Years ago if you wanted a program to explain steps in mathematics, algebra or other complex math as a tutor would, you would have to buy a specialized software package built for some specific operating system (I forget the name… it may still be around?) Of course there was always open source software like Maxima to do powerful symbolic (or numeric, or graphing) math, but to know what to do one almost needs a manual, and while extremely powerful it was not helpful for beginners. I recently found a similarly useful free math solver on Microsoft’s site, https://mathsolver.microsoft.com:
This will let you go step by step through basic algebra, which could be very helpful for new students, but it doesn’t always give the most informative or entertaining answer.
For example, Look at x7 = 1 and it shows a graph going up and down, but no chart showing the circle of 7th roots as explained in Wolfam’s Roots of Complex Numbers explanation. Nth roots of a number have n answers through the complex plane, for example x4 = 1 has 4 answers, 1, -1, i (i*i = -1, and -1*-1 is 1), and -i (-i*-i = 1 and 1*1 = 1). This gives 4 points around the zero of the complex plane, (1,0i), (0,1i), (-1, 0i), (0, -1i).
Why doesn’t Microsoft Math show this cool fact? Why does it show the four answers above as the solution to x4 = 1, while fourth root of 1 is show as just “one” – and it literally says, do the calculation and it’s one, in the steps.
There is actually a bug in which if you solve an equation, then enter a non-solvable one such as “x = x+1”, rather than say can’t-solve-it, it will just refresh the last answer. Furthermore after showing a unsolvable answer it won’t show you an answer if you enter a solvable problem.
Furthermore some answers don’t give much explanation, such as sin(x)=1:
x=2πn1+π/2 is not a very clear way to say x = half pi, 2.5 pi, 4.5pi… or 90degrees, 270degrees, etc.
Microsoft’s math tool is a lot better than most calculators in that it has quizzes and video review below its answer and explanation.
Great mathematicians are often ones that practice and go over what they have learned, and in the left bar Microsoft math has some examples of Algebra, Trig, Calculus problems for you to view. Some may make you wonder at their choice of example (limit of x goes to 0 for “5”??) but many have good examples and even note things you wouldn’t usually get from a computer algebra system – like their solve-for-variable that notes the denominator will not equal zero, and integration solving noting that an integration will be plus-any-constant.
This is quite a useful tool for any math student and and definitely something to bookmark along with the well-known Wolfram Alpha.