13 ms·

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many o

by ekidd 12y ago

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's free textbook: http://joshua.smcvt.edu/linearalgebra/ http://joshua.smcvt.edu/linearalgebra/ (GFDL license, LaTeX source available) (I get nothing out of recommending this open source textbook other than the joy of sharing a book I loved.)

jimhefferon 12y ago
Hey, thanks!
- jsuskin 12y ago
  That was really cool.
jseliger 12y ago
until I read Jim Hefferon's free textbook I still prefer reading textbooks in paper, and one interesting note: it looks like a couple of companies and individuals are offering paper copies on Amazon, but none of them appear to be Henderson himself. And the companies or individual offering paper copies still charge $20 – $30!
- coopaq 12y ago
  http://joshua.smcvt.edu/linearalgebra/book.pdf http://joshua.smcvt.edu/linearalgebra/book.pdf
- krussell 12y ago
  I just noticed under the "Download Linear Algebra" section on http://joshua.smcvt.edu/linearalgebra/ http://joshua.smcvt.edu/linearalgebra/ , he gives a link to a paperback version of Linear Algebra on Amazon (ISBN-13: 978-0989897563).
- jimhefferon 12y ago
  > And the companies or individual offering paper copies still charge $20 – $30! $20 for the official version (see the book's web page for a link). That is, essentially, the price of printing and binding.
dcosson 12y ago
Thanks for the link to the book. I had a similar experience where my college linear algebra class was not good, taught by a grad student who seemed to have no enthusiasm for the material or for teaching, plus his accent was hard to understand at times. It was also the first exposure to proofs in the math curriculum so from the beginning I remember being overwhelmed by those and totally losing sight of the forest for the trees. I sat through the whole semester thinking it was a pretty useless subject. My senior year I happened to take a machine learning and a quantum mechanics class at the same time and had a big ah-ha moment when I realized how big a role linear algebra plays in such a wide range of subjects. I went back through my old textbook and notes at that point and that new perspective made a huge difference, it was like it was completely different material and it was a lot easier to understand.
- samatman 12y ago
  As an aside, I get really confused and disheartened when I hear that someone's first exposure to proof was in college in a linear algebra class. I had a somewhat old-fashioned education for an American, and learned proof via Euclid when I was 12. And again, but poorly, when I was 16, but that's another story. Proof is supposed to be learned a) thoroughly b) early and c) as a part of geometry. What's the point in even studying Euclid if you don't learn the method of proof?
sporkenfang 12y ago
BLESS YOU. I have a computer vision exam on Tuesday. Naturally, the prof is awful at explaining math and only seems to care about the theory part.
ams6110 12y ago
As a programmer, I've used calculus and linear algebra exactly never in my professional (20+ years) career. It just doesn't really come up doing web apps, sysadmin or dba work.
- taeric 12y ago
  A lot of this is whether or not you are looking for it, honestly. It is easy to stay away from it, though it is also easy to find if you look for it.
- jstelly 12y ago
  I work on games. I use linear algebra daily and calculus frequently, but far less often. Both are extremely relevant to game development although you can get by without calculus and only light linear algebra if you limit your scope or specialize (in something other than graphics or simulation).
- mcguire 12y ago
  In my 20-odd years, I'd agree---uses of calc or linear algebra have been vanishingly rare, although my current project is changing that a bit. Not because I didn't have opportunities to use it, but because I didn't seek out those opportunities. On the other hand, I'm prepared to defend to the death the statement that programming is applied formal logic. (Or possibly abstract algebra; that is likely more appropriate for some more modern things. On the other hand, I grew up in the land of Dijkstra, so....)
- mannykannot 12y ago
  Mechanics don't use calculus, even many engineers don't, but those working in R&D, especially towards the R side, do.
deleted 12y ago
[deleted]
vowelless 12y ago
I agree although I work in robotics / computer vision. What I wish I had done a lot more of is statistics. Being able to reason about probabilities clearly, getting an idea of how a system performs given various variables, and most importantly, being able to communicate this to others has been very useful to me. I think anyone (front end, backend, etc) can benefit from learning about statistics.
- edanm 12y ago
  Do you have a recommendation for a good statistics textbook, for someone who is mathematically literate, but doesn't know almost any statistics?
  - brendano 12y ago
    This book is great and designed for exactly this type of audience: http://www.stat.cmu.edu/~larry/all-of-statistics/ http://www.stat.cmu.edu/~larry/all-of-statistics/
  - jsalvatier 12y ago
    http://smile.amazon.com/Introduction-Bayesian-Statistics-2nd-Edition/dp/0470141158?sa-no-redirect=1 http://smile.amazon.com/Introduction-Bayesian-Statistics-2nd... Was extremely gentle and mind blowing.
- peterfirefly 12y ago
  But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.
  - tel 12y ago
    Don't know why you're being downvoted. This is totally true.
    - 12y ago
superobserver 12y ago
Thank you for the link. I had the same experience in uni. It's a general issue that plagues mathematics education, I think: theory should come after some basic understanding of applications, not before.
IndianAstronaut 12y ago
For some coding puzzles I was given during interviews, I found that sometimes linear algebra solutions can be used. I submitted such a solution once to a company for a take home problem, they rejected me but it was still an interesting experience.
mathattack 12y ago
Linear Algebra is also important in Finance too. Stats are useful in almost every field, as well as for developing a probability-based state of mind. I wonder why the imbalance exists. Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry?
- eli_gottlieb 12y ago
  > Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry? Yes. Computer Science curricula tend to focus overmuch on preparing students to work as software engineers, and Mathematics curricula tend to focus overmuch on analysis (to the point that once you get past Calc 1+2+3, Linear Algebra, Differential Equations, Mathematical Analysis/Epsilon-Delta Calculus-with-proofs, and Real Analysis, things like Algebra and Topology are senior-year electives).
  - mathattack 12y ago
    Yes - it's too bad they keep the fun stuff for the end. I've been rediscovering the fun of number theory via Project Euler.
UUMMUU 12y ago
ekidd - thanks for the link! Also, I know it's not free (the coursera course is free) but it's still a great read and seriously applicable http://codingthematrix.com/ http://codingthematrix.com/

