Major in Mathematics at Stephen F. Austin State University
Required Courses (36 hours): MTH 233, 234, 311, 312, 317, 333, 337, 439, 440, plus six hours from MTH 305, 415, 419, 451. CSC 102 is also required.
MTH 233, 234, 333: The Calculus Sequence
A traditional three-course calculus sequence with Mathematica lab component is the foundation of our major. Some students may want to prepare for calculus by taking Pre-calculus, MTH 140.
MTH 311: Introduction to Modern Mathematics
This course is a formal introduction to logic and proof, giving practice writing rigorous mathematics and a preview of how to think like a mathematician.
MTH 312: Introduction to Algebraic Systems
Usually referred to as Abstract Algebra, this course introduces the student to algebraic structures such as groups, rings, and fields. Abstract Algebra it is a must-have course for those who will teach in secondary schools to realize the basis for high school algebra. Students will exercise the skills they learned in MTH 311 since MTH 312 is a proof-based course.
MTH 317: Linear Algebra
While Linear Algebra is another proof-based course, the theory of linear systems, matrices, determinants and other topics in the course supports many of our applied mathematics courses and statistics courses. Computational linear algebra is used in other disciplines—chemistry, physics, biology—as well.
MTH 337: Differential Equations
This course introduces methods of solving differential equations that arise in various applications in physics, chemistry and engineering. Differential equations give a glimpse of how mathematics might be used in careers in industry.
MTH 439, 440:Advanced Calculus I and II
This sequence serves somewhat as a capstone experience for our majors. The students revisit topics discussed in the calculus sequence, but with a greater degree of rigor and depth. Many of our students feel that these are the courses that crowned their mathematical maturity.
MTH 305: Introduction to Numerical Methods
Numerical Methods is another of our courses that introduces and explores how mathematical problems are solved in careers in industry. Some instructors use graphing calculators for programming experience and others encourage the use of programming languages to write code for approximation of roots of functions, numerical integration and curve-fitting.
MTH 415: Number Theory
This course includes a rich survey of topics in number theory including applications of modular arithmetic, Diophantine equations, and studies of primes.It is a natural course to come right after or concurrently with abstract algebra, as it is very much proof-based, but the only prerequisite is MTH 311; students can take it early in their sequence of courses.
MTH 419: Probability Theory
Probability Theory provides an introduction to elementary probability laws, random variables, and other probability topics. It differs from MTH 220 in that this course does require prerequisite knowledge of calculus, and is thus a more advanced course in which the student will learn more powerful techniques of probabilistic analysis.
MTH 451: College Geometry
College Geometry is another must-have course for those who plan to teach in secondary schools. The course provides a survey of topics from classical and modern Euclidean geometry, transformational geometry, as well as some non-Euclidean geometry. Geometry leans heavily on the logic and proof practice that the student starts in MTH 311.
WHAT CAN A MAJOR IN MATHEMATICS DO FOR ME?
Studying mathematics develops such skills as arguing logically and rigorously, thinking abstractly, formulating and solving problems, analyzing data, and creating and analyzing mathematical models. Employers value these skills; consequently, math majors find themselves in demand by employers for careers in a wide spectrum of fields.
A study of college students' scores on admission tests for graduate and professional schools (LSAT and GMAT) showed that students majoring in mathematics received scores substantially higher than the average on each of the tests studied. In addition, math majors can expect to earn more and have a higher job satisfaction rating than other majors. Check it out at http://www.math.duke.edu/major/whyMajor.html!
WHAT DO MATHEMATICIANS DO?
Teaching
The teaching of mathematics at the K-12 level is a high-demand field and the need is expected to grow in the future. The place to go for explicit career information is the National Council of Teachers of Mathematics homepage.
Actuarial Science
Actuarial science takes mathematics and statistics and applies them to finance and insurance. Actuarial science includes a number of interrelating disciplines, including probability and statistics, finance, and economics. Check out the website Be An Actuary.
Computer Science
Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. Mathematicians, with their training in logical and precise thinking, are highly prized in this field. See the student section of the Association for Computing Machinery for career advice.
Operations Research
Operations research is an interdisciplinary branch of mathematics which uses mathematical methods to arrive at optimal decisions to problems in maximizing or minimizing things like costs or profits. The eventual intention behind using Operations Research is to elicit a best possible solution to a problem mathematically, which improves or optimizes the performance of the system. The group INFORMS is the world's largest society devoted to operations research/management science.
Biomathematics
Mathematical biology or biomathematics is an interdisciplinary field of study. It models natural and biological processes using mathematical techniques and tools. Results have been applied to areas such as cellular neurobiology, epidemic modeling, and population genetics. The education page of the Society for Mathematical Biology links to schools offering bio-math degrees along with a description of the coursework needed.
Cryptography
Cryptography is the practice and study of hiding information. Cryptography is considered to be a branch of both mathematics and computer science. Not just for spies anymore, cryptography applications include the security of ATM cards and computer passwords.
Finance
Finance is a field that studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. Mathematicians can build models to help explain and predict the behavior of financial markets. Several schools offer Master's degrees in Financial Mathematics. A quick web search will take you to their web pages.
Career information and statistics taken from http://www.math.duke.edu/major/whyMajor.html and http://www.maa.org/careers/.