The Mathematical Association of America (MAA) is the largest mathematical society in the world that focuses on mathematics for students, faculty, professional mathematicians, and all who are interested in the mathematical sciences; that is, mathematics at the undergraduate level. Our members include university, college, and high school teachers; high school, undergraduate and graduate students; and others in academia, government, business, and industry. Our core interests are Education, Research, Professional Development, Public Policy, and Public Appreciation. The student web pages cover topics in academics, careers, research/summer opportunities, meetings for students, and more.
There are a lot of questions that come up when someone wants to major in mathematics. What is it good for? (lots of things) How is the job market for mathematicians? (very good) What does a math major study? (a wide variety of both pure and applied topics)
I'm sure we won't answer all of your questions, so please e-mail me, Robert Vallin, with any that you might have. More than likely, you're not the only one with that question. Asking it may help others out. Often times, I will direct you to links that will give good answers, rather than reproduce what is already available.
What does a math major do in college?
The study of mathematics isn't just about finding better ways to crunch numbers. While computation is always involved, the heart of mathematics is developing the ability to come up with new ideas and prove they work. Math gives students a structured and logical perspective while still encouraging creativity. This balanced thought process can really pay off. Mathematicians are prized for their ability to think in this manner. For example, the National Institute of Education compared the LSAT and GMAT scores of 550,000 colege students. For the Law School Admission Test, math majors scored 12.8% above average while for the 13.3% above average on the Graduate Management Admission Test. When going directly to the workplace a math major earns 37.7% over the average undergraduate salary1.
All mathematics majors take the same core classes: Calculus sequence, Differential Equations, Abstract Algebra, Real Variables/Advanced Calculus, and Linear Algebra. The following descriptions come from a course catalog2.
Caculus I – Functions, graphs, limits, derivatives, rules of differentiation, definite integrals, the Fundamental Theorem of Calculus, applications.
Calculus II – Techniques and applications of integrals, elementary differential equations, sequences and series, power series.
Calculus III – Vectors, vector algebra, and vector functions. Functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integration, line and surface integrals, Green's Theorem, Stokes' Theorem, applications.
Differential Equations – First-order differential equations with applications, second order linear differential equations with applications, systems of linear equations and applications, Laplace transforms, Fourier series.
Abstract Algebra – Sets and mappings, equivalence relations, rings, integral domains, ordered integral domains, rings of integers.
Real Variables / Advanced Calculus – The Real numbers system, functions and limits, topology on the real line, contiuity, differential and integral calculus for functions of one variable, infinite series, uniform convergence.
Linear Algebra – Linear equation operations with matrices, row echelon form, determinants, vector spaces, linear independence, bases, dimension, orthogonality, eigenvalues, reduction of matrices to diagonal forms, applications to differential equations and quadratic forms.
After these classes are finished, there are many directions in which coursework can go and each school does things slightly differently. Most programs require their majors to specialize in a second subject (not necessarily earning a minor in it). Choices include actuarial science, physics, chemistry, operations research, statistics, finance, or biology.
What can be done outside of class?
When not in class, students can choose to join their department's Math Club or Student MAA Chapter. Meeting regularly, most chapters discuss mathematical subjects not seen in the classroom, bring in outside speakers, play games like Math Jeopardy, and look at issues like finding jobs utilizing math degrees or traveling to meetings. Meetings are also an important part of the math life. Whether a small, regional meeting or large international gathering, it is important for young mathematicians to see cutting-edge ideas not only is math itself, but also in the teaching of mathematics. Speakers at meetings are faculty, graduate students, and even undergraduates.
Undergraduate students are also starting to do more and more research in mathematics. This can be done one-on-one with a professor, as part of a group project at the home institution, or during a summer research program. Researchers then go to local, national, and even international meeting to either speak on their results or present their finding at a poster session. This is an exciting and rewarding part of the undergraduate experience.
What summer opportunities or internships are available?
Summertime can mean great opportunities for many college students. An internship can offer a chance to see what people with a degree do for a living. In addition to that, there are several summer programs called research experiences for undergraduates. These programs are highly selective and are held at various universities around the country. An intense period of lecture and study is followed by an equally intense, though fun, time spent working on and solving research questions. These REU's do include a stipend so that students are not hurt by lost wages. For more infomation on REU's and internships, go the the MAA page for undergraduates.
What jobs are available to math majors?
There's a large variety of jobs for people with degrees in math. Statistician, actuary, operations researcher, and teacher is just the beginning. Math majors also work in finance, cryptography, and biotech industries. In The Jobs Rated Almanac 250 jobs are ranked in terms of income, stress, physical demands, potential growth, job security, and work environment. Mathematician is #5 on the list, while actuary is #2. It was noted above the salary differential for math majors is 37.7%. A similar 2009 study showed that the top three best jobs in terms of these factors were careers suited for math majors. For more about careers, go to the MAA Career Page.
1Source: 2005 salary survey by the National Association of Colleges and Employers
2Content may vary slightly from university to university.