### Chair

**Emily Stone**

Email

The Department of Mathematical Sciences offers various undergraduate degrees:

- a
**B.A. in Mathematics**(with several concentrations) - an interdisciplinary
**B.S. with a Combined Major in Computer Science and the Mathematical Sciences** - a
**Certificate in Big Data Analytics**(offered jointly with the Departments of Computer Science and Management Information Systems) - a
**Minor in Mathematics** - a
**Teaching Minor in Mathematics**(for secondary education majors in other fields)

At the graduate level, both M.A. and Ph.D. degrees in the Mathematical Sciences are available.

Many students chose to enhance their math major by specializing in one or more areas of the mathematical sciences. At UM, such a specialization is called a concentration (or "option"). Concentrations are optional, and students can graduate with a B.A. in Mathematics without satisfying the requirements for one of the concentrations.

Below, you can find a bit of information about each of the five available concentrations. For more information on a specific concentration, talk to the faculty members in that area (see the listing of faculty members by research areas). The specific degree requirements for the B.A. in Mathematics and its concentrations can be found in the UM Catalog.

Applied mathematics refers to those topics in mathematics that are most useful for analyzing real world applications in engineering, physics, chemistry, earth sciences and biological sciences. The emphasis is often on constructing a (sometimes nonlinear) model of the real world application, and then applying analytic and numerical/computational solution techniques to the differential, difference or integral equations that result. Job opportunities for applied mathematicians exist in most industries, as well as in the National Laboratories (e.g. Sandia, Los Alamos and Lawrence Livermore). Academic opportunities are also available for applied mathematicians with an advanced degree.

At UM, the applied mathematics group works in the areas of numerical analysis, perturbation methods and dynamical systems, with applications in astronomy, chemistry, biology, forestry, medical imaging, and pharmaceutical science, to name a few. Model development for problems in these studies is central, followed by the analysis of these models using numerical and analytical techniques, with the goal of a better understanding of the mechanisms at work in the phenomena. We offer courses in solution techniques (Ordinary Differential Equations, Partial Differential Equations, Numerical Methods, Linear Algebra) and modeling and qualitative analysis (Deterministic Models and Statistical, Dynamical and Computational Modeling).

The applied mathematics concentration also requires the ability to do rigorous analysis, so this option can be chosen by students planning to do graduate work in an applied science or in mathematics. Students in this concentration are urged to learn a computer language such as Matlab or Python, as these are often valuable in the analysis of applied problems.

For more information about this concentration, talk to the faculty members in Combinatorics & Optimization.

Often students who are good in mathematics accept the challenge of developing mathematical power in others. The University of Montana mathematics program offers a concentration in mathematics education to train teachers of mathematics. Graduates with this concentration are certified to teach mathematics in grades 5 through 12 in Montana.

This concentration contains a broad range of mathematics courses, including number theory, geometry, statistics, mathematical structures and the history of mathematics. Students explore the use of technology as a learning and teaching tool in the mathematics classroom. The concentration also includes the education, psychology, teaching methods and field experiences necessary for teacher certification.

The mathematics and general components of the mathematics education concentration reflect the developing changes in the secondary school mathematics curriculum. Prospective teachers are required to know enough about mathematics and enough about teaching to adapt to the increasing complexity of the interactions of learners with mathematics.

Students who find mathematics challenging, fascinating, beautiful or enjoyable will probably want to follow at least one of the sequences in the pure mathematics concentration. These courses will help build knowledge of, appreciation for, and experience with the abstract ideas at the heart of mathematics. Courses in this concentration will enhance your ability to do rigorous proof-oriented mathematics. The problems considered while not excluding calculation, often also involve constructing arguments and proofs related to these theories. If an advanced degree in mathematics is your goal, many graduate programs require familiarity with all or part of the material in the courses required for the pure mathematics concentration.

Statistics is the study of techniques for the collection, analysis, interpretation and presentation of data. Careers exist in fields from insurance to engineering, from biology to economics, from business to education; in fact, statistical concepts are used almost everywhere. Most careers in statistics require a master's degree. Undergraduate courses give a general background in the field, and more specialized courses are taught at the graduate level. For advanced work, a good knowledge of calculus, linear algebra and analysis is required. Numerical analysis and mathematical modeling are also useful. Computers are used extensively and many types of statistical packages exist. A good statistician also has good reading, writing, speaking and listening skills. The knowledge of a second discipline outside of the mathematics/statistics area shows scientific interest and flexibility in a student who wishes to pursue an industrial career.

For more information about Big Data Analytics and Data Science, visit our page on Mathematics and Big Data. The degree requirements for the Big Data Analytics Certificate are in the UM Catalog.

The purpose of the combined program is to provide a thorough background in both allied disciplines and to inculcate a deeper understanding of their goals and methods. The combined major requires less course work in mathematics than a regular mathematics major, but also substantial course work in computer science. One can describe it informally as a “2/3 mathematics, 2/3 computer science” major. More precisely, a student must complete 60 credits in the two disciplines: 30 of these credits in Computer Science courses and 30 of these credits in Mathematical Sciences courses. Each student plans a program in consultation with both a Computer Science and a Mathematical Sciences advisor.