by ekidd 12y ago

jimhefferon 12y ago

Hey, thanks!

jsuskin 12y ago
That was really cool.

jseliger 12y ago

until I read Jim Hefferon's free textbook I still prefer reading textbooks in paper, and one interesting note: it looks like a couple of companies and individuals are offering paper copies on Amazon, but none of them appear to be Henderson himself. And the companies or individual offering paper copies still charge $20 – $30!

coopaq 12y ago
http://joshua.smcvt.edu/linearalgebra/book.pdf http://joshua.smcvt.edu/linearalgebra/book.pdf
krussell 12y ago
I just noticed under the "Download Linear Algebra" section on http://joshua.smcvt.edu/linearalgebra/ http://joshua.smcvt.edu/linearalgebra/ , he gives a link to a paperback version of Linear Algebra on Amazon (ISBN-13: 978-0989897563).
jimhefferon 12y ago
> And the companies or individual offering paper copies still charge $20 – $30! $20 for the official version (see the book's web page for a link). That is, essentially, the price of printing and binding.

dcosson 12y ago

Thanks for the link to the book. I had a similar experience where my college linear algebra class was not good, taught by a grad student who seemed to have no enthusiasm for the material or for teaching, plus his accent was hard to understand at times. It was also the first exposure to proofs in the math curriculum so from the beginning I remember being overwhelmed by those and totally losing sight of the forest for the trees. I sat through the whole semester thinking it was a pretty useless subject. My senior year I happened to take a machine learning and a quantum mechanics class at the same time and had a big ah-ha moment when I realized how big a role linear algebra plays in such a wide range of subjects. I went back through my old textbook and notes at that point and that new perspective made a huge difference, it was like it was completely different material and it was a lot easier to understand.

