Mathematics Education

Master of Arts Degree

 

Program of Study

The Master of Arts in Mathematics Education degree program is designed primarily for secondary mathematics school teachers interested in professional growth and graduate certification in mathematics teaching. Emphasis in this program is given to developing depth and breadth in mathematics teaching and learning, appropriate to the role of the secondary school teacher.

 

Additional Admission Requirements

In addition to the general requirements for admission to the Graduate School, the following are required for graduate study in Mathematics Education:

1)       Twenty-seven hours of undergraduate coursework in Mathematics beyond the freshman level, or evidence of equivalent academic preparation.

2)       Possession of a North Carolina "A" teacher's license or the equivalent from another state. An applicant may be admitted on the condition that he/she satisfies the Class "A" requirements early in his/her course of study. Work applied to the Class "A" deficiency may not be applied toward the degree.

3)       Two years of full-time experience teaching mathematics in a secondary school or other acceptable teaching experience.

4)       A satisfactory score is required on the Aptitude Portion of the Graduate Record Examination.

 

Degree Requirements

The Master of Arts in Mathematics Education degree requires successful completion of a minimum of 36 semester hours of graduate credit or the equivalent. Of these, 18 hours must be in courses numbered 6000 or above. Programs of study beyond these 36 hours may be required to remove deficiencies in undergraduate programs or to develop areas of need, interest, or desired experience.

 

Core Courses

Each candidate must complete:

18 hours of graduate-level Mathematics courses selected in consultation with the program Coordinator, with at least 9 hours of courses at the 6000-level. A recommended plan of study includes:

MATH 6100  Foundations of Mathematics (3)

MATH 6101  Foundations of Real Analysis (3)

MATH 6102  Calculus from an Advanced Viewpoint (3)

MATH 6106  Modern Algebra (3)

MATH 6107  Linear Algebra (3)

MATH 6118  Non-Euclidean Geometry (3)

 

12 hours of graduate-level courses covering mathematics education learning theory, research, and contemporary topics in secondary mathematics teaching. These courses include:

MAED 6120  Research in Mathematics Education (3)

MAED 6122  Theoretical Foundations of Learning Mathematics (3)

MAED 6124  Issues in the Teaching of Secondary School Mathematics (3)

RSCH 6101    Educational Research Methods (3)

 

3)             6 hours of graduate-level professional education courses including:

MDSK 6260   Principles of Teacher Leadership (3)

 

An additional three hours of graduate-level Mathematics, Mathematics Education, or Education courses selected in consultation with the student's adviser.

 

4)             A Basic Portfolio consisting of documents and artifacts that provides evidence of the student's professional growth during the program. By the end of his/her first semester in the program, each student will select a member of the Mathematics Education faculty who will serve as his/her Graduate Advisor throughout the program.

 

Approval of the program of each student and provision of advice regarding progress toward the degree are the responsibility of the Graduate Advisor.

 

Comprehensive Exam

Upon successful completion of all coursework, each candidate for the degree in Mathematics Education must pass a comprehensive final exam consisting of two parts. The student must pass an oral exam on the mathematics content courses. The second part of the exam involves the student presenting documentation that demonstrates their professional growth as teachers and educational researchers. The student has the option of presenting either a research-based project or a comprehensive portfolio. The Graduate Advisor will advise and assist the student in planning his/her Comprehensive Portfolio or Final Research Report.

 

 

Courses In Mathematics, Mathematics Education And Statistics

 

Mathematics

MATH 5000. Topics in Foundations or History of Mathematics. (2-3) Prerequisite: consent of the department. Topics in the foundations or the history of mathematics selected to supplement regular course offerings in this area of mathematics. May be repeated for credit with approval of the department. Credit for the M.A. degree in mathematics requires approval of the department. (On demand)

 

MATH 5040. Topics in Analysis. (2-3) Prerequisite: consent of the department. Topics in the foundations or the history of mathematics selected to supplement regular course offerings in this area of mathematics. May be repeated for credit with the approval of the department. Credit for the M.A. degree in mathematics requires approval of the department. (On demand)

 

