WHAT DOES A MATHEMATICS MAJOR STUDY?
Mathematics is one of the fundamental areas of human knowledge. It has held an established position among the humanities for over two thousand years, and in recent centuries it has played a vital role in the sciences. The body of mathematical knowledge is growing today faster than ever before, with old questions being answered and new ones asked at an unprecedented rate.
In the paragraphs below, we sketch some of the courses and topics which mathematics majors study at Wright State University. In each case, the illustrations of what students learn are only small samples of the full curriculum.
Mathematics majors typically begin their college mathematics studies with three semesters of Calculus. Calculus is both the cornerstone of “analysis,” one of the major branches of pure mathematics, and an indispensable tool for most of the sciences and engineering. Students learn to discover for themselves familiar formulas from high school geometry -- e.g., area of circle = πr2, volume of sphere = (4/3) πr3 -- and they learn how to investigate similar issues in more complex settings, as illustrated to the right. Students study mathematics describing such diverse phenomena as conservation of energy laws from physics, and continuously compounded interest from banking.
All mathematics majors also take one semester of Linear Algebra, usually by the beginning of the junior year. This basic topic resides within another major branch of pure mathematics, “algebra” and is also of critical importance in an extensive range of applications of mathematics, from management to structural engineering to telecommunications. In linear algebra, the study of linear equations, like those in beginning high school algebra -- but with the possibility of thousands of equations in thousands of unknowns -- leads to abstract mathematical spaces.
The Department of Mathematics and Statistics offers a variety of more advanced courses. Students decide which of these to take according to their interests and the particular degree which they seek.
For example, students apply multivariable calculus in probability and the mathematical foundations of statistical inference in Theory of Statistics. Related choices include Statistical Methods and Introduction to Experimental Designs, in which one learns how to collect and analyze data, for instance in scientific and industrial experiments.
Similarly, students can choose mathematics courses with special significance in computer science. A prime example is Applied Graph Theory, featuring mathematical models and algorithms applicable to such problems as traffic systems, activity scheduling, and design layout. Others are Cryptography (how to encrypt data securely) and Coding Theory (how to send messages that self-correct transmission errors).
Other courses in applied mathematics emphasize mathematical theory and problem solving methods directed toward the physical sciences and engineering. An illustrative example at the junior level is Partial Differential Equations involving several variables (e.g., both space and time). They describe such phenomena as the propagation of electromagnetic waves through space, and the flow of heat in solids.
Courses in pure mathematics concentrate upon the theoretical foundations of algebra, calculus, and other elementary courses, and at the same time point the way toward more advanced topics in modern mathematics. To illustrate, students in Real Variables (or theoretical advanced calculus) learn why the facts and computational methods learned in ordinary calculus are correct; in Modern Algebra, students study various abstract systems which include the familiar objects of school mathematics as special cases (whole numbers, rational numbers, real numbers, etc.)
In addition to taking many courses in the major field of study, every undergraduate at Wright State University is required to take a comprehensive program of General Education studies, including courses in history, English, economics, the sciences, and several other disciplines. Moreover, some degree programs allow students to take "free electives," or courses chosen by students from essentially any area. Wright State's degree programs in mathematics have a generous allotment of these free electives.