What are some ways to effectively practice and apply Maths learning?
I’ve been doing a lot of learning and found that practicing on paper is generally easier than Latex or a cobbled syntax in electronic documents, but would like to know if I just really need to bite the bullet and do it this way (Latex or similar).
Once I have (what I believe) an understanding of the problem types, I will generally write code to do it for me as doing this makes it even clearer in my head. Problem is though, once I do the code, I generally don’t practice on paper anymore and I am not sure if this is going to be hindrance in understanding more complex topics.
My end goal is to be able to read and understand the maths in any AI focused research paper, and then be able to do some maths which isn’t just practice examples but I am not sure on how to get to that last step.
I have heard (I have no citation and it’s probably apocryphal, but I found the anecdote enlightening) that Enrico Fermi’s way of reading articles was to read the abstract, put the paper away, do the maths by himself and once he was done, compare his results with the article. That’s probably a bit hardcore, but you should be able to start from somewhere in the paper’s reasoning and do a few steps forward.
But where are you in your paper reading at the moment ? Is there a particular problem that spurred this question ?
That technique would be beyond me at this stage—I have done courses in Calculus, Linear Algebra and Logic and can finally understand most of the syntax and flow in research papers, though I still don’t feel at all competent, seeing that I feel I could not recreate the proofs they come up with.
I think that is my issue—I can read lots of maths, I can do the exercises but I am not sure how to go about ‘doing something real’ - ask me to write any software you can think of and I can do that, but I feel I am missing some fundamental point / learning in maths. Or maybe I am over thinking this, and haven’t had a concrete problem to play with.
Good point, I should learn it anyway. But in terms of learning and solving problems, do you work them out using LaTex or do you use pen and paper / whiteboard?
I write everything on paper, although I duplicate all the important parts to LaTeX. This means that I go through a notebook approximately every 3 weeks, but it’s definitely worth it. I only use LaTeX to communicate with others and store really important bits (although recently I’ve also just been scanning my paper). I believe this is pretty much standard among my peers.
I’ve done different things at different parts of my life. I used to work everything out on paper first, but that got too time intensive. For most of grad school I worked in LaTeX exclusively, but I gather from my peer group that being able to do this is kind of rare. I bought a Surface Pro 2 a couple months ago, so now I do both simultaneously, sketching out bits in windows notebook while writing exposition in LaTeX.
I don’t think there’s really a general best practice to be found here; I think you just need to try different things until you find a workflow that you can live with.
LaTex is for typesetting. I know of nobody who “does the math” in LaTex; they do the math on paper and write it up in LaTex for presentation or publication (or if they need to ask a question on MathOverflow, or something like that).
That said, you should learn LaTex if you ever want to do research in anything mathematical.
I started using LaTeX for my physics homework because I kept making algebraic mistakes (mostly sign errors) when I’d copy expressions between steps. Ended up saving me time on net.
I use vim now (with syntax highlighting plus some useful macros), but I used nano for a few years and it wasn’t too bad either. I compile in the command line and have a pdf open in another window.
I use Kile. Being able to commit, tag and branch in git (heck, just being able to erase a part in the middle and rewrite it without ending up with a chain of arrows across three different pieces of paper) makes things easier to be worth the (slight) writing slowdown, and most of the time I can express myself in latex—after a while it just becomes the language you think in, \int becomes the symbol for integration and so on. Very occasionally I’ll write something I know is incorrect notation but close enough that I’ll know what I meant, and can go back and correct it later.
Last year I made a deliberate choice to produce all my maths assignments in LaTeX, the upshot of which is that I’m now pretty comfortable with LaTeX. I’m pretty damn sure you wouldn’t want to use it as substitute to pencil-and-paper working, though.
What are some ways to effectively practice and apply Maths learning?
I’ve been doing a lot of learning and found that practicing on paper is generally easier than Latex or a cobbled syntax in electronic documents, but would like to know if I just really need to bite the bullet and do it this way (Latex or similar).
