Fernando’s Notes for Majors in Mathematics and Mathematical Sciences
One of the messages we hear from alumni is that they would have
liked 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: we don’t really know what you will need. 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
These are my recommendations, not the
department’s. But I suspect a lot of my colleagues would
- Always remember the distinction between what is required
and what is useful. No department wants to scare students by
requiring too many courses for their major. That does not mean that
they think it would be a good idea to take only the courses
- Take Mathematical Reasoning 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
even more so if you go on to graduate school in any mathematical
field). Students who are thinking of going to graduate school in
Economics should also take this course.
- I once heard from a student that Linear Algebra was the most
useful course she took, in the sense that ideas from that course
kept coming up in all the other courses she took, both in
Mathematics and in Computer Science. She is right!
- 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
- Getting into a good graduate school is made much easier if you attend
a summer REU program. Not only does it give you a chance to see what
doing mathematics research feels like, it also means you get to know a
professor from some other college. It’s always good to have a
recommendation from a professor in another college!
- The strongest possible mathematics major: take all the required
courses for both the Mathematics and the Mathematical Sciences majors, as
many 300-level and Topics courses as you can fit, and the complete
Statistics minor. Do an REU in the summer. Do an honors thesis. Of
course, if you can pull this off, you must have super-powers.
- Take a programming course. If you think you might go on to the
“real world” and not graduate school, 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
- 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. All mathematics
majors are automatically members of
the Mathematical Association of
America. There are others you can belong to. In many cases the
department can give you a free membership. When you graduate,
continue your membership of at least one. This is an easy way to
“pay it forward”, and you may also benefit directly.