6y agoSure, if you're doing it all with a framework that handles all that for you. If you program a game in Unity, you're a "programmer that deals with simulated 3D spaces" and you don't need a lick of math. I think plenty of programmers go the route of using a tool that does everything for them, to slowly learning the underlying nuts and bolts (math, etc) that allow them to modify the framework itself.
- sokoloff 6y agoWas working on a 3D game with a programmer who didn't demonstrate knowledge of LA. (Maybe he had it, but he hid it well.) Several times we'd find him multiplying by matrix A and then by matrix A' (or doing multiplications by some random constant and then dividing the result by that same constant to get the sizing correct) because he was in the habit of jiggling things just until they weren't obviously broken. I always assumed that he was just a one-off, but I suspect this could easily arise from copy/paste and framework usage. (I'm also not sure I think this is universally bad; I think it's great that early teenagers can whip up a Minecraft-ish demo without having to learn all of linear algebra first.)
- skohan 6y agoas SamBam said, there are a ways to touch these domains without linear algebra. But what I meant is that it feels so powerful to unlock these domains. Once you develop a comfort level it opens up these really cool, magical things you can do with a computer, like graphics, simulation, ML, image processing etc. And the linear algebra skills you learn in one domain are often transferable to other really cool, interesting domains. This is what feels like a super power.
- jimhefferon 6y agoAuthor here. I like to look over HN during breakfast, so a surprise this morning. I appreciate folks's kind words. Can I slide in the back story? The course I had as an undergrad was very computational. Matrix multiplication is associative because the indices combine in this way and then you distribute the a_i,j's, etc. I could follow it line-by-line but I didn't feel any real understanding. In grad school I learned that it all makes beautiful sense. So when I started teaching, I wanted an approach that conveyed the sense. I adopted a book that is a great book, very clear and clean, but students did not understand it. They were good students, but they just were not ready. They needed more examples, and by-hand calculations, for instance. I resolved to find a presentation that helped bring them to where they would be ready, or at any rate formed part of a deliberate effort by an undergrad program to work on maturity. I didn't find a book that worked for me, so I wrote one. So although there are a lot of examples and a lot of computation, like the text I had as an undergrad, this development keeps trying to direct the attention of students toward the understanding that they get from higher-level ideas. I often see online where someone asks "What is the right book for XXX?" It seems to me that often there is no one best. Often, it depends on the audience. For the students that I see, this approach accomplishes a lot, it seems to me.
- zeebeecee 6y agoAt least for me, doing examples and computations is the best way to learn math, and also very important in research. Often an opaque general statement becomes clear after doing a few small examples. In linear algebra, I personally find some of the courses have too few computations, some concepts are best learned by working an hour by hand on some annoying 6 x 6 matrix..
- cgriswald 6y agoI like this course by Philip Klein of Brown University for a computational approach: http://cs.brown.edu/courses/cs053/current/index.htm http://cs.brown.edu/courses/cs053/current/index.htm That said, "working an hour by hand on some annoying 6 x 6 matrix" is how I was taught linear algebra. I got a rare B in the course (even though I aced all the tests!) because there was so much busy work I just refused to do it all. I got literally nothing out of the course in terms of understanding (there was neither time to think nor any real direction given) and a year later I couldn't even do the work anymore. I ended up picking up Axler.
- dboreham 6y agoReading this, I realized I need a browser-side PDF viewer that provides kindle-like features (bookmarks, current reading position, highlighting, ...) layered over a bare PDF file fetched from a server like this one. I'm guessing that thing exists somewhere?
- ayewo 6y agoNo affiliation whatsoever but you could try using Hypothesis’ browser-based annotation tool to take PDF notes: https://web.hypothes.is/ https://web.hypothes.is/ They build on top of Mozilla’s PDF.js: https://github.com/hypothesis/pdf.js-hypothes.is https://github.com/hypothesis/pdf.js-hypothes.is https://web.hypothes.is/help/annotating-locally-saved-pdfs/ https://web.hypothes.is/help/annotating-locally-saved-pdfs/
- SeeManDo 6y agoThe content and context of this book surpasses any course on Linear Algebra I took while attending UT Austin.