Applied mathematics is generally an interdisciplinary field. Students in a bachelor's degree program may study engineering and science, in addition to a core mathematics curriculum. Typically, schools expect incoming students to have a strong mathematics background with previous coursework in advanced mathematic subjects, such as calculus and trigonometry.
Some programs may be offered completely online. Students may need to attend courses on campus in some programs because some schools may not offer all courses within the program through their online learning system. Those schools that offer the program fully online may also offer orientation online, but in some cases orientation must be completed on campus, even if all the program courses are offered online.
In most cases, students are expected to own or have regular access to a computer to complete online courses. Some schools may offer special accommodations for students who don't have regular access to a computer.
Courses in an applied mathematics bachelor's program encompass science, engineering and mathematics. The core courses in a program focus on advanced mathematic concepts. Elective courses generally cover the engineering and science parts of the program, allowing students to choose the courses that suit their goals and needs.
A bachelor's level program will usually include multiple courses in calculus that cover concepts such as limits, derivatives, partial fractions, sequences and series, partial derivatives, saddle points and vector fields. Students also study different calculus techniques, theories and applications.
Linear algebra courses usually examine the linear equation, as well as concepts like vector spaces and eigenvalues. Most linear algebra courses require prerequisite work in calculus and a mastery of fundamental algebra skills.
A statistics course will usually cover the basic concepts of statistics and probability. Students examine probability models and use concepts such as hypotheses testing, estimation of statistics, distributions and quality control. Students usually need to have completed prerequisite courses in calculus.
Applied mathematics master's programs focus on how mathematics is used as a language within various fields other than mathematics. A degree at this level may serve as a complement to undergraduate studies in science, engineering or computers. Flexibility is often allowed with electives to help students tailor their program.
Master's programs usually require at least 36 credits, which is a combination of core mathematic courses and electives in various subject areas, such as engineering, science and computer science. Most programs offer all courses online, but projects, final exams and any practical work may have to be completed offline.
The courses in a master's level applied mathematics program usually are interdisciplinary, allowing students to study the use of mathematics in various fields. Most programs are designed to allow students to focus on their personal career field.
In this type of course, students study the relationship between computers and math. Students explore of how computers can be used to solve mathematic equations and other related problems.
Some master's programs in applied mathematics will include multiple courses in partial differential equations, which cover a range of concepts, techniques and methods related to this subject. Courses may cover numerical methods, equations and analysis methods.
Complex variables courses may deal with mathematics in science and engineering. Students may study integral theorems, branch points, Taylor and Laurent series, conformal mapping and Schwarz-Christoffel transformation.
Courses in dynamical systems typically focus on the theory behind partial differential equations. Topics and concepts examined may include chaos and periodic orbits.
Master's level numerical methods courses introduce students to optimization problem solving methods. Students may examine concepts including quasi-Newton methods, multiplier methods, nonsmooth optimization and quadratic programming.
Graduates of an applied mathematics program at the undergraduate or graduate level have the opportunity to enter into a variety of fields in the areas of science, mathematics and engineering. Many fields outside those areas, such as finance or data mining, are also starting to find use for individuals with an applied mathematic degree.
Graduates may find job opportunities with government agencies, research facilities or corporations. Independent consulting work is also a common career choice. According to the Society for Industrial and Applied Mathematics, those with an applied mathematics degree have found work with the Ford Motor Company, DuPont, Verizon, Microsoft Research, Philips Research, Citibank, Baxter Healthcare and the U.S. Department of Energy (www.siam.org).
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