### Department of Mathematical Sciences, College of Arts and Sciences

#### Graduate Courses in Mathematics (MAT)

#### Additional offerings by the department include courses in Statistics (STT)

Mark Ginn, Department Chair

**MAT 5015. Advanced Seminar in Secondary Mathematics Education (3).F. **This course will include an examination of the North Carolina Mathematics Curriculum for high school with emphases on geometry and other selected topics. Class discussions, group activities, written assignments, and oral presentation will be integral parts of the course. A field experience and other professional development activities are required outside of class. Prerequisite: permission of the instructor. [Dual-listed with MAT 4015.]

**MAT 5125. History of Mathematics (3).On Demand.** The history and development of mathematical thought and theory from ancient to modern times, with particular attention to the history of geometry, algebra, calculus, differential equations, linear algebra, and statistics, and to the persons who made significant contributions to these areas of mathematics.

**MAT 5160. Complex Variables (3).On Demand.** An introduction to the study of complex variables to include such topics as line integrals, the Cauchy theorem, the Cauchy integral formula, Morera's theorem, and the Laurent series.

**MAT 5210. Abstract Algebra (3).On Demand.** A study of intermediate group theory, including group actions and the Sylow theorems; and ring theory, including polynomial rings, factorizations in principal ideal domains, and modules. Prerequisite: MAT 3110 (Introduction to Modern Algebra) or permission of the instructor. [Dual-listed with MAT 4720.]

**MAT 5220. Abstract Algebra II (3).On Demand.** A study of some advanced topics from abstract algebra, including splitting fields, finite fields, geometric constructions, and Galois theory. Prerequisite: MAT 5210 or permission of the instructor.

**MAT 5230. Linear Algebra (3).F.** A study of finite dimensional vector spaces. Among the topics covered are matrices, linear transformations, change of basis, eigenvalues, canonical forms, quadratic forms and quasi- inverses. Prerequisite: MAT 2240 (Linear Algebra) or MAT 3110 (Modern Algebra).

**MAT 5310. Numerical Analysis with Computer Applications (3).On Demand.** A study of methods of solving systems of linear and non-linear equations, differential equations and numerical integrations with emphasis on convergence properties and error analysis. Prerequisites: MAT 3220 (Introduction to Real Analysis I), and CS 1440 (Computer Science I). Corequisite: MAT 5610. (Same as CS 5310.)

**MAT 5330. Mathematical Models (3).On Demand.** A problems oriented course. The student uses mathematics to model a number of different situations. Among the tools used will be calculus, probability, statistics, linear algebra, differential equations, and computer simulation. Prerequisites: Background in at least three of the utilized tools.

**MAT 5340. Introduction to Operations Research (3).On Demand.** A thorough study of linear programming including duality theory and sensitivity analysis. At least two other topics related to mathematical applications in the management sciences queuing theory, Markov processes, game theory, decision analysis, network analysis, etc. will be covered. Prerequisites: MAT 2240 (Linear Algebra) and either STT 3850 (Statistical Data Analysis) or STT 4250 (Probability Modeling with Applications). [Dual-listed with MAT 4340.]

**MAT 5390. Numerical Linear Algebra (3).S.On Demand.** Methods for solving systems of linear equations with an emphasis on large, sparse systems. LU factorization including storage schemes, graph theory, ordering algorithms, and block factorization. Iterative methods including Jacobi, SOR, and conjugate gradient. Eigenvalue methods including power method, QR factorization, and Lanczos methods. Parallel matrix computations. Prerequisite: MAT 4310 (Numerical Methods). [Dual-listed with MAT 4990.]

**MAT 5415. Seminar in the Pedagogy of Mathematics (1).S.** Topics from mathematical content, pedagogy, and epistemology are examined, such as current trends in mathematics education, alternative learning styles, teaching developmental and adult students, and teaching with technology. This course may be repeated once for a total credit of two semester hours.

**MAT 5420. Teaching Apprenticeship (1).F;S.** This course provides a supervised experience in teaching in the mathematical sciences through direct participation in a classroom situation. Each student will work closely with a university faculty mentor and will be actively engaged in instructional practices, such as the development of activities and assignments or other relevant experiences. This course may be repeated for a total credit of two semester hours.