samatman 12y ago
As an aside, I get really confused and disheartened when I hear that someone's first exposure to proof was in college in a linear algebra class. I had a somewhat old-fashioned education for an American, and learned proof via Euclid when I was 12. And again, but poorly, when I was 16, but that's another story. Proof is supposed to be learned a) thoroughly b) early and c) as a part of geometry. What's the point in even studying Euclid if you don't learn the method of proof?

sporkenfang 12y ago

BLESS YOU. I have a computer vision exam on Tuesday. Naturally, the prof is awful at explaining math and only seems to care about the theory part.

ams6110 12y ago

As a programmer, I've used calculus and linear algebra exactly never in my professional (20+ years) career. It just doesn't really come up doing web apps, sysadmin or dba work.

taeric 12y ago
A lot of this is whether or not you are looking for it, honestly. It is easy to stay away from it, though it is also easy to find if you look for it.
jstelly 12y ago
I work on games. I use linear algebra daily and calculus frequently, but far less often. Both are extremely relevant to game development although you can get by without calculus and only light linear algebra if you limit your scope or specialize (in something other than graphics or simulation).
mcguire 12y ago
In my 20-odd years, I'd agree---uses of calc or linear algebra have been vanishingly rare, although my current project is changing that a bit. Not because I didn't have opportunities to use it, but because I didn't seek out those opportunities. On the other hand, I'm prepared to defend to the death the statement that programming is applied formal logic. (Or possibly abstract algebra; that is likely more appropriate for some more modern things. On the other hand, I grew up in the land of Dijkstra, so....)
mannykannot 12y ago
Mechanics don't use calculus, even many engineers don't, but those working in R&D, especially towards the R side, do.

deleted 12y ago

[deleted]

vowelless 12y ago

I agree although I work in robotics / computer vision. What I wish I had done a lot more of is statistics. Being able to reason about probabilities clearly, getting an idea of how a system performs given various variables, and most importantly, being able to communicate this to others has been very useful to me. I think anyone (front end, backend, etc) can benefit from learning about statistics.

edanm 12y ago
Do you have a recommendation for a good statistics textbook, for someone who is mathematically literate, but doesn't know almost any statistics?
- brendano 12y ago
  This book is great and designed for exactly this type of audience: http://www.stat.cmu.edu/~larry/all-of-statistics/ http://www.stat.cmu.edu/~larry/all-of-statistics/
- jsalvatier 12y ago
  http://smile.amazon.com/Introduction-Bayesian-Statistics-2nd-Edition/dp/0470141158?sa-no-redirect=1 http://smile.amazon.com/Introduction-Bayesian-Statistics-2nd... Was extremely gentle and mind blowing.
peterfirefly 12y ago
But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.
- tel 12y ago
  Don't know why you're being downvoted. This is totally true.
  - 12y ago

superobserver 12y ago

Thank you for the link. I had the same experience in uni. It's a general issue that plagues mathematics education, I think: theory should come after some basic understanding of applications, not before.

IndianAstronaut 12y ago

For some coding puzzles I was given during interviews, I found that sometimes linear algebra solutions can be used. I submitted such a solution once to a company for a take home problem, they rejected me but it was still an interesting experience.

mathattack 12y ago

Linear Algebra is also important in Finance too. Stats are useful in almost every field, as well as for developing a probability-based state of mind. I wonder why the imbalance exists. Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry?

eli_gottlieb 12y ago
> Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry? Yes. Computer Science curricula tend to focus overmuch on preparing students to work as software engineers, and Mathematics curricula tend to focus overmuch on analysis (to the point that once you get past Calc 1+2+3, Linear Algebra, Differential Equations, Mathematical Analysis/Epsilon-Delta Calculus-with-proofs, and Real Analysis, things like Algebra and Topology are senior-year electives).
- mathattack 12y ago
  Yes - it's too bad they keep the fun stuff for the end. I've been rediscovering the fun of number theory via Project Euler.

UUMMUU 12y ago

ekidd - thanks for the link! Also, I know it's not free (the coursera course is free) but it's still a great read and seriously applicable http://codingthematrix.com/ http://codingthematrix.com/