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Very nicely put. I'm a big fan of linear algebra because it's the best example of why learning math is useful. Sure knowing about equation and calculus come in

by ivan_ah 11y ago

Very nicely put. I'm a big fan of linear algebra because it's the best example of why learning math is useful. Sure knowing about equation and calculus come in handy, but linear algebra is pure modelling superpowers and a much more valuable tool overall. Related: An awesome LA introductory lecture by Prof. Strang: 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-... Related 2: A short tutorial on LA that I wrote: http://minireference.com/static/tutorials/linear_algebra_in_4_pages.pdf http://minireference.com/static/tutorials/linear_algebra_in_...

johncolanduoni 11y ago
I definitely think linear algebra has a lot of practical applications, but I'm not sure I would necessarily call it the "best" nor the "most valuable tool overall". It certainly provides the most bang for your buck if you are doing certain kinds of modeling, but even just within modeling which tool will be the most useful will depend a ton on what you are doing. For example, for dynamical systems you may be using linear algebra, but mostly as a computational tool for solving differential equations. In this case, analysis of your problem at the level of calculus is extremely important if you want to come up with an accurate and computationally feasible model.
- ivan_ah 11y ago
  Agreed. The "best" in my comment was entirely in the bang-for-your-buck sense.
andrepd 11y ago
I don't think you can say of any topic in mathematics that it's the best example of why learning math is useful. What about calculus? It's an immensely powerful tool that, by harnessing the power of the infinite and the infinitesimal, unlocks a massive body of practical applications in nearly every field of quantitative knowledge. And what about discrete math? Without it there would be no such thing as a computer. Differential equations, the tool for modeling dynamical systems? Mathematics is a vast topic that every quantitative discipline must necessarily draw from. Each field of study will benefit more from certain topics of it.
- ivan_ah 11y ago
  > What about calculus [...and...] differential equations ? I agree that calculus and diff. equations techniques are important, but if you look closely, you'll see they are only "necessary" for engineers and physicists, and other "hard" sciences, and not so essential for non-science studies. Imagine "pitching" the benefits of learning university-level math to a class of Arts students. Can you honestly say their lives will be improved if they were to learn about a bunch of techniques of integration? On the other hand, I wouldn't hesitate to recommend learning LA to them. Thinking about operators, vector spaces, dimensions, etc. is applicable much more widely. (I speak from experience here, because I've been "finishing up" the applications chapter in my LA book and I keep finding new applications to cover: balancing chemical equations, electric currents and other network flows, nutrition, least squares approximations, linear programming, cryptography, network coding, error correcting codes, Fourier analysis, prob. theory, and quantum mechanics. The LA party just don't stop ;)
  - mooreds 11y ago
    I remember in my college linear algebra class (I think it was) that my prof made the joke that his wife was the projection of the vector representing all the attributes of his ideal woman into the space that represented the pool of all women who would date him. I thought it was hilarious. Almost made me want to be a math major (I was just a physics major). Which makes me think of: https://www.xkcd.com/435/ https://www.xkcd.com/435/
    - paulmd 11y ago
      I can't decide whether to go for the "null vector" joke or the "yo mamma's magnitude is so great"...
  - zeroonetwothree 11y ago
    I certainly wouldn't pick linear algebra as generally useful for "Arts students". Certainly something like probability or statistics is of much more general benefit to a typical person.
  - 11y ago

by ivan_ah 11y ago

johncolanduoni 11y ago

I definitely think linear algebra has a lot of practical applications, but I'm not sure I would necessarily call it the "best" nor the "most valuable tool overall". It certainly provides the most bang for your buck if you are doing certain kinds of modeling, but even just within modeling which tool will be the most useful will depend a ton on what you are doing. For example, for dynamical systems you may be using linear algebra, but mostly as a computational tool for solving differential equations. In this case, analysis of your problem at the level of calculus is extremely important if you want to come up with an accurate and computationally feasible model.

ivan_ah 11y ago
Agreed. The "best" in my comment was entirely in the bang-for-your-buck sense.

andrepd 11y ago

I don't think you can say of any topic in mathematics that it's the best example of why learning math is useful. What about calculus? It's an immensely powerful tool that, by harnessing the power of the infinite and the infinitesimal, unlocks a massive body of practical applications in nearly every field of quantitative knowledge. And what about discrete math? Without it there would be no such thing as a computer. Differential equations, the tool for modeling dynamical systems? Mathematics is a vast topic that every quantitative discipline must necessarily draw from. Each field of study will benefit more from certain topics of it.

ivan_ah 11y ago
> What about calculus [...and...] differential equations ? I agree that calculus and diff. equations techniques are important, but if you look closely, you'll see they are only "necessary" for engineers and physicists, and other "hard" sciences, and not so essential for non-science studies. Imagine "pitching" the benefits of learning university-level math to a class of Arts students. Can you honestly say their lives will be improved if they were to learn about a bunch of techniques of integration? On the other hand, I wouldn't hesitate to recommend learning LA to them. Thinking about operators, vector spaces, dimensions, etc. is applicable much more widely. (I speak from experience here, because I've been "finishing up" the applications chapter in my LA book and I keep finding new applications to cover: balancing chemical equations, electric currents and other network flows, nutrition, least squares approximations, linear programming, cryptography, network coding, error correcting codes, Fourier analysis, prob. theory, and quantum mechanics. The LA party just don't stop ;)
- mooreds 11y ago
  I remember in my college linear algebra class (I think it was) that my prof made the joke that his wife was the projection of the vector representing all the attributes of his ideal woman into the space that represented the pool of all women who would date him. I thought it was hilarious. Almost made me want to be a math major (I was just a physics major). Which makes me think of: https://www.xkcd.com/435/ https://www.xkcd.com/435/
  - paulmd 11y ago
    I can't decide whether to go for the "null vector" joke or the "yo mamma's magnitude is so great"...
- zeroonetwothree 11y ago
  I certainly wouldn't pick linear algebra as generally useful for "Arts students". Certainly something like probability or statistics is of much more general benefit to a typical person.
- 11y ago