MATH 5060. Topics in Algebra. (2-3) Prerequisite: consent of the department. Topics in algebra selected to supplement regular course offerings in this area of mathematics. May be repeated for credit with the approval of the department. Credit for the M.A. degree in mathematics requires approval of the department. (On demand)

 

MATH 5080. Topics in Geometry and Topology. (3) Prerequisite: consent of the department. Topics in geometry or topology selected as to supplement regular course offerings in this area of mathematics. May be repeated for credit with approval of the department. Credit for M.A. degree in mathematics requires approval of the department. (On demand)

 

MATH 5109. History of Mathematical Thought. (3) Prerequisite: MATH 1241 or consent of the department. A study of the development of mathematics in its historical setting from the earliest beginnings to modern times. Not approved for the M.A. in mathematics degree. (Fall) (Evenings)

 

MATH 5128. Applied Probability I. (3) Prerequisite: MATH/STAT 3122 and MATH 2171 or consent of the department. Finite and countable Markov chains, Markov Decision Processes, and optimal stopping. Other topics selected from: queuing theory, inventory models, reliability theory, game theory, recurrent events, information theory, stochastic control, stochastic control with incomplete information and Kalman filtering. (Fall)(Alternate years)

 

MATH 5129 Applied Probability II. (3) Prerequisite: MATH 5128 or consent of the department. Continuation of MATH 5128. (Spring)(Alternate years)

 

MATH 5143. Analysis I. (3) Prerequisite: MATH 3141 with a grade of B or better, or consent of the department. First course of a two-semester sequence providing a rigorous treatment of continuity, differentiability and integration of functions of one and several real variables. (Fall)

 

MATH 5144. Analysis II. (3) Prerequisite: MATH 5143 with a grade of B or better or consent of the department. Continuation of MATH 5143. (Spring)

 

MATH 5161. Number Theory. (3) Prerequisite: MATH 3163 with a grade of C or better or consent of the department. A study of the elements of classical number theory including divisibility, congruences, diophantine equations, prime numbers and their distribution, quadratic reciprocity, number-theoretic functions, and famous unsolved problems. Not approved for the M.A. in mathematics degree. (Spring) (Alternate years)

 

MATH 5163. Modern Algebra. (3) Prerequisite: MATH 3163 or consent of the department. Groups, rings, integral domains, fields. (Fall) (Alternate years)

 

MATH 5164. Abstract Linear Algebra. (3) Prerequisite: MATH 3163 and 2164 or consent of the department. Vector spaces over arbitrary fields, linear transformations, canonical forms, multilinear algebra. (Spring) (Alternate years)

 

MATH 5165. Numerical Linear Algebra. (3) Prerequisites: CSCI 1100 or 1201 and 1201L, MATH 2164 and 2171, all with a grade of C or better, or consent of the Department. Gaussian elimination and LU decomposition methods for linear systems. Vector and matrix norms, condition numbers and accuracy of solutions. Solutions of large sparse matrix systems using skyline solvers, and Jacobi, Gauss-Seidel, and SOR iterative methods. Solution of nonlinear systems. Least squares methods using the QR factorization. Selected problems will be programmed for computer solution. (Fall) (Alternate years)

 

MATH 5171. Numerical Solution of Ordinary Differential Equations. (3) Prerequisites: CSCI 1100 or 1201 and 1201L, MATH 2241, 2164, and 2171, all with a grade of C or better, or consent of the Department. Numerical solution techniques for ordinary differential equations such as Runga-kutta, multistep and extrapolation methods. Stiff solvers and stability criteria. Comparative work with modern robust codes and visualization methods. (On demand)

 

MATH 5172. The Finite Element Method. (3) Prerequisites: CSCI 1100 or 1201 and 1201L, MATH 2241, 2164, and 2171, all with a grade of C or better, or consent of the department. Boundary value problems and their variational form. Finite element basis functions, computational techniques, isoparametric elements and curved boundaries, alternate methods, singular problems, eigenvalue problems. Some practical experience with an F.E.M. program and graphical output. (Spring) (Alternate years)

 

MATH 5173. Ordinary Differential Equations. (3) Prerequisites: MATH 2171 and MATH 3142, or consent of the department. Existence and uniqueness theorems for initial value problems; continuous dependence of solutions on initial values and right hand sides; linear differential equations in R2 and Rn; non-linear differential equations in R2 and Rn: phase portraits, singularities, cycles; invariant manifolds; linearization; singularities of planar systems; Lyapunov stability; examples: van der Pol oscillator, Liénard systems, Volterra-Lotka equations. (Spring)

