Online Graduate Certificate in Mathematics

• MATH 5100 - Advanced Linear Algebra
  The study of vector spaces and related concepts such as span, linear independence, matrices, linear transformations, invariant subspaces and eigenspaces of a single linear operator. Additional topics such as inner product spaces, canonical forms, and error correcting codes may be included.
• MATH 5110 - Computational Linear Algebra with Python
  This course covers basic concepts of algorithms for solving problems in linear algebra. Theoretical and experimental results will be studied with an emphasis on cost, stability, and convergence. Students will implement and analyze direct and iterative algorithms for solving linear systems, calculate eigenvalues and eigenvectors, and perform matrix decompositions. Applications to a variety of areas will be explored. Learning and using Python and the NumPy library form an essential component of the course. Details of the language will be developed concurrently with necessary algorithms, so knowledge of Python is not required. Some prior programming experience is helpful but not required.
• MATH 5200 - Foundations of Geometry
  Rigorous study of Euclidean and non-Euclidean geometry from an axiomatic point of view. Examination of the axiomatic approach, and its role in organizing mathematical knowledge. The history of the development of non-Euclidean geometry, and an introduction to transformational geometry.
• MATH 5210 - Abstract Algebra 1
  This course covers the mathematical structures of groups and rings. Group theory topics include groups, permutations, subgroups, isomorphisms, homomorphisms, and quotient groups, the Sylow theorems, and finite abelian groups are covered. Ring theory topics include homorophisms, ideals, quotient rings, Euclidean Domains, and polynomial rings.
• MATH 5220 - Abstract Algebra 2
  This course covers the mathematical structures of vector spaces, modules, fields, and linear transformations. Topics include linear extension fields, Galois Theory, and canonical forms of linear transformations.
• MATH 5300 - Number Theory
  This course investigates the properties of the natural numbers and integers. Topics include factorization, Euclidean algorithm, Diophantine equations, congruence, and divisibility.
• MATH 5400 - Probability I
  This course begins with detailed review of basic probability including single random variables and jointly distributed random variables. Conditional probability, conditional expectation, and applications are included. Markov Chains and applications are also covered. Poisson processes are also covered if time permits.
• MATH 5500 - Regression I
  This is an applied linear regression course that will initially focus on strengthening the student's undergraduate background in statistics. Topics for this section will include: sampling distributions, point estimates, confidence intervals, hypothesis testing, ANOVA, and sample size calculations. The second part of the course will introduce maximum likelihood estimation and topics in linear and non-linear regression. The course will blend hands-on data analysis and a theoretical framework.
• MATH 5555 - Complex Variables
  General Algebra of complex numbers, analytic functions, mappings, Cauchy Integral theory, Residue theory, and applications.
• MATH 5610 - Mathematical Analysis I
  This is the first course in a two-sequence course that is an in-depth exploration of Calculus topics in an abstract setting. Topics include the real number system, metric spaces, compact sets, sequences, limits of functions, and continuous functions.
• MATH 5620 - Mathematical Analysis II
  This is the second course in a two-sequence course that is an in-depth exploration of Calculus topics in an abstract setting. Topics include series of real numbers, differentiation, Riemann Stieltjes integral, convergence of sequence and series of functions, analytic functions, and examinations of some special functions such as exponential, logarithmic, trigonometric, and gamma function.
• MATH 5800 - Topology
  Concepts of general topological space, metric space. Compact and connected subsets. Separation axioms. Additional topics as time permits.
• MATH 6500 - Regression II
  This is a second course in applied linear regression. Topics will include: logistic regression, diagnostic procedures, general linear F-tests and sequential sum of squares, multicollinearity, piecewise regression, selection of the best subset of predictors, more advanced diagnostic procedures, and non-parametric regression. The course will blend hands-on data analysis and a theoretical framework.
• MATH 6610 - Quantitative Methods I (2 credit hours)
  This course will introduce students to multivariate statistical methods that may be used in education research. The focus of the class will be on conducting, interpreting, and presenting the results for common multivariate statistical procedures, such as independent and dependent samples t-tests, ANOVA, two and three-way ANOVA, chi-square tests of independence and goodness of fit, ANCOVA, and repeated measures ANOVA.
• MATH 6620 - Quantitative Methods II and Test Theory (2 credit hours)
  This course is a continuation of MATH 6610 Quantitative Methods I. In this course, students will be introduced to additional multivariate statistical methods that may be used in education research such as MANOVA, MANCOVA, and non-parametric techniques. Students will also be introduced to measurement concepts and modern test theory, primarily focusing on Classical Test Theory and Item Response Theory including issues central to measurement such as reliability, validity, test construction, and equating.

MATH 4610 Mathematical Analysis and MATH 4210 Modern Algebra will be used as prep courses for students who need a stronger foundation in undergraduate math. These courses will not count toward the 18 credit hours required for the certificate. Credit for the research sequence in the MS in Mathematics (MATH 6996, MATH 6997, and MATH 6998) cannot be used for completion of the certificate.