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
1) Twenty-seven hours of undergraduate
coursework in Mathematics beyond the freshman level, or evidence of equivalent
academic preparation.
2) Possession of a
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
MATH 5129 Applied Probability II. (3) Prerequisite: MATH 5128 or consent
of the department. Continuation of MATH 5128. (Spring)(Alternate years)
MATH 5143.
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
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
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
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.