Efficient Math Commands for Wolfram Alpha

Wolfram Alpha is a free, online, computational engine. It provides some of the power of a computational algebra system (CAS) such as Maple or Mathematica without having to learn the proper syntax. However, it takes a little bit of practice to get WA to give exactly what you want.

Here, I'll give a list of queries that are commonly used in math classes:

• Solving an equation in one variable:  solve 3x^2-1=0 
  
• Solving an equation for one variable in terms of another:  solve 3x+2y=-8 for y
• Factor an expression: factor (4x^2-16y^2) 
• Simplify an expression: simplify (x+3(x+2)^2-2(x-y)) 
  
• Plot a function:  plot x^3-x^2
  
• Plotting a function on a given interval:  plot sin(x), x=-pi..pi
• Take the derivative of a function: derivative of (x^3+sin(x))
  
• Higher derivatives: second derivative of (x^3+sin(x)) 
• Higher derivatives, symbolic:  d^2/dx^2(x^3+sin(x))
• Integration:  integrate (x^3+sin (x))
• Definite Integrals: integrate (x^3+sin (x)), x=-2..3 

There are many, many more cool things you can do with Wolfram Alpha and I have only scratched the surface here. But the commands above should take care of most of the solving equations and graphing chapters in algebra, and the differentiation and integration material in calculus. I've told my students about it so that they can check their homework.

One thing to note is that WA will often give both graphical and algebraic representations for solutions of equations. It really helps students to connect those concepts.  However, it is not going to help a student set up and solve a word problem or help them to interpret a solution or a graph. If you're interested in teaching or learning both math concepts and skills, then WA is an extremely useful tool.

 

Free Multimedia Algebra Review

There are seemingly an infinite number of free math resources on the Internet. However, very few provide the comprehensive content that are usually found in textbooks. One of these rare sites is Hippocampus. It is part of the Monterey Institute for Technology and Education and provides free multimedia ebooks for a variety of high school subjects and introductory college level courses. Of particular note are the algebra and calculus ebooks that they have on hippocampus.org. I found their online material to be engaging, and have directed my students to the site for review purposes. They have also added a new "mini-site" just for algebra review.

Instructors looking for really good online videos an a wide range of math topics can also check out Brightstorm and MathTV.

(Not affiliated with any of these folks - just passing along some good study aids.)