# Math software for checking solutions and proofs?

1. Jul 21, 2010

### abelgalois

Hello guys, I don't know where else to post this but here goes.

I'm going to be catching up on a looot of math this year. Unfortunately a lot of the math books that I'll be using only provide the answers to odd numbered questions. And the answers that they do provide a lot of the times "do not show the work". Is there software out there that will provide detailed proofs and solutions to most precalculus-calculus math problems?

Thanks.

2. Jul 21, 2010

### abelgalois

3. Jul 21, 2010

### naele

Neither will provide a step by step solution. I think Maple might, actually if you use the tutor but that's only for differentiation and integration, last time I checked. I don't think it'll do anything else though.

4. Jul 22, 2010

### abelgalois

Ah thanks. It looks like I'll have to rely on the good people on the homework forum to check key proofs.

I'm genuinely sad that "Principles of Mathematics" by Oakley doesn't have may detailed solutions to its 2300 or so problems. I actually compared the book with Sullivan's "Algebra and Trigonometry" and the differences between the two was startling. In Sullivan's text one of the first things you learn about quadratics is how to solve a quadratic equation by factoring. In "Principle's of Mathematics" quadratic equations are introduced like this:

"Earlier we saw that the quadratic equation $$x^2 = 2$$ could not be solved
in the field of rational numbers and that $$x^ 2 = -1$$ could not be
solved in the field of real numbers. Thus it is clear that the axioms
of a field are not strong enough to assure that every solution of
every quadratic equation . It was the reason that we invented the
field of complex numbers, in which every quadratic equation has a
solution. In order to prove this consider the equation:

$$ax^2 + bx + c = 0$$"

And then it derives theorems and proofs based on that. So we're actually expected to follow the chains of reasoning which led to this conclusion or that. And we're expected to understand them by proving certain things ourselves.

I can't believe this book is 70 years old.... I think if I do every single problem in this book, Courant or Apostol will be a breeze.

Last edited: Jul 22, 2010
5. Jul 23, 2010

### Sankaku

Not sure of your level, but there are answer books available for many intro-level Math texts (Calc, Linear Algebra, ODEs) that give more detail for the answers than the ones at the back of the book. You can find many of the older editions for very cheap 2nd hand. Some Schaum's outlines contain a lot of worked proofs as well, but you have to watch for errors.

Maxima is a free (GPL) computer algebra system somewhat like Maple. Although it will not do any proofs, it can be useful for exploring aspects of math that can be tedious by hand.

http://maxima.sourceforge.net/