Mathematics

Prerequisite: Admission to the CCP Math Graduate Certificate program. This course is designed to equip high school teachers with the foundational knowledge and skills in data science necessary for teaching College Credit Plus (CCP) courses. The curriculum covers fundamental data science concepts, data manipulation and analysis techniques, statistical modeling, data visualization, and R programming. One of the topics will be on curriculum design and integrating data science projects into existing high school curricula.

Prerequisite: Departmental permission. Origin and development of mathematical ideas. Course does not meet degree requirements in the department. (Formerly 3450:501)

Prerequisite: Admission to the CCP Math Graduate Certificate program. This course is an introduction to mathematical proofs and rigor and is designed to equip high school teachers with the foundational knowledge and skills necessary to succeed in subsequent courses in the CCP Math Graduate Certificate. Topics include sets and their properties; basic logic; mathematical proof techniques, equivalence relations, functions, various forms of mathematical induction, basic definitions and proof techniques for calculus and abstract algebra.

Prerequisites: Admission to the CCP Math Graduate Certificate program and MATH 507. This course is designed to equip high school teachers with the foundational knowledge and skills regarding mathematical analysis. Topics include: the axiomatic definition of the real numbers; the theory of sequences and convergence; the theory of infinite series and convergence; the theory of continuous functions of a single variable; the theory of differentiable functions of a single variable; constructing basic proofs for these topics

Prerequisite: Departmental permission. Study of vector spaces, linear transformation, canonical and quadratic forms, inner product spaces. (Formerly 3450:510)

Prerequisite: Departmental permission. Study of groups, rings, fields, integral domains, vector spaces, field extensions. Galois theory. May not be used to meet master's degree requirements in mathematics. (Formerly 3450:511)

Prerequisite: MATH 511 or departmental permission. Study of groups, rings, fields, integral domains, vector spaces, field extensions, Galois theory. (Formerly 3450:512)

Prerequisite: Departmental permission. Euclidean algorithm, unique factorization theorem, congruences, primitive roots, indices, quadratic residues, number-theoretic functions, Gaussian integers and continued fractions. (Formerly 3450:513)

Prerequisite: Departmental permission. Introduction to basic ideas and techniques of mathematical counting; properties of structure of systems. (Formerly 3450:515)

Sequential. Prerequisite: Departmental permission. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergences and uniform convergences, power series, improper integrals, transformations, line and surface integrals. May not be used to meet master's degree requirements for mathematics or applied mathematics. (Formerly 3450:521)

Sequential. Prerequisite: Departmental permission. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergence and uniform convergence, power series, improper integrals, transformations, line and surface integrals. (Formerly 3450:522)

Prerequisite: Departmental permission. Complex variables; elementary functions, differentiation and analytic functions; integration and Cauchy's theorem; power series and Laurent series; residue theorem; applications such as conformal mappings, inversion of integral transform. (Formerly 3450:525)

Prerequisite: departmental permission. Numerical methods in polynomial interpolation, root finding, numerical integration, and numerical linear algebra. May not be used to meet master's degree requirements for applied mathematics. (Formerly 3450:527)

Prerequisite: Departmental permission. Numerical methods in the solution of ordinary and partial differential equations. Numerical differentiation, Runge-Kutta methods, and iterative methods for ODEs, finite differences for PDEs. (Formerly 3450:528)

Prerequisite: Departmental permission. Studies of various aspects of the analysis of Partial Differential Equations, including the construction of solutions, their uniqueness, behavior and qualitative properties. (Formerly 3450:532)

Prerequisites: Departmental permission. Analysis, solution of systems of equations, linear, nonlinear. Topics: stability theory, perturbation methods, asymptotic methods, applications from physical, social sciences. (Formerly 3450:535)

Prerequisite: Departmental permission. Formulation and analysis of mathematical models in social and physical sciences. Analysis of deterministic and stochastic models. Topics may include stochastic processes, linear programming, graph theory, theory of measurement. (Formerly 3450:536)

Prerequisite: Departmental permission. Matrices, eigenvalue problems, systems of ODEs, vector analysis, complex variables. May not be used to meet master's requirements for applied mathematics. (Formerly 3450:538)

Prerequisite: Departmental permission. Special functions, fourier series and transforms, PDEs. (Formerly 3450:539)

Prerequisite: Departmental permission. Axiomatic treatment of both Euclidean and non-Euclidean geometries. Other concepts included are finite geometry, transformations, constructions and inversions. (Formerly 3450:541)

Prerequisite: Departmental permission. Introduction to topological spaces and topologies, mapping, cardinality, homeomorphisms, connected spaces, metric spaces. (Formerly 3450:545)

Prerequisite: Permission of department. Topics include convexity, convex optimization problems, Lagrangian duality, optimality conditions and optimization in machine learning. Algorithmic topics will include the gradient descent and its variants, Newton’s and quasi-Newton methods. Applications will emphasize topics in data science.

Prerequisite: Permission of department. Introduction to the basic concepts, theories, and practices of traditional and modern neural networks in the area of deep learning. Materials are grouped in the following categories (i) machine learning basics, (ii) multilayer perceptrons and modern neural networks, (iii) applications and advanced techniques. Students will gain experiences in implementing the concepts and methods for applications.

