All of the courses in the program are offered online, and the entire program can be completed in that format.

It is also be possible to take approved on-campus courses as alternatives to online courses. There is a regular schedule of online classes each semester, including the summer sessions. A student need not have majored in mathematics to be admitted. However, it is expected that the student has completed a standard 3-semester calculus sequence and has had at least 9 semester hours of mathematics at the junior or senior level, preferably in courses such as abstract algebra, linear algebra, advanced calculus, differential equations, or geometry. Prerequisites :Three semesters of calculus, or consent of instructor.

Mathematics of the ancient world, classical Greek mathematics, the development of calculus, notable mathematicians and their accomplishments. The theory of groups is used to discuss the most important concepts and constructions in abstract algebra. Systems of linear equations, matrices, vector spaces, linear independence and linear dependence, determinants, eigenvalues; applications of the linear algebra concepts will be illustrated by a variety of projects.

Prerequisites :MATH or consent of instructor. Linear and nonlinear systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; higher dimensional systems; Laplace transforms. Theory and applications illustrated by computer assignments and by projects. MATH Analysis. A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications are used to motivate and to illustrate the concepts. Many of our faculty members have published articles in respected journals, worked as consultants for various businesses and companies, and presented research at conferences and seminars.

Most of them are involved in research ranging from chaos and dynamical systems to topology. UNT provides a wide variety of services exclusively to graduate students. The Graduate Writing Support Center can help you with writing, and the Office of Research Consulting offers assistance with statistical research. Many of the workshops are available online for your convenience. This includes upper-division courses in algebra and advanced calculus classical analysis and, when possible, topology.

You must also meet the admission requirements for the graduate school that include:. More information on the admission requirements for the graduate school can be found at their website.

Specific department requirements are outlined on our website. About half of the courses should be level or higher. The exam is primarily a defense of the dissertation. This degree requires 36 credit hours of approved coursework, proficiency in computer programming and a final oral exam. A thesis is optional. This degree requires 24 credit hours of approved coursework and 6 credit hours of thesis. In addition, you must demonstrate proficiency in a foreign language. A final oral exam will be your thesis defense. Information about specific degree requirements is available on our website.

### Graduate opportunities

Teaching fellows also are eligible for 1. Supported students receive a tuition benefit covering at least six credit hours of their tuition per semester. Pieter Allaart , Associate Professor; Ph. Probability and stochastic processes; fractal geometry; real analysis.

Nicolae Anghel , Associate Professor; Ph. Complex analysis of one and several variables; differential geometry; geometric analysis; mathematical physics. Statistical genetics.

### Program Overview

Stephen Jackson , Regents Professor; Ph. Logic; set theory; descriptive set theory, especially the influence of the axiom of determinacy. Robert R. Kallman , Distinguished Research Professor; Ph.

Optimization; parallel computing and engineering design; topological groups; operator algebras and unitary representations of locally compact groups. John Krueger , Assistant Professor; Ph.

## Graduate Program

Mathematical logic and set theory with an emphasis on forcing, consistency results, combinatorial set theory and inner model theory. Joseph Kung , Professor; Ph. Discrete mathematics; combinatorics; discrete and computational geometry; lattice theory; computational aspects of geometric configurations. Optimization; scientific computation; applied mathematics. Applied probability; stochastic geometry; percolation thresholds; random heterogeneous materials.

Olav Richter , Associate Professor; Ph. Number theory in particular Jacobi forms, Siegel modular forms, Maass forms, mock theta functions. Bunyamin Sari , Associate Professor; Ph.

## AMS eMonographs

Banach spaces; operator ideals. Anne Shepler , Associate Professor; Ph. Noncommutative algebras; deformation theory; invariant theory; reflection groups; hyperplane arrangements. Kai-Sheng Song , Professor; Ph. Statistical algorithms; nonparametric and semiparametric inference; biomedical signal processing and imaging; time series and mathematical finance.

## Master of Science in Mathematics (MSc)

Mariusz Urbanski , Professor; Ph. Dynamical systems; ergodic theory; fractal sets; conformal dynamical systems; topology. Statistics; applications to mapping complex disease genes and to economic phenomena.