4 ms·

Ask HN: learning Basic Math, Reading Math

11 points by justlearning 17y ago

Lately after couple of posts including the latest http://news.ycombinator.com/item?id=666407 , I gathered the courage to ask this: problem description : I want to finish "Introductions to Algorithms" (Cormen et al) and the math is holding me back. I have been trying and am too impatient. Previous comments from (do you buy books for long term) and a couple more helped me understand that this is normal to spend couple of hours on a single paragraph/page. But sometimes I don't get it for the lack of basics (it's been a while away from academics). I know I should work hard at going back, but however back I go, it feels like I don't know it. the longer it takes, more depressing it is. Sometimes, I feel my whole life is going to be depressed in this pursuit. My problem in one line: I want to READ Maths like I read english (when i read the word mountain- i visualize a mountain, when i read an equation i see greek letters with an equals sign... you get the idea?) my self analysis - too impatient, want to code the pseudo-code eagerly, hate (or lazy?) to take the pen/paper, look for solutions without trying hard = typing/reading the solution rather than understanding, have no big picture of implementing math - project to work on (people reading math that helps in their work vs me doing math with no implementation makes my brain go to sleep.) I have been trying to get into about math for a while. I have done my research and read few excellent blogs (including from atleast one member of HN) for know-hows. Books I know I should have to cover the basics: *Discrete Mathematics with Applications by Susanna S. Epp *How to prove it? *Concrete Mathematics - Knuth (I got along well with Knuth for the first chapter and after a while my lack of basics >> depression >> stop and do something else.) Which books have helped you? which one should I pick first? How can I achieve my goal? I need books basic enough to teach me discrete math (to achieve my goal of finishing introduction to algorithms) and in the long run read math like english. I am looking for your experiences - obstacles you faced... something like this [ http://news.ycombinator.com/item?id=666615 ; i can't relate to few points - eg: not qualified to decide if a book is badly written]- anything i can relate to, any anecdotes? perhaps..my sub conscious will probably hold back my depression! Everyone of you have truly enchanting stories. I know I am taking your time, but I HAVE to do this. disclaimer: i am not a comp sci student. <cough>my experience has been as an enterprise developer</cough>. pls don't be hard on me. ...and thanks for your precious time

RiderOfGiraffes 17y ago
One person's opinion ... You will never read math like English. I'm a Ph.D., I've had this discussion with many other graduates and post-graduates. Math is different from English (or any other natural language). In my circles of math, programming and education there is even a phrase "Read like Math" as opposed to "Read like a comic book". Math is its own language, and it is dense. When interpreted into English a single equation can become several paragraphs. Learning to read and visualize an equation is possible, but always necessary. Simple equations are easy, but if there's real content, it's hard. You need to ask what you're trying to accomplish, really. If you want to learn stuff, you need to do it. You can learn about it by reading about it, but you can only learn to do it by doing it (under guidance or with hints). See also: http://news.ycombinator.com/item?id=672067 http://news.ycombinator.com/item?id=672067 http://www.scientificblogging.com/carl_wieman/why_not_try_scientific_approach_science_education http://www.scientificblogging.com/carl_wieman/why_not_try_sc... EDIT: added reference: http://c2.com/cgi/wiki?MathForProgrammers http://c2.com/cgi/wiki?MathForProgrammers Quoting from the this last: I'm not certain that reading like prose is a benefit. When algebra was first invented, people didn't use variables, operators or other notation. They just wrote things out in natural language. Here is an example from Al-Khwarizmi's famous book: If the instance be, 'ten and thing to be multiplied by thing less ten,' then this is the same as 'if it were said thing and ten by thing less ten. You say, therefore, thing multiplied by thing is a square positive; and ten by thing is ten things positive; and minus ten by thing is ten things negative. You now remove the positive by the negative, then there only remains a square. Minus ten multiplied by ten is a hundred, to be subtracted from the square. This, therefore, altogether, is a square less a hundred dirhems. Compare this to (x+10)*(x-10) = x*x + 10*x - 10*x - 10*10 = x*x - 100 Now imagine trying to do even simple calculus like this. If there's a lot of essential complexity, I claim that natural language becomes much harder to understand than specialized notation, which is why notation exists in the first place. A good notation is understood on its own terms, not in terms of translation to some natural language statement, for instance, algebraic manipulations are done according to certain rules, without having to re-justify them each time, because of the underlying soundness of algebra.
- 17y ago

11 points by justlearning 17y ago

RiderOfGiraffes 17y ago

One person's opinion ... You will never read math like English. I'm a Ph.D., I've had this discussion with many other graduates and post-graduates. Math is different from English (or any other natural language). In my circles of math, programming and education there is even a phrase "Read like Math" as opposed to "Read like a comic book". Math is its own language, and it is dense. When interpreted into English a single equation can become several paragraphs. Learning to read and visualize an equation is possible, but always necessary. Simple equations are easy, but if there's real content, it's hard. You need to ask what you're trying to accomplish, really. If you want to learn stuff, you need to do it. You can learn about it by reading about it, but you can only learn to do it by doing it (under guidance or with hints). See also: http://news.ycombinator.com/item?id=672067 http://news.ycombinator.com/item?id=672067 http://www.scientificblogging.com/carl_wieman/why_not_try_scientific_approach_science_education http://www.scientificblogging.com/carl_wieman/why_not_try_sc... EDIT: added reference: http://c2.com/cgi/wiki?MathForProgrammers http://c2.com/cgi/wiki?MathForProgrammers Quoting from the this last: I'm not certain that reading like prose is a benefit. When algebra was first invented, people didn't use variables, operators or other notation. They just wrote things out in natural language. Here is an example from Al-Khwarizmi's famous book: If the instance be, 'ten and thing to be multiplied by thing less ten,' then this is the same as 'if it were said thing and ten by thing less ten. You say, therefore, thing multiplied by thing is a square positive; and ten by thing is ten things positive; and minus ten by thing is ten things negative. You now remove the positive by the negative, then there only remains a square. Minus ten multiplied by ten is a hundred, to be subtracted from the square. This, therefore, altogether, is a square less a hundred dirhems. Compare this to (x+10)*(x-10) = x*x + 10*x - 10*x - 10*10 = x*x - 100 Now imagine trying to do even simple calculus like this. If there's a lot of essential complexity, I claim that natural language becomes much harder to understand than specialized notation, which is why notation exists in the first place. A good notation is understood on its own terms, not in terms of translation to some natural language statement, for instance, algebraic manipulations are done according to certain rules, without having to re-justify them each time, because of the underlying soundness of algebra.

17y ago