Fernando’s Notes for Majors in Mathematics and Mathematical Sciences
One of the messages we hear from alumni is that it would have been
useful to have some guidance as to what electives would have been most
useful for them. To some extent, that is asking us to predict the future,
but it is certainly possible to list a few basic
recommendations. I’ve never been shy about sharing my opinions with
the world, so here goes.
- Take MA274 early. No, don’t wait. Take it now. This is the
course that defines the majors we offer, and also the course that will be
most useful as you take other courses and go on to graduate school.
- If you are seriously considering graduate school in mathematics,
applied mathematics, or in mathematics-intensive areas such as economics,
theoretical physics, or operations research, you really should be taking
the heavy proof-oriented courses. Real Analysis, in particular, is
- Take a programming course. If you think you might go on to the
“real word”, take a programming course. If you think you're
more likely to go to graduate school, take a programming course. Learn to
use Excel, Mathematica, Python, Sage, R.
- If teaching is your goal, you should definitely take Abstract Algebra,
Number Theory, History of Mathematics, Probability, and Mathematical
Modeling. They will all be useful to you in the classroom.
- If you’re thinking you want to go to graduate school in
mathematics or applied mathematics, take every course you can, but most
especially Real Analysis, Abstract Algebra, Vector Calculus, Complex
Analysis, Number Theory, and Differential Equations. And any geometry
course you can find.
- If applied mathematics is your game, make sure you take Probability,
Real Analysis, Differential Equations, and Mathematical Modeling. Oh yes,
and a programming course.
- Talk to your advisor. Figure out what interests you, and ask your
advisor what is relevant.
- Go to the library, check out books on mathematics, and read the first
chapters. If you're interested, read more. But just the first chapter
will give you an idea of what that part of mathematics is about.
- Go to the colloquium talks. Ask questions. Sure, a goodly amount of
what you hear will make little sense to you. That’s ok, learn to
extract something worthwhile anyway.
- Be a member of your professional association. This is an easy way to
“pay it forward”, and you may also benefit directly. If you
want, ask the department to give you a free membership… and after
you graduate, continue to be a member.
Fernando Q. Gouvêa ---- email@example.com