 

MATH 5174. Partial Differential Equations. (3) Prerequisites: MATH 2164 and MATH 3141, or consent of department. Classification of types of partial differential equations. Separation of variables, Sturm-Liouville problems, boundary and eigenvalue problems, fundamental solutions and Green's theorem, Fourier series and integrals, Laplace transforms. (Fall)

 

MATH 5176. Numerical Methods for Partial Differential Equations. (3) Prerequisite: CSCI 1100 or 1201 and 1201L, MATH 2241, 2164, and 2171 all with a grade of C or better, or consent of the department. Basic finite difference schemes for the solutions of elliptic, parabolic and hyperbolic equations. Van Neuman analysis, characteristics, boundary conditions. (Fall) (Alternate years)

 

MATH 5181. Introduction to Topology. (3) Prerequisite: MATH 2164 with a grade of C or better. Topics from set theory and point set topology such as cardinality, order, topological spaces, metric spaces, separation axioms, compactness and connectedness. (Fall) (Alternate years)

 

MATH 5691. Seminar. (1-6) Prerequisite: consent of the department. Individual or group investigation and exposition of selected topics in mathematics. (On demand)

 

MATH 5692. Seminar. (1-6) Prerequisite: consent of the department. A continuation of MATH 5691. (On demand)

 

MATH 6004. Topics in Analysis. (3) Prerequisite: MATH 6101 or consent of department. Topics in analysis selected so as to complement regular course offerings in this area of mathematics. May be repeated for credit with the consent of department. (On demand)

 

MATH 6008. Topics in Geometry and Topology. (3) Prerequisite: consent of department. Topics selected from Euclidean geometry, non-Euclidean geometry, projective geometry, differential geometry, point-set topology, algebraic topology. May be repeated for credit with approval of department. (On demand)

 

MATH 6100. Foundations of Mathematics. (3) Prerequisite: consent of department. Logic, sets and axiomatic systems. (Fall, Summer) (Alternate years)

 

MATH 6101. Foundations of Real Analysis. (3) Prerequisite: MATH 6100 or consent of department. Axiomatic and historical development of the real and complex numbers; rigorous development of limits and continuity of functions, intermediate and extreme value theorems. (Fall) (Alternate years)

 

MATH 6102. Calculus from an Advanced Viewpoint. (3) Prerequisite: MATH 6101 or its equivalent. A continuation of MATH 6101. A rigorous approach to differentiation and integration of functions of one real variable. (Spring) (Alternate years)

 

MATH 6103. Computer Techniques and Numerical Methods. (3) Prerequisite: MATH 6101 or consent of department. Computer systems, programming, and the computer solution of numerical problems. (Summer) (Alternate years)

 

MATH 6105. Problem Solving in Discrete Mathematics. (3) Prerequisite: consent of department. Propositional and predicate calculus, counting techniques, partially ordered sets, lattices, graphs and trees. (Alternate years)

 

MATH 6106. Modern Algebra. (3) Prerequisite: MATH 3163 or its equivalent or consent of department. Topics chosen from group theory, rings and ideals, integral domains, fields and elementary Galois theory. (Summer) (Alternate years)

 

MATH 6107. Linear Algebra. (3) Prerequisite: MATH 2164 or its equivalent or consent of department. Systems of linear equations, matrices, vector spaces, linear transformations, determinants, canonical forms of matrices, inner products. (Summer) (Alternate years)

 

MATH 6118. Non-Euclidean Geometry. (3) Prerequisite: consent of department. History of Euclid's Fifth Postulate and attempts to prove it; work of Gauss, Bolyai, Lobachevsky and others; systematic development of hyperbolic geometry; relative consistency of hyperbolic geometry; relative consistency of hyperbolic and Euclidean geometries. (Alternate years)

 

MATH 6171. Advanced Applied Mathematics I. (3) Prerequisites: MATH 2241 and 2171 with grades of C or better, or consent of department. Power series solutions of ordinary differential equations, vector calculus, line and surface integrals, partial differential equations and Fourier integrals. (Fall) (Evenings)

