41–50 of 88 posts
Just follow the usual path for education in relatively applied math. Here is a nutshell description: The standard high school level subjects are algebra, plane geometry, second year algebra, trigonometry, and solid geometry. The standard college level subjects are calculus, abstract algebra, linear algebra, advanced calculus, ordinary differential equations. Might also take elementary courses in probability and stati…
I'm going to second Arun2009's recommendation for How to Solve It by Polya. And then I'm going to recommend Haskell. I recently realized how much my understand of set theory improved and was solidified purely by programming Haskell a lot.
http://www.reddit.com/r/math/comments/eohrr/to_everyone_who_...
It then follows something similar to a university-level curriculum in Europe (continental, perhaps not UK), which might lead all the way to research maths, but perhaps it is not the most appropriate path for computer science because it entirely misses the mathematical concept of computability.
Just follow the usual path for education in relatively applied math. Here is a nutshell description: The standard high school level subjects are algebra, plane geometry, second year algebra, trigonometry, and solid geometry. The standard college level subjects are calculus, abstract algebra, linear algebra, advanced calculus, ordinary differential equations. Might also take elementary courses in probability and stati…
You are right that you do need algebra, linear algebra, just enough calculus to understand infinite series (which is usually put in the second calculus course), etc.
You left out graph theory and combinatorics, both of which are extremely important to CS.
Use something lke Khan Academy to fill in the blanks.
The benefit of DIY maths is that you get to focus on what your interest is, whether that be algebra or geometry or stats/data analysis or discrete maths or foundations or whatever. (Contrary to some answers here, I don't think trig, measure theory, or planar geometry are necessary, unless you read something and it catches your fancy.) If your goal is just to do more maths, then just throw away anything that bores you and dive into anything that interests you.
If you're interested in C.S. applications then I think discrete maths is the thing to focus on. Eg, "Concrete Mathematics" by Knuth. But you can go an even more direct route and if algorithms is your goal, there are some free courses available online that do just that.
MIT OCW and AcademicEarth are excellent for in-depth (course-length) treatments of material by seasoned teachers. Wikipedia and math.StackExchange are good for broad overviews and quick Q's, respectively.
For "proofs, and other practical applications" -- that's quite broad. OCW has a course on geophysics and a course on signal processing -- both are "practical applications" but I don't know if that's what you have in mind. Most of the OCW stuff -- whether it's chemistry, materials sci, DSP, whatever -- is aimed at engineers (other than the upper level pure maths), and therefore practical.
As for proofs, you will see them in almost any maths textbook. Spivak makes some challenging ones and if you haven't taken calculus or linear algebra then Flanigan & Kazdan might be worth a skim. But if you're interested in CS applications then you can find those kinds of argumentation in an algorithms course.
BTW, I do not recommend the Khan Academy. It gets a lot of press but I have not found it so great. (It is fine but so is just surfing Youtube -- a lot of people make videos besides SK.)
Also, if you can still edit this question, you might give us some idea of where you're starting from and how much time you expect to spend, to elicit better answers.
HTH.
PS By "the hard way" do you mean doing exercises? Because pretty much all mathematics texts expect you to do it "the hard way" if that's what you mean.
I may have answered your question here: http://isomorphismes.tumblr.com/post/15431506533/i-never-did... . The benefit of DIY maths is that you get to focus on what your interest is, whether that be algebra or geometry or stats/data analysis or discrete maths or foundations or whatever. (Contrary to some answers here, I don't think trig, measure theory, or planar geometry are necessary, unless you read something and i…
I may have answered your question here: http://isomorphismes.tumblr.com/post/15431506533/i-never-did... . The benefit of DIY maths is that you get to focus on what your interest is, whether that be algebra or geometry or stats/data analysis or discrete maths or foundations or whatever. (Contrary to some answers here, I don't think trig, measure theory, or planar geometry are necessary, unless you read something and i…
It's bizarre that you start your list of recommended books on mathematics for "people who never got far with it at school" with Penrose's _The Road to Reality_. No one should follow that recommendation. The book is not really readable without a background of a Ph.D.-level knowledge in math.
Just follow the usual path for education in relatively applied math. Here is a nutshell description: The standard high school level subjects are algebra, plane geometry, second year algebra, trigonometry, and solid geometry. The standard college level subjects are calculus, abstract algebra, linear algebra, advanced calculus, ordinary differential equations. Might also take elementary courses in probability and stati…