# Online Graduate Math Courses Overview

## Online Graduate Courses in Math

The following descriptions profile some commonly offered online graduate math courses.

• History of Mathematics Course: This course covers major events and themes in the evolution of math, starting with the development of the concept of numbers. Mathematical reasoning, philosophy, cultural significance and techniques are discussed. Students learn about the development of different branches of math and advances in teaching methods. This course ends with an overview of the latest technological advances in the field.
• Abstract and Linear Algebra Course: In this course, students broaden their knowledge of the algebraic system and learn about algebraic structures, such as modules, rings, groups, fields and particularly vector or linear spaces. They also explore problem-solving topics, including group, spectral and duality theory, eigenvalue problems and decomposition, numerical methods for solving linear systems of equations, matrix computation, iterative methods and error analysis.
• Higher Geometry Course: This course covers developments and techniques in differential, algebraic axiomatic and projective geometry. It covers both Euclidean and non-Euclidean geometries. Participants learn to apply geometric techniques through the utilization of multivariable calculus, linear algebra and ordinary differential equations. Students collaboratively explore open-ended geometric problems and focus on geometric modeling and graphs, visual representation systems and characteristics of shapes.
• Advanced Statistics Course: Students in this course take on statistical methods and analysis. This includes an in-depth study of the collection, selection, categorization, representation, modeling and analysis of data. Descriptive statistics, variance analysis, model assessment and regression are also discussed. Probability is a central focus, covering the topics of combinatorics, variables, distributions, correlations, regression, estimation and testing. This course may require specific software, such as Minitab and Microsoft Excel.
• Advanced Calculus Course: This course provides an overview of multivariable calculus. Integral theorems, contour integration and line-surface integrals are covered. Students learn about ordinary and partial differential equations, convergence, axioms of the real number system and applications of vector differential calculus.
• Technology in Mathematics Course: Students learn about various techniques for communicating mathematics electronically. This includes typesetting of mathematical information, Web resources and online publication of work, math computer programs and methods for displaying information in audience-friendly ways. Special technical requirements for this course might include math and graphics editors, as well as software programs such as Maple, Mathematica or Matlab.
• Scientific Computing Course: This course teaches computational mathematics applications in physical science, economics, medicine and more. Students will use advanced Matlab to complete assignments and coursework. The course will also cover best methods for data presentation.
• Partial Differential Equations Course: This course covers the methods that can be used to solve partial differential equations. Students are introduced to separation of variables, Fourier series and transforms, Sturm-Liouville theory, eigenfunction expansions and Green's functions.
• Computational Methods for Data Analysis Course: In this course, students learn about the mathematical methods that are used to analyze data in the physical and biological sciences. Topics include image processing, spectral analysis and orthogonal mode decomposition.

### Program Information

Online graduate math courses are often part of master's degree programs in mathematics, applied mathematics or mathematics education. Programs in math education typically prepare students to teach in elementary, middle or secondary schools or in the first two years of postsecondary education. Math master's degree programs can also lay the foundation for pursuing a Ph.D. in the field or for specializing in applied mathematics specific to engineering, computer science, operations research or actuarial sciences. Some courses may require special math and graphics editors, such as TeX and MathType. Other technical requirements might include math programs such as Maple, Matlab, Mathematica.

Experienced math students who are interested in advanced studies or math education can find a variety of graduate-level course offerings online.

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