Arithmetic and calculus trainers

I want to train my mental arithmetic and calculus skills. Do you know of any games or libraries that can generate questions up to freshman level calculus? (Preferably Scheme or Haskell)

Calculus is a pseudoscience.

On a side node, how do you know if dividing by an integer i will result in a repeating decimal?

>>3
1/0 = 999999999999999999...

>>3
It always will.

>>3
Depends on the base of your number system.

>>3
(A) if a/b is a repeating decimal so is 10a/b.
(B) if a/b is an integer it is not a repeating decimal.
(C) (by A and B) if 10^k a/b is an integer for some k, then a/b is not a repeating decimal
(D) (by the contrapositive of C) if 10^k a/b is not an integer for any k, then a/b is a repeating decimal

>>7
(by the contrapositive of C)
That's the inverse, and it's not always true.

http://brain.oxfordjournals.org/content/123/11/2240.full

Much of multiplication and addition is rote skills, subtraction and negatives stem from addition, division stems from subtraction and multiplication.

I've been tossing around a dual-objective game, probably with Tux. One "path" of the game would start with addition of numbers, possibly earlier. Second path would start with addition of bars, shapes, or some uncountable but measure-able object. The goal would be to train both the rote/exact mechanisms and also train the approximation mechanisms because they're so rarely touched on.

I could even arrange the levels in sort of a tree diagram, so I could demonstrate the concept that certain math understanding is based on prerequisites, and you shouldn't be doing it if you can't understand the prereqs.

Probably pretty early I'd bring in dual-question problems. Like I'd say if this bar is 5, how much is this bar, and extend it with multiplication, divisions, etc. I could even have animated tutorials on how the math looks for approximation methods, and tables for rote methods.

I'd probably also include a basic dual-n back option, as short-term memory makes it easier to toss around labels of values.

>>7
The contrapositive of C is if a/b is a repeating decimal, then 10^k a/b is not an integer for some k.

>>8
>>10
oh damn that was a really dumb mistake. thanks.

fix:

(C) if a/b is not a repeating decimal, then 10^k a/b is an integer for some k

>>9

That's a good plan. My plan was originally to just train the user in the type of questions people get asked on trading jobs interiews, but those skills are important as well.

>>9
Nobody likes Tux

>>13
Yeah! Linux needs cooler animeish mascots with big eyes. Tux looks like a retarded pokemon.