Thursday, December 30, 2010

Math != Calculating

This is an interesting talk:

Math >> Calculating

1. Pose the right questions.
2. Real world problem --> math formulation
3. Computation
4. Math formulation --> real world problem and verification

Maybe not spend so much time on step 3?  Use computer programming to nail down understanding!  These are very interesting ideas.


Thursday, December 2, 2010

Adding and Subtracting Rational Expressions

To simplify a rational expression:
Step 1:  Factor all denominators as a means to easily determine the LCD.
Step 2Multiply by the appropriate factors to obtain equivalent terms with a common denominator. 
Step 3Add or subtract the numerators and place the result over the common denominator. 
Step 4:  Simplify the resulting algebraic fraction.

A more involved example follows:

It is always a good idea to state the restrictions.  Remember that the restrictions are the values that produce zero in the denominator.


Mandelbrot Explorer using Flash

Give the below flash movie a minute to download. Move the looking glass over the picture and release it to zoom.

The orbit is displayed, real time, in the corner.