Ok, so here it is...

[Arta]

Arta is a maths retard. I haven't studied maths for 8 years, and even then, it was pretty basic. I've forgotten most of it. I have some old textbooks and have been looking at things (and doing reasonably well) but I need to brush up on my basics. Today I was adding polynomials and I forgot that a minus outside a bracket changes the signs inside the bracket: this is the kind of thing I mean! It drives me nuts that I forget these little things and thus, make stupid mistakes... especially on long problems where one gets something wrong at the beginning and then has to start all over again.

Does anyone know of some good (preferably online and interactive) resources I could use to brush up on these basics before I get back to the more interesting stuff?

[Akamas]

Silly Harry, math is for Yoni.

[Arta]

Well, I want some too. Greedy Yoni should stop hogging it.

[Rule]

At what level are you presently comfortable?  Maybe give some examples of what you have been reading about and understand.

[Akamas]

Well, I want some too. Greedy Yoni should stop hogging it.

Yoni: He eats math, it's how he survives.

[Arta]

Rule: I've done some factorising, manipulating polynomials, solving linear/simultaneous/quadtratic  equations, some functions. I generally understand the principles of these things after I've read about them and practiced a bit, but it's the basic little things that I often get wrong. For example, the brackets thing -- my gf (she has degree-level maths) said that -(...) actually means -1 * (...), and that's why the signs change. I'll remember that now, because it makes sense to me rather than being some seemingly arbitrary rule. I'd like to understand the reasons why these basic rules work. The only practical way to do that is to go back to the beginning! Algebra 101! I think a brief look at things that simple (which I expect I'll mostly be able to do in my sleep) might help me to stop making dumb mistakes in more complicated problems.

[Rule]

Rule: I've done some factorising, manipulating polynomials, solving linear/simultaneous/quadtratic  equations, some functions. I generally understand the principles of these things after I've read about them and practiced a bit, but it's the basic little things that I often get wrong. For example, the brackets thing -- my gf (she has degree-level maths) said that -(...) actually means -1 * (...), and that's why the signs change. I'll remember that now, because it makes sense to me rather than being some seemingly arbitrary rule. I'd like to understand the reasons why these basic rules work. The only practical way to do that is to go back to the beginning! Algebra 101! I think a brief look at things that simple (which I expect I'll mostly be able to do in my sleep) might help me to stop making dumb mistakes in more complicated problems.

Becoming proficient with using mathematics as a tool is much like learning a programming language (something I'm sure you're quite used to): I imagine you already have many of the skills and habits necessary to make it a rather easy process!  The best way to quickly gain confidence and avoid making careless errors is to completely immerse yourself in solving practice problems -- do as many as you can in as short a time interval as you can; (unsurprisingly, this parallels how one should learn a spoken language).  And then for details use texts as references.

If you are craving a very deep understanding of the underlying concepts in mathematics, then books like Rudin's, Principles of Analysis (or for a slightly less intimidating treatment, "Analysis with an introduction to proof" by Steven R. Lay) will more than satisfy your cravings.  In these books you will find an incredibly rigorous and precise explanation of real numbers, sets and functions, proof techniques, cardinality, sequences, series and limits, mathematical operations (addition, subtraction, ...), using only the most basic and fundamental axioms in mathematics.  This approach to mathematics is nice in that you start from absolutely nothing and aren't left hanging on anything -- nothing could be less ambiguous.  However, they probably won't help you "bootstrap" your math for practical use.  For example, in parts it is possible you would find a discussion on something like why a+b = b+a for scalar real numbers a, b. Also, while most of the explanations won't require any prerequiste knowledge (after all, they start from the most basic axioms in mathematics!), many readers would find the discourse hard to follow without a certain level of mathematical maturity or experience with high-level abstract (e.g. philosophical) thinking.  Typically these books would be used in an university 3rd year honours course in analysis or abstract mathematics, in order to re-teach students math properly once they're at a point where they won't be intimidated to death.

In short, I think you'd be best off just working through a bunch of algebraic problems.  Do every question in the books that you have from past schooling.  If you stall on a point that would be hard to look up, it seems like you have a great resource at your disposal .  After you've had some good practice doing things that you already are a little familiar with, start reading about trigonometry, then go into pre-calculus texts.  And, finally, if you have a crippling psychological disorder like me, and want an (obsessive compulsive), deep and precise understanding of the basics, then try looking for those texts I mentioned.

[Arta]

Ok. Shall report back   Thanks.