I've been watching some of Gilbert Strang's lectures on linear algebra methods in data analytics. I've taken two courses in linear algebra and I'm interested in studying computer linear algebra. The former is taught in Matlab and the latter in R. Right now I'm taking courses in computational mathematics and computer statistics. (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?
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So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix?Īs a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower? I have more questions but they're mostly rhetorical at this point.
Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C? See what they offer and what people have done with them. If proprietary ones aren't your cup of tea, play with Octave (and its Octave Forge package collection), Maxima, and R, and if you want throw in Julia, SymPy, Axiom, or Metamath too. Surely you're not in mathematics just to pass exams and absorb/explore at whatever rate teachers and classes set? You should really give such tools a try. I think we're in danger of raising a generation of Eloi. I'm very critical of the way technology has infiltrated the modern classroom. It's like teaching people how to use Microsoft Word instead of how to write their own word processor. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). In the course of my education, I am learning how all of the layers fit together. On the other hand, typing the matrix into Mathematica and calling the diagonalize function demonstrates very little other than that you know how to command the magic box to give you the answer. Being able to diagonalize a matrix by hand may not be a useful real world skill but the ability to do it on an exam demonstrates that you understand the process. It doesn't hold much use for me (yet) because it's not allowed on any of my exams. because if not I still likely have a phone.īoth you and chongli ought to consider this argument (ignore the stuff about violent video games): because I'm likely at my computer already when this comes up, 2. If I want to be more accurate then I would use a computer - 1. > How much is the 1.35% annual property tax on a million-dollar house, per month?Ībout 1e6/1e2/1e1, or $1000.
Complicating this problem can make a need to calculate (or count) more apparent, but further complications can also make a need to compute with a program more apparent too. Unless I have another box under consideration, then I probably intend to fit as many as possible, so I'll just fill. > How many bottled liters of water can I fit in this box?
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This would never come up, because my phone navigation will tell me at any point along the trip how long it will take, more accurately because it has my full speed data plus knowledge about traffic and other hazards ahead. > If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? What if I have a recipe for three servings but five dinner guests?
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