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Study HN: Linear Algebra 1. We're on.
A couple of weeks ago, a bunch of us decided to put our internet time to better use and (re-)learn linear algebra together (http://news.ycombinator.com/item?id=2993321). Most have the book by now, so... let's do this! If you missed that thread and want to join, please do so. There's nothing you have to do other than learn.
The book is "Linear Algebra And Its Applications" by Strang, 4th ed., ISBN 0030105676. We'll work through one chapter every two weeks. There are a lot of exercises. Let's discuss ones that are interesting, nontrivial or both. Questions and insights about the material are welcome. The first 5 chapters have Review Exercises at the end. Let's call those "mandatory" and discuss them at the end of the two weeks.
Housekeeping:
1. We'll do this on HN unless it becomes intractable or the landlord asks us to leave.
2. Put "Study HN: Linear Algebra 1" in the subject line. Then we can find posts like this: http://www.hnsearch.com/search#request/all&q=%22linear+algebra+1%22
3. If you want to be emailed when something relevant happens, email me at the address in my HN profile and I'll put you on the list.
Finally, not all of us have the above book. Some are using an earlier edition or a different text altogether. Others have the 4th edition, but in a cheaper Indian format that is sold as identical, but - warning! - is not. Presumably to thwart students from getting away with using the cheaper edition for courses, the publisher has tastelessly scrambled the order of the exercises. How, then, are we going refer to exercises? Let's experiment to see what works. In the meantime:
4. To avoid confusion, only reference exercises by number (e.g. "Ex. 10 of 1.2") when they are from the official book (the 4th edition, expensive non-Indian format). If you don't have that text, and want to play along, email me and we'll figure something out.
So, HN: what's interesting in the early sections of Chapter 1? I have a few things, but let's hear from others. How about we stick to 1.1, 1.2, and 1.3 at first - up to Gaussian elimination, but not yet matrices.
- ColinWright 15y agoClickable: http://www.hnsearch.com/search#request/all&q=%22linear+algebra+1%22 http://www.hnsearch.com/search#request/all&q=%22linear+a...
- fuzzythinker 15y agoFor me, I don't think we should do the calculations by hand just for the sake of doing it. It should be done only as a means for understanding the core concepts. That is I much prefer to do exercises where the understanding of core concepts is brought to the attention. So the question is "What are the core concepts up to 1.3"? I'm sure singular vs. non-singular is one. Are pivots a core concept? I think open-ended questions in the 2nd half of 1.3 questions are good candidates for deeper understanding.
- gruseom 15y agoAre pivots a core concept? Good question. They don't feel that way to me. They seem more like the implementation detail of an algorithm (Gaussian elimination). Is the algorithm itself a core concept? Hard to say no to that, I guess, but I wonder. What about what Strang calls the "row picture" vs. the "column picture"? There you have two fundamentally different geometric interpretations of linear equations. That was a revelation to me. When I studied linear algebra a long time ago, I don't remember encountering the column interpretation. Perhaps I did and didn't pay attention; I was more interested in symbolic manipulation at the time, whereas now I want a sense of what the symbols mean geometrically.
- tptacek 15y agoThe intro lecture on row/column pictures made this click for me better than the book did: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-1-the-geometry-of-linear-equations http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... 22:00 in.
- mechanical_fish 15y agoAmusingly, I'm in the entirely opposite boat. I managed to get an entire Ph.D. in solid state physics without taking an actual course in linear algebra (a procedure that I do not recommend, but everyone is young and foolish once). So I've got some idea of what vector spaces are about geometrically -- otherwise, graduate quantum mechanics would have been impossible to navigate -- but I'm really bad at manipulating the actual symbols. And, incidentally, I'm planning to attempt most of the problems. I've cherry-picked my way through this subject before, and I was ultimately displeased with the results. They say that the problem with an autodidact is that he has a fool for a teacher, and with linear algebra I learned that the hard way. Fortunately, now they've invented Open Courseware, Amazon.com, and HN, so I'll give the fool another chance.
- gruseom 15y agoI propose that we explicitly mention any exercises that we stumble over. Yeah it may make us look like idiots but we're destined to look like idiots anyway, and there's a major upside: we're going to stumble over different things, which means we can provide good explanations to one another, and learn better. I have a few examples of this sitting at home but am hacking at the library at the moment. It is heavenly quiet here. I will post them later.
- tptacek 15y agoJust for what it's worth: I'm playing catchup on 1.1-1.3 tomorrow and Tuesday, and I'm sure others haven't started yet too, so feel free to keep posting here and we'll try to keep paying attention to the thread.
- tptacek 15y ago(it took me an hour to get through the first 9 in 1.2. I'll get there! but console yourself with the thought that you, whoever you are, are far from the worst at this in the group.)
- gruseom 15y agoWhether or not that's true, and I doubt that it is, we all know who is hands down the wittiest. I'm stuck on 1.3.21. What the hell is "the 1,2,1 pattern or the -1,2,-1 pattern"? Does he mean a pattern in the columns? I see 1,2,1 but not -1,2,-1. Is this like one of those duck-rabbit optical illusions? Edit: there is, however, a -1,2,-1 pattern in 1.3.24, and the system there is very similar to the one in 1.3.21.
- tptacek 15y agoYep: mechanical_fish. :P
- gruseom 15y agoHow's everybody doing? I'm barely into 1.4, so I'm planning to work through a fair bit this weekend in order to be done the chapter a week from now. Should we discuss specific solutions from 1.2-1.3? Did anybody do the exercise marked "very optional" (1.3.29)? Do we need to discuss ass-kicking tactics to keep ourselves on track?
- tptacek 15y agoI'm mostly through 1.2 but not on 1.3 yet. Paging just basic algebra back in was more annoying than I expected it to be (highly recommend for those like me that you grab some cheat sheets; most of the exercises in 1.2 are very straightforward if you have systems of equations in L1 head cache). I'll try my best to keep up with you. I'm in NYC next week but I can kill some hotel downtime with this too. Very yes, regarding ass-kicking tactics.
- gruseom 15y agoIt seems unlikely that we're going to hit the target of having Chapter 1 done a week from today, especially for anyone who wants to do all the exercises. Time to recalibrate? Ass-kicking makes sense only if there are slack resources that haven't been allocated to this, but could be. Is that your case? What do you think would make a difference? One idea that occurred to me is a buddy system wherein two people would agree to nag each other and perhaps review answers to exercises, or at least confirm that they were done. Another is to leverage public commitment somehow. If I promise to do something, and don't do it, I feel bad. Let's not forget the power of the forces we're up against. :)
- mechanical_fish 15y agoI'm through the first 16 exercises of the 1.3 problems. Probably won't find time for the rest for a couple of days. We definitely want to make sure that everyone gets the "Recommended" problem from 1.3. It's a very important concept.
- gruseom 15y agoDo you mean 1.3.18, which asks why it is impossible for a system of linear equations to have exactly two solutions? This is one where people would probably come up with a variety of different explanations. Algebraically, if X and Y are solutions, then aX + bY is a solution if a + b = 1. Geometrically, if two planes intersect at a line, and you try to add a third plane that shares two points with them, you're forced to "capture" the entire line. Comments and/or additional ways of looking at this?
- gruseom 15y agoHas anyone tried the "very optional" exercise (1.3.29)?