# Mathematics (SMA)

### The Discipline and the Major

Mathematics is a field that is vast and ancient. It encompasses the study of quantity, shapes, symmetries, patterns and change, among others. Mathematics is the language of science and engineering. Remarkably, the same mathematics used to solve problems in one area may be applicable in a completely unrelated field. Mathematicians look for generalities, use analogies and employ logic to verify conjectures.

The mathematics major has two tracks, one in pure and the other in applied mathematics designated, respectively, as Mathematics and Applied Mathematics. Both tracks offer honors versions for exceptional students. The Mathematics Department also administers a separate major in operations research and co-administers the major in quantitative economics described elsewhere.

Midshipmen in the pure mathematics track take seven required courses, four electives and a capstone project course. Those in the applied mathematics track take nine required courses, two electives and a capstone project course. The two tracks share a common third class year with required courses in fundamentals of mathematical reasoning, linear algebra, probability, and applied mathematics and modeling. Two additional required courses common to both tracks follow in second class year in the underpinnings of calculus (sequences, series and functions) and intermediate linear algebra. The remaining required course in the mathematics track is one in algebra which treats mathematical structures called groups, rings and fields. The remaining required courses in the applied mathematics track are an introduction to partial differential equations, complex variables, and scientific computing.

By choosing the applied mathematics track, mathematics majors may create and analyze mathematical models of natural phenomena, often using a computer for assistance. In the pure mathematics track, they may investigate and draw conclusions about more abstract problems which may even be unrelated to the physical world. The choice of track need not be made until the second semester of third class year. Students with both interests in both tracks may pick one track and take electives from the other.

### Opportunities

After graduation, mathematics majors are welcomed into all areas of the Navy and Marine Corps. Mathematics majors are valued in both the military and civilian worlds for their ability to reason carefully and logically. The mental training involved in learning mathematics is even more significant than any particular mathematical knowledge one acquires as an undergraduate major. As a result, midshipmen trained in mathematics may look forward to a wide range of careers inside and outside of the naval service. The first deck of Chauvenet Hall is full of small posters suggesting how advanced mathematics is useful in dozens of unexpected ways. Midshipmen majoring in mathematics will be exposed to new worlds of intrinsic interest and of great value to the Navy and Marine Corps.

### Considerations for those who might be interested in this major

Good performance in prior mathematics courses is necessary for success in the mathematics major. Mathematics rewards—and demands—patience, very careful use of language, and comfort with abstraction. While the “right answer” is important in mathematics, it is even more important to know why the answer is right. Careful reasoning is a hallmark of the major. Many midshipmen who are good at mathematics but unsure about an area of specialization choose this major because it is flexible and central to so many fields. This allows them to pursue graduate study in many other areas.

It is not surprising that graduates of the Naval Academy who majored in mathematics have achieved success in mathematics, science, engineering, law, and medicine.