 

MATH 6172. Advanced Applied Mathematics II. (3) Prerequisites: MATH 2241 and 2171 with grades of C or better or consent of department. Complex analysis; probability and statistics. (Spring) (Evenings)

 

MATH 6609. Seminar. (1-3) Prerequisite: consent of the department. A series of regularly scheduled meetings in which each student will present one or more topics selected by the instructor. May be repeated for credit with the consent of department. (On demand)

 

MATH 7028. Topics in Probability. (3) Prerequisite: MATH 7120 and 7121, or consent of department. Topics of current interest in probability and advanced topics in probability. May be repeated for credit with the consent of the department. (On demand)

 

MATH 7050. Topics in Mathematics. (2-3) Prerequisite: consent of department. Topics chosen from such fields as algebra, topology, analysis, applied mathematics, differential geometry, mathematical physics, graph theory, probability, statistics. May be repeated for credit as topics vary and with the approval of the department. (On demand)

 

MATH 7065. Topics in Applied Algebra and Algebraic Structures. (3) Prerequisite: consent of the department. Current topics in Applied Algebra and Algebraic Structure. (On demand)

 

MATH 7070. Topics in Numerical Analysis. (3) Prerequisite: consent of the department. Topics of current interest in numerical analysis. May be repeated for credit with the consent of the department. (On demand)

 

MATH 7071. Topics in Differential Equations. (3) Prerequisite: consent of the department. Topics of current interest in ODE, PDE, dynamical systems, inverse problems and related subjects. May be repeated for credit with the consent of the department. (On demand)

 

MATH 7120. Probability Theory I. (3) Prerequisites: MATH 7143 and MATH/STAT 3122 or consent of department. Topics include probability spaces, probability measures, sigma-algebras, characteristic functions, sequences of random variables, law of large numbers, general forms of the Central Limit Theorem. (Fall) (Alternate years)

 

MATH 7121. Probability Theory II. (3) Prerequisite: MATH 7120 or consent of the department. A continuation of MATH 7120. (Spring) (Alternate years)

 

MATH 7125. Stochastic Processes I. (3) Prerequisites: MATH 3122 and 7143 or consent of the department. Basic ideas in the study of stochastic processes, selected from: discrete and continuous time Markov processes, stationary and renewal processes, applications to queuing theory, reliability theory, stochastic differential equations, time-series analysis, filtering and stochastic control theory. (On demand)

 

MATH 7126. Stochastic Processes II. (3) Prerequisite: MATH 7125. A continuation of MATH 7125. (On demand)

 

MATH 7141. Complex Analysis I. (3) Prerequisite: MATH 5143 or consent of the department. Holomorphic functions, complex integration, residues, entire and meromorphic functions, conformal mapping, harmonic functions. (Spring) (Alternate years)

 

MATH 7142. Complex Analysis II. (3) Prerequisite: MATH 7141. A continuation of MATH 7141. (On demand)

 

MATH 7143. Real Analysis I. (3) Prerequisite: MATH 5144 or consent of the department. Lebesgue integration on the real line, Lp spaces, introduction to general measure and integration theory. (Fall)

 

MATH 7144. Real Analysis II. (3) Prerequisite: MATH 7143 or consent of the department. A continuation of MATH 7143. (Spring)

 

MATH 7147. Applied Functional Analysis. (3) Prerequisite: MATH 5144. Introduction to functional analysis and its applications to such areas as linear and non-linear differential equations, integral equations, and control theory. Topics chosen from Banach spaces, operators, the Hahn-Banach, open mapping and closed graph theorems, Sobolev spaces, spectral theory, operators in Hilbert space. (Summer) (On Demand)

 

MATH 7148. Functional Analysis. (3) Prerequisite: MATH 7144 or consent of the department. Material selected from: spectral theory, spectral theory of differential operators, groups and semigroups of operators, nonlinear functional analysis, asymptotic analysis, integral equations, Fourier analysis, distributions, and Sobolev spaces. (Fall)(Alternate years)

 

