Month: August 2015

Banach-Tarski Paradox and A Great Discussion About Infinity

College Mathematics

This video is a rich discussion about about infinity. It starts from the famous infinite chocolate problem, countable infinity, uncountable infinity, Cantor’s diagonalization system, Hilbert’s hotel, and the Banach-Tarski Paradox. Although the last part is a bit too much for the level of this blog, the explanations before it of the concepts before it are extremely clear and helpful.

I had several discussions about infinity in this blog particularly the content of Counting the Real Numbers, The Grand Hotel Paradox, and One to One Correspondence. You might want to check them out.

Leave a comment ,

3 Free Whiteboard Software for Mac Users

Math Software, Resources and Freebies

If you are a Mac user, and if you want to use a whiteboard software in your class or if you want to screencast your lectures, then you can choose among the three whiteboard software below. The first two are free and the third one has a free version.

3 Free Whiteboard Software for Mac Users

1. Paintbrush

Not many people use it, but Paint for Mac is a very useful software. It is a Mac equivalent Paint in Windows. I was using Paint before I migrated to Mac and I’m still using it often particularly in simple image editing particularly cropping. Paint can also be used as a whiteboard software. I myself have used it many times.  » Read more

Leave a comment , ,

The Curve Sketching Series

High School Mathematics

This series discusses the strategies on graphing different functions particularly linear, quadratic, and rational functions.

Curve Sketching 1 is a discussion of the four strategies in graphing linear functions. This includes two points, slope and intercept, translation, and x and y intercepts.

Curve Sketching 2 is a discussion about sketching the graph of quadratic functions. To be able to graph this function you need its critical points such as maximum or minimum, x intercepts, and y-intercept. It is also important to know where the graph opens and the axis of symmetry.

Curve Sketching 3 is a discussion about the vertical and horizontal asymptotes of rational functions. The vertical asymptote of a function is what makes f(x) = n/0 and the horizontal asymptote is the quotient of the leading terms if they have the same power.

asymptote

Curve Sketching 4 is a discussion about the oblique asymptote of rational functions. An oblique asymptote exists if the degree of the numerator is 1 more than the degree of the denominator.

Leave a comment , , , ,
1 2