**MAT 5500. Independent Study (1-3).F;S.** Prerequisite: 12 hours of graduate mathematics.

**MAT 5520. Capstone Project in Secondary Education (1-2).On Demand.** A curriculum/action research project will be chosen, formulated, and implemented by the student under the guidance of a faculty member. This project should use knowledge gained in the secondary mathematics graduate program and apply it in the secondary classroom. A final written paper and presentation are required. MAT 5520 must be taken for a total credit of two semester hours. Graded on an S/U basis. Prerequisite: MAT 5910.

**MAT 5525. Product of Learning (1-3).F;S.On Demand.** Graded on an S/U basis.

**MAT 5530-5549. Selected Topics (1-4).On Demand.**

**MAT 5590. Advanced Topics in Differential Equations (3).S.** Development and application of advanced topics in differential equations. Topics may include foundational theories of differential equations, partial differential equations, perturbation theory, calculus of variations, distribution theory, transform theory, or other advanced topics. Prerequisite: MAT 3130 (Introduction to Differential Equations). Barring duplication of content, MAT 5590 may be repeated for a total credit of six semester hours. [Dual-listed with MAT 4590.]

**MAT 5600. Directed Research in Mathematical Sciences (1-3).On Demand.** A research project will be chosen, formulated, and executed by the student under the guidance of a faculty member. The project may investigate a mathematical sciences or a mathematics pedagogy topic. A final written report and presentation are required. MAT 5600 must be taken for a total credit of three semester hours. Graded on an S/U basis.

**MAT 5610. Analysis I (3).F.** A rigorous treatment of the topology of the real numbers, continuity, differentiation, integration, and sequences and series of functions. Prerequisite: MAT 3220 (Introduction to Real Analysis I) or permission of the instructor.

**MAT 5620. Analysis II (3).S.** A continuation of MAT 5610, including a rigorous development of differentiation and integration of functions of several variables, vector analysis, and Lebesgue theory. Prerequisite: MAT 5610 or permission of the instructor.

**MAT 5710. Introduction to Topology (3).On Demand.** A study of the basic concepts of general topological spaces including such topics as metric spaces, continuous functions, connectedness, product spaces, and compactness. Prerequisite: MAT 3220 (Introduction to Real Analysis I). [Dual-listed with MAT 4710.]

**MAT 5720. Topology (3).On Demand.** A study of topology to include such topics as general product spaces, complete metric spaces, compactifications, embedding, metrization theorems, and quotient spaces. Prerequisite: MAT 5710.

**MAT 5910. Investigation in the Teaching of Mathematics (3).On Demand.** An examination of recent research and experimental programs in the teaching of secondary school and undergraduate mathematics, with a focus on characteristics of research designs (including action research, curriculum development and analysis, teaching experiments, and case studies). Prerequisite: undergraduate mathematics major or permission of the instructor.

**MAT 5923. Geometry & Spatial Visualization: K-5 Assessment (3).F;S.** Formative and summative assessment strategies of students' geometric thinking in elementary grades; concept development of 2- and 3-dimensional geometry. Attention also given to diagnosis of student errors. Does not count for the Master of Arts in Mathematics. Prerequisite: CI 5922. (Same as CI 5923.)

**MAT 5924. Algebraic Reasoning: K-5 Discourse & Questioning (3).F;S.** Focus on the early algebra concepts of functional thinking and generalized arithmetic in relationship to pedagogical practices centered on questioning in the mathematics classroom. Does not count for the Master of Arts in Mathematics. Prerequisite: CI 5922. (Same as CI 5924.)

**MAT 5925. Data Analysis and Measurement: K-5 Classroom Interactions (3).F;S.** Focus on statistical literacy of elementary teachers and the teaching of data analysis and measurement to K-5 students; attention is also given to learning methods which facilitate appropriate classroom interactions. Does not count for the Master of Arts in Mathematics. Prerequisite: CI 5922. (Same as CI 5925.)

**MAT 5935. Basic Concepts of Probability and Statistics (3).On Demand.** This course examines the concepts underlying the elementary and middle school curriculum in probability and statistics. Probability models will be studied using both mathematical approaches and simulations. Statistics will be presented as a problem solving process involving question formulation, data collection, data analysis and the interpretation of results. Does not count for the Master of Arts in Mathematics. Prerequisite: MAT 3910. Introduction to the Logic and Structure of Mathematics I or MAT 3920. Introduction to the Logic and Structure of Mathematics II or permission of the instructor. [Dual-listed with MAT 4930.]