MATH 7163. Modern Algebra I. (3) Prerequisite: MATH 4163 and 4164 or consent of department. Topics will be selected from Galois theory, commutative algebra, modules, ring theory, homological algebra. (Fall) (Alternate years)

 

MATH 7164. Modern Algebra II. (3) Prerequisite: MATH 7163. A continuation of MATH 7163. (On demand)

 

MATH 7172. Partial Differential Equations. (3) Prerequisite: MATH 5174 and 7144 or consent of department. Harmonic functions, mean-value theorem, maximum principle, Green's representation for the solution of the Dirichlet problem for Laplace's equation; Poisson's equations and the Poisson formula; statement and proof of the existence theorem for general second-order elliptic operators, generalized maximum principles; Sobolev spaces. Evolution equations involving elliptic operators, such as the heat or wave equations, may also be introduced. (Spring) (Alternate years)

 

MATH 7173. Evolution Equations. (3) Prerequisite: MATH 7144 and 7172 or consent of the department. Semigroups of operators and their generators, examples of semigroups. The heat equation, examples of elliptic operators that generate semigroups, Hille-Yosida theory, analytic semigroups; examples, fractional powers of operators. (On demand)

 

MATH 7174. Linear and Non-linear Waves. (3) Prerequisite: MATH 5124 and 7144 or consent of the department. Hyperbolic waves, characteristics, Riemann invariants, conservation laws, weak solutions, shock structure. Burger's equation, gas dynamics, dispersive waves, group velocity, water waves, non-linear optics. (On demand)

 

MATH 7175. Inverse Problems. (3) Prerequisite: MATH 7144 and MATH 5174 or consent of the department. Ill-posed problems and numerical methods for them. Applications of inverse problems to real processes. One dimensional inverse problems. Multi-dimensional inverse problems: uniqueness and numerical methods. Inverse scattering problems. (On demand)

 

MATH 7176. Advanced Numerical Analysis. (3) Prerequisites: MATH 2164, 2171 and 5176 or consent of the department. A selection of topics from such areas as iterative methods of solving linear and non-linear systems of equations, approximation theory, splines, and finite element methods for partial differential equations. (Spring) (Alternate years)

 

MATH 7177. Applied Optimal Control. (3) Prerequisites: MATH 5143 or consent of the department. Examples of control systems and optimization problems, optimal control of discrete-time systems, solutions of the general discrete-time optimization problem, optimal control of continuous-time systems, the calculus of variations, solution of the general continuous optimization problem, applications of the Pontryagin Maximum Principle, Dynamic programming, and Bang-bang control. Controllability and differential games may also be introduced. (Spring) (Alternate years)

 

MATH 7178. Computational Methods for Fluid Dynamics. (3) Prerequisite: CSCI 1100 or 1201 and 1201L, MATH 2242, 2171, 5174 and 5176 or consent of the department. Topics on various numerical techniques for the solution of incompressible and compressible flows. Finite difference, finite element and spectral methods, and shock capturing and fitting methods. Multi-grid method and acceleration techniques. (On demand)

 

MATH 7179. Advanced Finite Difference Methods. (3) Prerequisite: consent of the department. Accuracy analysis and design of high order schemes, stability theory of schemes with variable coefficients, stability theory of schemes for initial-boundary value problems, convergence theory for nonlinear cases. (On demand)

 

MATH 7181. Topology I. (3) Prerequisite: consent of department. Topological spaces, continuous functions, connectedness, compactness, and metrizability, and further topics from point-set, geometric or algebraic topology. (On demand)

 

MATH 7182. Topology II. (3) Prerequisite: MATH 7181. A continuation of MATH 7181. (On demand)

 

MATH 7184. Differential Geometry I. (3) Prerequisite: consent of the department. Manifolds, differential structures, tangent bundles, embeddings, immersions, inverse function theorem, Morse-Sard theorem, transversality, Borsuk-Ulam theorem, vector bundles, Euler characteristics, Morse theory, Stokes theorem, Gauss-Bonnet theorem, Whitney embedding theorem. (On demand)

 

MATH 7185. Differential Geometry II. (3) Prerequisite: consent of the department. Differentiable manifolds, differential forms, critical points, local and global theory of curves, local and global theory of surfaces, connections, geodesics, curvature, spaces of constant curvature, Lie groups and Lie algebras. (On demand)