Once I have (what I believe) an understanding of the problem types, I will generally write code to do it for me as doing this makes it even clearer in my head. Problem is though, once I do the code, I generally don’t practice on paper anymore and I am not sure if this is going to be hindrance in understanding more complex topics.
My end goal is to be able to read and understand the maths in any AI focused research paper, and then be able to do some maths which isn’t just practice examples but I am not sure on how to get to that last step.
I have heard (I have no citation and it’s probably apocryphal, but I found the anecdote enlightening) that Enrico Fermi’s way of reading articles was to read the abstract, put the paper away, do the maths by himself and once he was done, compare his results with the article. That’s probably a bit hardcore, but you should be able to start from somewhere in the paper’s reasoning and do a few steps forward.
But where are you in your paper reading at the moment ? Is there a particular problem that spurred this question ?
That technique would be beyond me at this stage—I have done courses in Calculus, Linear Algebra and Logic and can finally understand most of the syntax and flow in research papers, though I still don’t feel at all competent, seeing that I feel I could not recreate the proofs they come up with.
I think that is my issue—I can read lots of maths, I can do the exercises but I am not sure how to go about ‘doing something real’ - ask me to write any software you can think of and I can do that, but I feel I am missing some fundamental point / learning in maths. Or maybe I am over thinking this, and haven’t had a concrete problem to play with.
Try taking a thing you know how to do, and figure out why it works.
Why does integration-by-parts work, say?
If you ever want to communicate with others, LaTeX is the lingua franca of mathematics.
Good point, I should learn it anyway. But in terms of learning and solving problems, do you work them out using LaTex or do you use pen and paper / whiteboard?
I write everything on paper, although I duplicate all the important parts to LaTeX. This means that I go through a notebook approximately every 3 weeks, but it’s definitely worth it. I only use LaTeX to communicate with others and store really important bits (although recently I’ve also just been scanning my paper). I believe this is pretty much standard among my peers.
I’ve done different things at different parts of my life. I used to work everything out on paper first, but that got too time intensive. For most of grad school I worked in LaTeX exclusively, but I gather from my peer group that being able to do this is kind of rare. I bought a Surface Pro 2 a couple months ago, so now I do both simultaneously, sketching out bits in windows notebook while writing exposition in LaTeX.
I don’t think there’s really a general best practice to be found here; I think you just need to try different things until you find a workflow that you can live with.
LaTex is for typesetting. I know of nobody who “does the math” in LaTex; they do the math on paper and write it up in LaTex for presentation or publication (or if they need to ask a question on MathOverflow, or something like that).
That said, you should learn LaTex if you ever want to do research in anything mathematical.
Hello! Nice to meet you!
My questions are how (what editor) and why?
LaTeX seems an awful way to do scratch work, which is most of math.
I started using LaTeX for my physics homework because I kept making algebraic mistakes (mostly sign errors) when I’d copy expressions between steps. Ended up saving me time on net.
I use vim now (with syntax highlighting plus some useful macros), but I used nano for a few years and it wasn’t too bad either. I compile in the command line and have a pdf open in another window.
I use Kile. Being able to commit, tag and branch in git (heck, just being able to erase a part in the middle and rewrite it without ending up with a chain of arrows across three different pieces of paper) makes things easier to be worth the (slight) writing slowdown, and most of the time I can express myself in latex—after a while it just becomes the language you think in, \int becomes the symbol for integration and so on. Very occasionally I’ll write something I know is incorrect notation but close enough that I’ll know what I meant, and can go back and correct it later.
I totally do some math in latex :). It’s just easier to convert mentally sometimes than get paper out.
Last year I made a deliberate choice to produce all my maths assignments in LaTeX, the upshot of which is that I’m now pretty comfortable with LaTeX. I’m pretty damn sure you wouldn’t want to use it as substitute to pencil-and-paper working, though.