**MAT 5941. Technology for Teaching Mathematics (3).On Demand.** The use of current computer and calculator technology in various mathematics content areas will be studied. Technology use in these areas will involve problem solving, exploring patterns, experimentation, conjecturing and generalization of findings. Appropriate use of technology will be stressed. Prerequisite: undergraduate major in mathematics, or permission of the instructor.

**MAT 5952. Problem Solving (3).On Demand.** Problem solving is the focus of this course. There is an emphasis on building new mathematical knowledge through work with problems and applying a wide variety of strategies to solve problems and adapt the strategies to new situations. Problems may be drawn from algebra, geometry, number theory, calculus, probability and statistics. Prerequisites: knowledge in all the areas from which the problems will be drawn.

**MAT 5961. Foundations of Geometry (3).SS.** A treatment of projective geometry including both the synthetic and the analytic approach. Also to be considered is a study of the relation of Euclidean, affine and hyperbolic geometries to projective geometry. Prerequisites: MAT 2240 (Linear Algebra) and MAT 3610 (Geometry).

**MAT 5965. Informal Geometry (3).F.** This course is an informal treatment of the geometric concepts in the elementary and middle school mathematics curriculum. The topics considered include polygons, congruence, similarity, tilings, transformations, symmetry, angles, constructions, area, perimeter, circles, and polyhedra. Does not count for the Master of Arts in Mathematics. Prerequisite: MAT 3910. Introduction to the Logic and Structure of Mathematics I or MAT 3920. Introduction to the Logic and Structure of Mathematics II or permission of the instructor. [Dual-listed with MAT 4910.]

**MAT 5970. Number Theory Concepts (3).SS.** Designed primarily for secondary teachers, this course is a study of the traditional number theory concepts and theorems with special attention to those of significance to the high school curriculum. Emphasis will be on the historical as well as the theoretical development of the subject. Prerequisites: undergraduate major in mathematics or permission of the instructor.

**MAT 5971. Number Systems and Algebra for Middle Grades Teachers (3).On Demand.** Designed primarily for teachers of mathematics at Grades 6-8, this course is a deep and connected study of number and operations, and of algebra, including rational numbers, proportional reasoning, and linear relations. Emphasis will be on rich tasks using representational tools and models to explore mathematical relationships. Problem solving, reasoning and proof, and mathematical communication will also be emphasized. Does not count for the Master of Arts in Mathematics. Prerequisite: enrollment in the Master of Arts in Middle Grades Education program, or permission of the instructor.

**MAT 5972. Geometry and Measurement for Middle Grades Teachers (3).On Demand.** Designed primarily for teachers of mathematics at Grades 6-8, this course is a deep and connected study of geometry and measurement, including the van Hiele model of geometric learning; shape, size, and symmetry; perimeter, area, surface area, and volume; classical and transformational geometry; the golden ratio, tessellations, and spherical geometry. Emphasis will be on rich tasks using representational tools and models to explore mathematical relationships. Problem solving, reasoning and proof, and mathematical communication will also be emphasized. Does not count for the Master of Arts in Mathematics. Prerequisite: enrollment in the Master of Arts in Middle Grades Education program, or permission of the instructor.

**MAT 5973. Data Analysis and Probability for Middle Grades Teachers (3).On Demand.** Designed primarily for teachers of mathematics at Grades 6-8, this course is a deep and connected study of data analysis and probability, including data collection, organization, and display; measures of spread and center; inferences and predictions based on data; and basic concepts of probability. Emphasis will be on rich tasks using representational tools and models to explore mathematical relationships. Problem solving, reasoning and proof, and mathematical communication will also be emphasized. Does not count for the Master of Arts in Mathematics. Prerequisite: enrollment in the Master of Arts in Middle Grades Education program, or permission of the instructor.

**MAT 5980. Special Topics in Mathematics Education (1-3).F;S.** A flexible program of reading, study, planning, and writing designed to meet the needs of individual teachers or groups of teachers in the field of secondary school mathematics. Prerequisite: Undergraduate major in mathematics and recommendation of graduate advisor. May be taken up to a total of fifteen semester hours.

**MAT 5989. Graduate Research (1-9).F;S.** This course is designed to provide access to University facilities for continuing graduate research at the master's and specialist's levels. Graded on an S/U basis. MAT 5989 does not count toward a degree.

**MAT 5999. Thesis (1-6).F;S.** Graded on an SP/UP basis until the thesis has been successfully defended and received final approval, at which time all grades will be changed to S.