 

MATH 7273. Advanced Finite Element Analysis. (3) Prerequisite: MATH 5172 and 5174 or consent of the department. Selection of topics from such areas of finite element analysis as convergence theorems (Ciarlet), hierarchical basis functions, the h-p method, adaptive grid techniques and solution methods for nonlinear equations. (Fall)(Alternate years)

 

MATH 7275. Dynamical Systems I. (3) Prerequisites: MATH 5143 and MATH 5173 or consent of the department. Cycles and separatrix cycles, Poincaré first-return map: diffeomorphisms, Poincaré-Bendixson Theory, flows on the two-torus; structural stability, genericity, Peixoto's theorem; singularities of planar systems. Degenerate singularities, Hopf bifurcation, saddle-node bifurcation, center bifurcation. (On demand)

 

MATH 7276. Dynamical Systems II. (3) Prerequisite: MATH 7275 or consent of the department. Method of averaging, Melnikov functions, hyperbolic structure, symbolic dynamics, homoclinic and heteroclinic orbits, global bifurcations, infinite dimensional dynamical systems, inertial manifolds, Lyapunov exponents and dimension of attractors, codimension-two bifurcations, Duffing's equation, Lorenz equations, finite dimensional systems of dimension at least three. (On demand)

 

MATH 7277. Bifurcation Theory. (3) Prerequisite: MATH 7275 or consent of the department. Implicit function theorem, manifolds and transversality, Newton polygons, Lyapunov center theorem, variational methods, Ljusternik-Schnirelman theory, mountain-pass theorem, bifurcations with one-dimensional null-spaces, Morse theory and global bifurcations, geometric theory of partial differential equations. (On demand)

 

MATH 7691. Research Seminar. (1-3) Prerequisite: consent of department. A seminar in which independent study may be pursued by the student or a group of students under the direction of a professor. (On demand)

 

MATH 7692. Research Seminar. (1-3) Prerequisite: consent of department. A continuation of MATH 7691. (On demand)

 

MATH 7893. Thesis. (1-3) Prerequisite: consent of department. Subject to the approval of the department Graduate Committee, the thesis may be original work, work of an expository nature, or the mathematical formulation and solution of a particular industrial or business problem suggested by the career interests of the student. The thesis must be defended in an oral presentation. May be repeated for credit with the consent of department. (Fall, Spring, Summer)

 

MATH 8028. Topics in Probability. (3) See MATH 7028 for Course Description.

 

MATH 8050. Topics in Mathematics. (2-3) See MATH 7071 for Course Description.

 

MATH 8065. Topics in Applied Algebra and Algebraic Structures. (3) See MATH 7065 for Course

Description.

 

MATH 8070. Topics in Numerical Analysis. (3) See MATH 7070 for Course Description.

 

MATH 8071. Topics in Differential Equations. (3) See MATH 7071 for Course Description.

 

MATH 8120. Probability Theory I. (3) See MATH 7120 for Course Description.

 

MATH 8121. Probability Theory II. (3) See MATH 7121 for Course Description.

 

MATH 8125. Stochastic Processes I. (3) See MATH 7125 for Course Description.

 

MATH 8126. Stochastic Processes II. (3) See MATH 7126 for Course Description.

MATH 8141. Complex Analysis I. (3) See MATH 7141 for Course Description.

 

MATH 8142. Complex Analysis II. (3) See MATH 7142 for Course Description.

 

MATH 8143. Real Analysis I. (3) See MATH 7143 for Course Description.

 

MATH 8144. Real Analysis II. (3) See MATH 7147 for Course Description.

 

MATH 8147. Applied Functional Analysis. (3) See MATH 7147 for Course Description.

 

MATH 8148. Functional Analysis. (3) See MATH 7148 for Course Description.

 

MATH 8163. Modern Algebra I. (3) See MATH 7163 for Course Description.

 

MATH 8164. Modern Algebra II. (3) See MATH 7164 for Course Description.

 

MATH 8172. Partial Differential Equations. (3) See MATH 7172 for Course Description.

 

MATH 8173. Evolution Equations. (3) See MATH 7173 for Course Description.

