Math became ludicrously easy for me as soon as I realized how to think about it. It wasn't the same method that they were suggesting in school, and I don't know that my method would work for everyone.
I will be very much interested in learning what method did you use.After dropping from regular education 12 years ago, I have tried to learn mathematics multiple times with moderate success only.
Please try to share your methods via a blog post/elaborate comment if you can spare some time.
But I'll be sure to put together a follow-up instructional blog that skips the vitriol, as nobody should actually have to just believe me. I do think that the very general attitude toward each problem is the only constant feature, and each topic has to be treated as a brand-new exploration, so I'll need to coagulate a topic to start off with. I'm leaning towards degrees of freedom, coordinate systems and the magic of Euler's formula. Sound good?
And if not, I'm serious about the last sentence. What topic gave you the most trouble when you tried to learn it?
I have tried to learn discrete mathematics topic however I have never made progress past Calculus.
I had multiple false starts on Linear Algebra, Probability,Graph theory,Set theory, and Logic. Somehow books on these topics tends to run into hundreds of pages with multiple exercises of similar type which kinda encourages me to drop it typically when it starts becoming repetitive.I am not sure how to cross this plateau.
Well to be honest, I'm not that far along into probably some of those same books myself, and I still get derailed by random curiosities and end up on Wikipedia or ordering a new book. The latest was a tangent into filter theory and digital signal processing, for a real-time audio project. It's hard to anticipate everything I should be able to do but I have some idea of the general order of things to study personally. If I needed to go in depth about Linear Algebra (and I definitely do), first I'd recall whatever I know about vectors and vector spaces, transformations and matrices and systems of equations, and start gathering articles and seeing if I'm missing any critical linked topics. After I get confident enough, I'd probably skip right to some textbook topic that caught my attention, say normed vector spaces, and try to make do with backward-skipping as a last resort.
Of course, that's just an artificial way of making the problem harder, basically, so that it's more interesting than safer but repetitive sets of exercises. The best way to be interested, by far, is to actually want to solve some problem. For now, anyway, I heartily recommend looking for problems that these disciplines can solve, and choosing one to solve yourself.
In my experience Calculus was a tough nut to crack. This was mainly because it is usually taught in a way that forces you to chew lots of preliminary materials which seem completely unmotivated.
But obviously, Calculus was not developed the way it is taught. I found historial approaches more motivating. That means either using infinitesimals (17th century approach), or starting from construction of the real number, say Dedekind cuts or Cauchy sequences (19th century approach).
If you're having trouble then I'd suggest that you pick up Calculus Made Easy by Silvanus P. Thompson. Best book I've read on the subject by a country mile.