(May be repeated for a total of 12 credits) Prerequisite: Permission of instructor. Selected topics in mathematics and applied mathematics at an advanced level. (Formerly 3450:589)

(May be repeated) Group studies of special topics in mathematics and applied mathematics. May not be used to meet undergraduate or graduate credit requirements in mathematics. May be used for elective credit only. (Formerly 3450:591)

Prerequisite: MATH 512 or departmental permission. Advanced study of selected topics in some of the following areas: semigroups, groups, rings, modules and fields. (Formerly 3450:611)

Prerequisite: MATH 522 or departmental permission. In-depth study of real analysis - metric spaces, normed vector spaces, integration theory, Hilbert spaces. (Formerly 3450:621)

Prerequisite: MATH 522 or departmental permission. Complex number system, holomorphic functions, continuity, differentiability, power series complex integration, residue theory, singularities, analytic continuation, asymptotic expansion. (Formerly 3450:625)

Prerequisites: MATH 522 (grade C- or better) and knowledge of C++, FORTRAN, or MATLAB or departmental permission. Error propagation; theoretical analysis of numerical methods in interpolation, integration and ordinary differential equations. (Formerly 3450:627)

Prerequisites: MATH 522 (grade C- or better) and knowledge of C++, FORTRAN, or MATLAB or departmental permission. Theoretical analysis of numerical methods in linear algebra. (Formerly 3450:628)

Prerequisite: Departmental permission. Problems with fixed and movable endpoints, problems with constraints, generalization to several variables, the maximality principle, linear time-optional problems, the connective between classical theory and the maximality principle. (Formerly 3450:631)

Prerequisite: MATH 532 or departmental permission. Existence, uniqueness and stability of solutions to general classes of partial differential equations. Methods for solving these classes introduced, emphasizing both analytical and numerical techniques. (Formerly 3450:632)

Prerequisite: MATH 539 or departmental permission. Methods of applied mathematics concentrating on techniques for analysis of differential and integral equations - applied complex analysis, integral transforms, partial differential equations, and integral equations. (Formerly 3450:633)

Prerequisite: MATH 539 or departmental permission. Methods of applied mathematics concentrating on techniques for analysis of differential and integral equations - applied complex analysis, integral transforms, partial differential equations, and integral equations. (Formerly 3450:634)

Prerequisite: MATH 522 or departmental permission. Unconstrained and constrained optimization theory and methods in applied problems. (Formerly 3450:635)

Prerequisite: Departmental permission. Theory and techniques of combinatorics as applied to network problems and graph theoretic problems. (Formerly 3450:636)

Prerequisite: Permission of instructor. Theory of wavelets and applications to signal and image analysis. Topics include time-frequency representations, filter bands, discrete and continuous wavelet transforms, wavelet packets, and applications. (Formerly 3450:638)

(May be repeated for a total of six credits) Prerequisite: Permission of advisor. Seminar-type discussion on topics in mathematics leading to supervised research project. No more than 2 credits apply to major requirements. (Formerly 3450:689)

Prerequisite: Permission of advisor. Seminar-type discussion on topics in mathematics leading to supervised research project. (Formerly 3450:692)

(May be repeated) Prerequisite: Graduate teaching assistant or permission. Training and experience in college teaching of mathematics. May not be used to meet degree requirements. Credit/noncredit. (Formerly 3450:695)

(May be repeated for a total of four credits) Prerequisites: Graduate standing and permission. Directed studies in mathematics at graduate level under guidance of selected faculty member. (Formerly 3450:697)

(May be repeated) Prerequisite: Permission of advisor. Research in suitable topics in mathematics or applied mathematics culminating in a research paper. May not be used to meet master's degree requirements for mathematics or applied mathematics. (Formerly 3450:698)

Prerequisite: Permission. A properly qualified candidate for the master's degree may obtain three credits for research that culminates in a public oral presentation of the faculty-supervised thesis. (Formerly 3450:699)

Prerequisites: [MATH 510 and MATH 621] or departmental permission. These courses are sequential. Study of normed linear spaces and transformations between them with an emphasis on the formulation and analysis of differential and integral equations as operator equations on these spaces. (Formerly 3450:721)

Prerequisites: [MATH 510 and MATH 621] or departmental permission. These courses are sequential. Study of normed linear spaces and transformations between them with an emphasis on the formulation and analysis of differential and integral equations as operator equations on these spaces. (Formerly 3450:722)

Prerequisite: Departmental permission. Basic Iterative methods, Matrix Properties and Concepts, Linear and Nonlinear equation solver, Semi-iterative and conjugate-gradient methods. (Formerly 3450:728)

Prerequisites: [MATH 522 and MATH 528], or MATH 628, or departmental permission. Derivation, analysis, and implementation of difference and variational-based methods for the solution of partial differential equations and systems of differential equations. (Formerly 3450:730)

Prerequisites: [MATH 522 and MATH 532] or departmental permission. Well-posedness of elliptic, hyperbolic and parabolic problems. Variational Methods for Elliptic problems, Conservation Laws and numerical methods, potential theory and integral equations. (Formerly 3450:732)

Prerequisites: [MATH 633 and MATH 634] or equivalent. Survey of asymptotic and perturbation methods as applied to integrals and differential equations. Topics: bifurcation and stability with applications from the physical sciences and engineering. (Formerly 3450:733)

Prerequisites: [MATH 633 and MATH 634] or equivalent. Survey of asymptotic and perturbation methods as applied to integrals and differential equations. Topics: bifurcation and stability with applications from the physical sciences and engineering. (Formerly 3450:734)

Prerequisite: MATH 522 or departmental permission. The study of mathematical models of systems which evolve over time. An introduction to maps and applications to ordinary differential equations. (Formerly 3450:735)