 

MATH 8174. Linear and Non-linear Waves. (3) See MATH 7174 for Course Description.

 

MATH 8175. Inverse Problems. (3) See MATH 7175 for Course Description.

 

MATH 8176. Advanced Numerical Analysis. (3) See MATH 7176 for Course Description.

 

MATH 8177. Applied Optimal Control. (3) See MATH 7177 for Course Description.

 

MATH 8178. Computational Methods for Fluid Dynamics. (3) See MATH 7178 for Course Description.

 

MATH 8181. Topology I. (3) See MATH 7181 for Course Description.

 

MATH 8182. Topology II. (3) See MATH 7182 for Course Description.

MATH 8184. Differential Geometry I. (3) See MATH 7184 for Course Description.

 

MATH 8185. Differential Geometry II. (3) See MATH 7185 for Course Description.

 

MATH 8273. Advanced Finite Element Analysis. (3) See MATH 7273 for Course Description.

 

MATH 8275. Dynamical Systems I. (3) See MATH 7276 for Course Description.

 

MATH 8276. Dynamical Systems II. (3) See MATH 7276 for Course Description.

 

MATH 8277. Bifurcation Theory. (3) See MATH 7277 for Course Description.

 

MATH 8691. Research Seminar. (1-3) See MATH 7691 for Course Description.

 

MATH 8692. Research Seminar. (1-3) See MATH 7692 for Course Description.

 

MATH 8994. Doctoral Research and Reading. (1-9) Prerequisite: consent of the department. May be repeated with consent of the department. (On demand)

 

Mathematics Education

MAED 5000. Topics in Mathematics Education, Early Childhood. (1-6) Prerequisite: consent of department. (On demand)

 

MAED 5040. Topics in Mathematics Education, Intermediate. (1-6) Prerequisite: consent of department. (On demand)

 

MAED 5070. Topics in Mathematics Education, Secondary. (1-6) Prerequisite: consent of department. (On demand)

 

MAED 5101. Arithmetic in the School. (3) Prerequisite: MATH 1100 or equivalent. A study of the number systems with emphasis placed upon the basic concepts and meanings, properties of addition, multiplication, inverses, systems of numeration and number line appropriate for each grade. (Does not count toward a major in mathematics. Open only to transfer students who have completed six semester hours of mathematics at another university.) (On demand)

 

MAED 5104. Microcomputing for Teachers. (3) Prerequisites: working knowledge of college algebra and trigonometry, and consent of department. Introduction to basic computer concepts, to microcomputer systems, to the design and development of programs to assist instruction in mathematics and computer sciences. A programming language such as BASIC or LOGO will be used. Each student will integrate skills learned by selecting, designing and developing a specific project. (No prior experience with computer programming required.) (Spring) (Evenings)

 

MAED 5105. Geometry for Teachers. (3) Prerequisite: MATH 2102 or MAED 5101 or consent of department. A study of the foundations of Euclidean geometry and a brief treatment of non-Euclidean geometry. Emphasis on learning activities and teaching techniques for teachers of mathematics K-12. (Spring) (Evenings)

MAED 5141. Mathematics for the Intermediate School Teacher. (3) Prerequisite: MATH 2102 or consent of department. A study of the algebraic properties of the real numbers; functions, equations, inequalities and their graphs, activities and applications related to upper elementary and intermediate grades. (Fall) (Evenings)

 

MAED 6120. Research in Mathematics Education. (3) Prerequisites: Students must be enrolled in the Masters of Arts in Mathematics Education Program. An introduction and overview of research in the teaching and learning of mathematics in K-12. Overview of contemporary research perspectives and paradigms; interpreting and synthesizing the research literature; survey of contemporary research problems in mathematics teaching and learning; development of classroom-based research studies. (Alternate years)

 

MAED 6122. Theoretical Foundations of Learning Mathematics. (3) Prerequisites: Students must be enrolled in the Masters of Arts in Mathematics Education Program. Introductions to theories of learning that have influenced the teaching of mathematics in K-12. An overview of theories that have guided reforms in mathematics teaching; contemporary constructivist theories of mathematics learning. (Alternate years)

 

