Mathematics

What it’s about:

Math majors develop the ability to explore, conjecture, and reason logically, as well as to use mathematical methods to solve problems. Mathematics is both a discipline and a tool used extensively in the sciences, medicine, engineering, and industry.

What study of this major is like:

Mathematics deals with how basic patterns and processes can be turned into abstract representations. As a math major, you work with increasingly abstract concepts in analytic, algebraic, and geometric math.

Analysis (the mathematics of dynamic change) begins with calculus. Calculus was developed in the seventeenth century to analyze changes in physical quantities-for example, the minimum distance between two planets or the maximum profit of a business enterprise. Through calculus, you can determine the lengths of curves and the volumes of solids, or investigate the acceleration of moving objects. Analysis continues with differential equations, in which you use the knowledge of the way things interact to predict their future state. Real analysis, complex analysis, and functional analysis provide tools that deal with unexpected phenomena.

Modern algebra involves integers, counting problems, and symmetries. It begins with linear algebra (probably the most useful undergrad course) and continues with combinatorics and number theory. You also study structures known as groups, rings, and fields, in order to explore such questions as “it pi rational?”

Discrete mathematics and combinatorics consider the finite nature of certain problems-for instance, in how many ways can a fixed number of vehicles in how many ways can a fixed number of vehicles visit multiple locations, and which schedule would be the least costly? Modern geometry and topology study the world of transformations and explore the deeper meaning of concepts such as shape, area, and distance.

Traditionally, math has been taught entirely through lectures, but this approach is changing. Many math courses now make use of computer; you do projects that help you explore a topic in depth; and in written assignments, you clarify difficult concepts, in addition, lectures themselves have changed. Today, many professors understand the importance of describing how particular mathematical concepts came about and of showing how mathematical insights can be applied outside the classroom.

Majoring in mathematics can be an intense experience. There are always new ideas to be mastered. Learning how to rely on precise definition, how to tackle an unfamiliar problem, and how to construct a proof is sometimes difficult. Many math majors find it helpful to form supportive study groups, in which participants share their struggles and insights. Activities such as annual COMAP modelling competitions are built on teamwork; good mathematics programs build strong camaraderie among majors.

Some colleges emphasize applied math or allow you to take an applied mathematics track. These programs typically replace advanced courses in analysis, algebra, and geometry with advanced work in statistics, operations research, and modelling. It is usually a less intense major that can be excellent preparation for the workplace.

Career options and trends:

Operations researcher*; business consultant; high school teacher*; statistician*; financial or securities analyst; college professor; actuary.

There is a steady, strong demand for math majors. Many employers (as well as graduate schools in professions such as law and medicine) will give preferential treatment to graduates with a degree in math. The study of mathematics is excellent preparation for a host of employment opportunities in business, finance, insurance, communications, electronics, scientific research of any type, and any field that has challenging problems to solve.

Source: CollegeBoard 2012 Book of Majors