THE PROFESSIONAL MATHEMATICS TRACK?
At MTSU, the Department of Mathematical Sciences has established the Professional Mathematics Track to provide the proper background for anyone wishing to pursue research mathematics as a career. This is the recommended track for anyone wishing to teach at the university level; however, today there are many other avenues open to research mathematicians. In recent times, the realm of theoretical mathematics has moved beyond the so-called "Ivory Tower" world of academicians such as Professor Littlewood, a great number theorist from the early twentieth century, who once said with pride that he had never worked on anything of practical value.
Today, abstract mathematical ideas of resounding power and beauty have found applications in many branches of science. Differential equations, game theory, and fractal geometry provide critical insights in biology. Group theory, dynamical systems, and advanced linear algebra undergird much of quantum physics and superstring theory. Geometry, topology, universal algebra, and analysis play a key role in diverse areas of computer science such as image processing, programming semantics, computer-aided design, and data transmission.
The primary goal of the Professional Mathematics track here at MTSU is to provide you with a sound background in classical mathematics. This is our goal because, just as the best modern musicians first trained in the classics of music, anyone wishing to participate in the growing dialogue between mathematics and the sciences must have a sound background in the classics of mathematics. Math majors opting for this track will receive a thorough exposure to the power, versatility, and beautiful computational economy of the calculus. This will be followed by an in-depth exploration proof techniques --- the tools used by professional mathematicians to create new mathematics. During this latter process, you will develop the theory underlying both algebra and the calculus.
Completing the Professional Mathematics track will give you a broad exposure to the key areas of classical mathematics --- calculus, linear and abstract algebra, and analysis --- which form the foundation upon which much of late twentieth-century mathematical research is based. You will also have the opportunity to explore other important areas such as topology, number theory, and graph theory, all of which have experienced tremendous growth in recent decades. While engaged in these pursuits, you will be developing familiarity with, and confidence in, use of proof techniques and analytical thought. Mastery of these tools, along with classical mathematical training, will place you in an excellent position to continue your studies at the Masters or Doctoral level.