MAED 6124. Issues in the Teaching of Secondary School Mathematics. (3) Prerequisites: Students must be enrolled in the Masters of Arts in Mathematics Education Program. Study of major issues affecting secondary mathematics education: analysis of the impact of learning theories on methods of teaching; assessment methods for improving mathematics learning; analysis of the historical and programmatic development of the secondary school mathematics curriculum leading to current trends, issues, and problems; and analysis of the role of technology in the secondary mathematics classroom. (Alternate years)

 

Statistics

STAT 5123. Applied Statistics I. (3) Prerequisites: MATH 2164 with a grade of C or better and junior standing, or consent of department. Review of stochastic variables and probability distributions, methods of estimating a parameter, hypothesis testing, confidence intervals, contingency tables. Linear and multiple regression, time series analysis. (Fall) (Evenings) (Alternate years)

 

STAT 5124. Applied Statistics II. (3) Prerequisite: STAT 5123 or consent of the department. Single factor analysis of variance. Multi-factor analysis of variance. Randomized complete-block designs, nested or hierarchical designs, Latin squares, factorial experiments. Design of experiments. (Spring) (Evenings) (Alternate years)

 

STAT 5126. Theory of Statistics I. (3) Prerequisite: STAT 3123 or consent of the department. Survey of the mathematical structure supporting applied statistics. Discrete and continuous distributions, moment-generating functions, sampling, point estimation, the multivariate normal distribution, sampling distributions. (Fall) (Alternate years)

 

STAT 5127. Theory of Statistics II. (3) Prerequisite: STAT 5126 or consent of the department. Point and interval estimations, hypothesis testing, regression and linear hypotheses, experimental designs and analysis, distribution-free methods. (Spring) (Alternate years)

 

STAT 7027. Topics in Statistics. (3) Prerequisite: consent of the department. Topics of current interest in statistics and/or applied statistics. May be repeated for credit with consent of the department. (On demand)

 

STAT 7122. Advanced Statistics I. (3) Prerequisite: MATH 7143 and STAT 5127 or consent of department. A survey of frequently used statistical techniques selected from: estimation theory and hypothesis testing, parametric goodness-of-fit criterion and tests for independence, measures of association, regression techniques, multi-sample inferential techniques, Bayes and minimax estimation, admissibility, minimax property. (On demand)

 

STAT 7123. Advanced Statistics II. (3) Prerequisites: STAT 7122 or consent of the department. Hypothesis testing, Neyman-Pearson Lemma, UMP tests, UMP unbiased tests, monotone likelihood ratio families of distributions, UMP invariant tests. Confidence bounds and regions, uniformly most accurate bounds, regression models, least squares estimates, normal equations, Gauss-Markov theorem. Large sample behavior of methods of moments estimates, maximum likelihood estimates, likelihood ratio tests, Chi-square tests, approximate confidence regions for large samples. (On demand)

 

STAT 7124. Sampling Theory. (3) Prerequisite: STAT 5126 or consent of the department. Methods and theory of survey sampling: simple, systematic, stratified, cluster multistage and specialized sampling schemes and the problems of their implementation and analysis. (On demand)

 

STAT 7127. Linear Statistical Models. (3) Prerequisites: MATH 2164 and 3123 or consent of the department. A selection of topics from the following list: distribution and quadratic forms, regression, dummy variables, models not of full rank, the two-way crossed classification, time series. (Fall) (Alternate years)

 

STAT 7133. Multivariate Analysis. (3) Prerequisite: STAT 5126 and 5127 or consent of the department. Multivariate distributions. Inference for the multivariate normal model. Further topics from the following: principal components, factor analysis, multidimensional scaling, canonical correlation, discriminant analysis, cluster analysis, multivariate linear models, special topics. (Fall) (Alternate years)

STAT 8027. Topics in Statistics. (3) See STAT 7027 for Course Description.

 

STAT 8122. Advanced Statistics I. (3) See STAT 7122 for Course Description.

 

STAT 8123. Advanced Statistics II. (3) See STAT 7123 for Course Description.

 

STAT 8124. Sampling Theory. (3) See STAT 7124 for Course Description.

 

STAT 8127. Linear Statistical Models. (3) See STAT 7127 for Course Description.

 

STAT 8133. Multivariate Analysis. (3) See STAT 7133 for Course Description.