## Majoring and Minoring in Mathematics & Statistics

Why study mathematics? Mathematics is perhaps the most intellectually challenging and practical major you can choose. Some major in math for the enjoyment and beauty of the subject. Others major in math for its practicality and applicability to the sciences, engineering, finance, and even the social sciences. Mathematics develops rigorous analytical thinking skills that are prized in all fields of human endeavor. |

Programs offered at SFA:

- Bachelor of Science in Mathematics
- Bachelor of Science in Mathematics with Secondary Teacher Certification
- Minor in Mathematics
- Minor in Applied Statistics
- Master of Science in Mathematical Sciences with an emphasis in Mathematics
- Master of Science in Mathematical Sciences with an emphasis in Statistics
- Master of Science in School Mathematics Teaching

What classes do I take as a math major?

A major in mathematics requires 40 hours: MTH 233, 234, 311, 317, 333, 337, 359, 360, 412, 439, 440, and 463 are required, plus three hours from MTH 305, 351, or 415. Secondary mathematics teaching certification requires MTH 233, 234, 311, 317, 333, 337, 351, 359, 360, 412, 439, 440, and 463 . CSC 102 is also required for all majors.

What classes do I take as a math minor?

For a math minor: MTH 233 and 234, plus courses selected from MTH 305, 311, 317, 333, 337, 359, 360, 412, 415, 439, 440, and 463 for a minimum of 18 semester hours.

For an applied statistics minor: MTH 144 or 233, MTH 220, STA 320, STA 321, STA 322, and STA 327.

What are these classes?

**MTH 220 Introduction to Probability and Statistics: **This course acts mainly as a service course for other disciplines; however, many mathematics students take this course early in their college career. This course provides an introduction to modeling random phenomenon using probability and an introduction to the analysis of data using statistics.

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 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 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 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 351 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.

MTH 359 Probability Modeling: This course is a calculus based introduction to constructing models for the uncertainty that persists in the natural world. The course provides an introduction to probability laws, random variables and the concept of distributions. These distributions along with other specific random processes provide the foundation for applied probability as well as prepare the student for additional courses in statistics.

**MTH 360 Statistical Inference:** The focus of MTH 360 is the statistical process by which conclusions about populations can be inferred from data collected on samples. This calculus based statistics course provides both the mathematical underpinning of estimation and hypothesis testing while also being sufficiently data-driven and application oriented. Appropriate technology which enhances the ability to analyze data is included throughout.

MTH 412 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 412 is a proof-based course.

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 439, 440 Introduction to Analysis 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 463 Seminar in Mathematics**: This seminar provides students with a survey of the tools and skills useful in advanced mathematics, including technical writing and oral presentation, mathematical pedagogy, computer algebra and electronic presentation systems, history of mathematics, professional organizations and their functions, and preparation for careers in mathematics or graduate school.

...and the statistics classes...

**STA 320 Statistical Methods: **As a second course in statistics, STA 320 gives a three-pronged introduction to the following areas of statistics: analysis of variance, regression, and nonparametric methods. This course makes use of a statistical computing package in order to analyze data sets. The techniques covered in this course, as well as STA 321, 322, and 327, all have applications in business, industry, agriculture, forestry, biomedical science, psychology, and sociology, among others.

**STA 321 Applied Nonparametric Statistics**: The statistical methods used in this course are very useful in attacking problems that cannot be solved using standard parametric procedures as introduced in MTH 220 and STA 320.

**STA 322 Statistical Modeling**: Of interest in this course is finding a mathematical relationship between two or more variables. The discovery and verification of such a relationship is accomplished by analyzing a data set with a statistical computing package.

**STA 327 Experimental Design and Analysis**: STA 327 extends some of the statistical methods introduced in STA 320. This course deals with setting up an appropriate experimental design in order to answer questions on how some treatment affects a particular variable.

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 kind of jobs can I get?

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/.