At the graduate level, it is possible for students to pursue a degree in mathematics entirely online. These degrees could prepare graduates for careers in a number of different fields like education, business, and research. We will learn about these programs in greater detail below by discussing common program course requirements, program duration, and other relevant information that students may be interested in.
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Information About Online Graduate Programs in Mathematics
While it is possible to pursue graduate degrees in specific types of sub-fields of mathematics, it is also possible to pursue a more generalized Master of Science in Mathematics program. These programs typically require students to complete between 30 and 40 credit hours, some of which are often required core curriculum courses while the rest are mathematics electives. Some programs may require that students select a concentration area within the degree, in which case their elective courses would likely be used to satisfy the concentration requirements. In general, online master's programs in mathematics do not require that students complete a thesis. Below are five course topics that are commonly found in online graduate programs in mathematics.
A course in advanced calculus is a common part of many online graduate programs in mathematics. In this course, students will build upon their prior knowledge in calculus and discuss topics like real number systems, sequencing, basic set theory, and limits. In addition, this course may cover mathematical logic, differentiation, and Riemann integration.
Rings and Fields
Students in mathematics graduate programs will also likely take courses that cover the concepts of rings and fields. Students will study the properties of rings and fields as well as ring and field theory. Topics that may be discussed include quadratic and cyclotomatic number fields, Dirichlet's unit theorem, Galois theory, isomorphism theorems, polynomial rings, and field extensions.
A course in complex variables will focus on building upon students' knowledge of variables by covering topics like elementary functions, holomorphic functions, and the complex plane. Other topics that may be discussed in such a course include the Laurent series, complex integral theorems, harmonic functions, and Picard's theorems.
It is also common for graduate programs in mathematics to require that students take some sort of class that covers linear algebra. Students may already be expected to have a foundation of understanding in linear algebra and graduate-level coursework would build on this understanding by covering topics like duality theory, multilinear algebra, and applications of linear algebra. The course may also focus on more specific types of linear algebra, like computational linear algebra or numerical linear algebra.
Graduate programs in mathematics generally require that students take one or more courses that are focused on geometry. Students may learn about non-Euclidean geometry, which highlights topics like the parallel postulate, elliptic geometry, and Hilbert's axioms, as well as projective geometry that focuses on topics like harmonic forms and polarities. Topics in algebraic geometry, differential geometry, and other areas of geometry may also be discussed.
Online Graduate Programs in Mathematics Admission Requirements
Students who are interested in enrolling in online graduate programs in mathematics will be required to meet certain admission standards and to submit a formal application to each program they are interested in. With their application, students will need to submit undergraduate transcripts and, often, letters of recommendation or references. Programs also commonly require that students submit GRE examination results, though not all programs require this. In addition, programs generally specify that students have already completed a certain number of credits of mathematics courses while completing their bachelor's degree, though it is not typically necessary to hold a degree in mathematics. Some programs require students to have earned a minimum GPA in their undergraduate coursework, though the exact figure varies by school.
To summarize, students who are interested in obtaining a graduate degree in mathematics are able to do so online. These degree programs typically require that students complete a certain number of require core curriculum courses and then can select electives that interest them or that are in line with their chosen concentration area.