Winter Quarter 2006-2007

MA 366 -- Functions of a Real Variable

Professors Carlson and Rickert         

(Read on to find out more about this picture!)

True or False:  The number of positive, even integers is less than the number of positive
                      integers.

True or False:  The number of irrational numbers is greater than the number of rational
                     numbers.

True or False:  The square root of 2 is an irrational number.

True or False:  There exists a function defined on [0,1] that is discontinuous at only the
                       rational numbers.

True or False:  There exists a continuous function that is not differentiable at any point.

True or False:  If f is the limit of continuous functions, then f is also a continuous function.

True or False:  If f is the limit of differentiable functions, then f is differentiable.

True or False:  If f is the limit of integrable functions, then f is integrable.

If you find the above questions appealing, captivating, or just plain interesting, then MA366 is a course for you!

We will be using the same text as last year, Understanding Analysis, by Stephen Abbott [Springer, Undergraduate Texts in Mathematics, 2000]. If you have any questions about the course, please contact Dr. Carlson or Dr. Rickert by e-mail or feel free to stop by one of their offices. 

Dr. Carlson: Carlson@Rose-Hulman.Edu
G-307, Crapo Hall

Dr. Rickert: Rickert@Rose-Hulman.Edu
G-215A, Crapo Hall

Okay, now about the picture above!  It is part of a sequence that illustrates the surprising nature of limits of functions.  To learn more about what the picture represents, and more, take a look at the following links:

http://www.math.ohio-state.edu/~fiedorow/math655/Peano.html

http://plus.maths.org/issue6/turner1/