On this page you will find random musings on various aspects of mathematics. There is not set schedule
for these thoughts. Keep coming back here often. I hope that you find it interesting.
Graduation season is upon us once again and summer is trying to make its appearance. To the
questions I posed last year
* What should you know now that you have a math major?
* What are employers who are seeking mathematically talented applicants asking?
I would like to add another
* What skills and talents should you hone to become a good mathematics student?
This past semester I enjoyed students in three wonderful courses
* Foundations of Mathematics
* Modern Algebra
* Data Structures (a computer science discipline)
aside from the students who presented projects in the Senior Seminar. You can view the presented
papers of these students at here.
I have had wonderful students in all of these courses. Not only were they wonderful because they
worked hard but because they exhibited both curiosity and enthusiasm for mathematics.
This summer the Department of Mathematics is sponsoring students to do research projects in
mathematics. As I prepare topics for these students I have been thinking of the mathematics that
excites me, the mathematics that excited me when I was starting out. Students applied for the
opportunity to work with faculty members over the summer and it was interesting to read about how
their attitudes and understanding of mathematics is evolving and in some cases has already progressed.
One student wrote
Before I came to college to study, the most important images of mathematics for me are numbers
and calculations. I thought math is number and calculation and all stuff related to numbers are
math. I believed lots of people who do not study high level math have the similar opinion with
I hope the students working this summer will learn how to ask questions about mathematics and
gleam what are interesting questions, at least what are interesting questions for those working
with them. Most of these students have a grounding in group theory and so a beginning
question, certainly not a question for someone just starting to learn group theory, is the
Let \( B \) be an abelian group with subgroup \( A \) and let \( n \) a positive integer.
Under what conditions is \( nA = A \cap nB \)?
One way to start is to just look at examples, i.e., calculate. But then how does one make the
leap to homology
from those calculations?