Courses for MATH (MATH)
CSCE
340/840
Numerical Analysis I LINKCrosslisted as MATH 340/840| Credit Hours: | 3 |
| Max credits per degree: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Algorithm formulation for the practical solution of problems, interpolation, roots of equations, differentiation, and integration. Effects of finite precision.
CSCE
441/841
Approximation of Functions LINKCrosslisted as MATH 441/841| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Polynomial interpolation, uniform approximation, orthogonal polynomails, least-first-power approximation, polynomial and spline interpolation, approximation and interpolation by rational functions.
CSCE
447/847
Numerical Analysis II LINKCrosslisted as MATH 447/847| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Numberical matrix methods and numerical solutions of ordinary differntial equations.
CSCE
942
Numerical Analysis III LINKCrosslisted as MATH 942| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Advanced topics in numerical analysis.
MATH
221/821
Differential Equations LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
| ACE Outcomes: | 3 |
| Groups: | Advanced Mathematics Courses |
Not open to MA or MS students in mathematics or statistics.
First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications.
MATH
238/838
Mathematical Methods for Biology and Medicine LINK| Credit Hours: | 5 |
| Course Format: | Lecture 5 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Mathematical modeling, discrete and continuous probability, parameter estimation, discrete and continuous dynamical systems, and Markov chains. Application of mathematical models in the life sciences. Methods include regression analysis, cobweb diagrams, the phase line, nullcline analysis, eigenvalue analysis, linearization, and likelihood analysis. Applications include fisheries, stage-structured populations, pharmacokinetics, epidemiology, and medical testing.
MATH
314/814
Applied Linear Algebra (Matrix Theory) LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| ACE Outcomes: | 3 |
| Groups: | Advanced Mathematics Courses |
Not open to MA or MS students in mathematics or statistics
Fundamental concepts of linear algebra from the point of view of matrix manipulation with emphasis on concepts that are most important in applications. Includes solving systems of linear equations, vector spaces, inner products, determinants, eigenvalues, similarity of matrices, and Jordan Canonical Form.
MATH
322/822
Advanced Calculus LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Not open to MA or MS students in mathematics or statistics
Uniform convergence of sequences and series of functions, Green's theorem, Stoke's theorem, divergence theorem, line integrals, implicit and inverse function theorems, and general coordinate transformations.
MATH
324/824
Introduction to Partial Differential Equations LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Prereqs:
Not open to MA or MS students in mathematics or statistics.
Derivation of the heat, wave, and potential equations; separation of variables method of solution; solutions of boundary value problems by use of Fourier series, Fourier transforms, eigenfunction expansions with emphasis on the Bessel and Legendre functions; interpretations of solutions in various physical settings.
MATH
409/809
Math for High School Teachers II, Using Math to Understand Our World LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
Math 310, Math 314, Math 380/Stat 380
Not open to MA or MS students in Mathematics. This course is for students seeking a mathematics major under the Education Option and for students in CEHS who are seeking their secondary mathematics teaching certificate.
This course is designed around a series of projects in which students create mathematical models to examine the mathematics underlying several socially-relevant questions.
MATH
415/815
Theory of Linear Transformations LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
Math 314/814 and either Math 325 or Math 310.
Topics fundamental to the study of linear transformations on finite and infinite dimensional vector spaces over the real and complex number fields including: subspaces, direct sums, quotient spaces, dual spaces, matrix of a transformation, adjoint map, invariant subspaces, triangularization and diagonalization. Additional topics may include: Riesz Representation theorem, projections, normal operators, spectral theorem, polar decomposition, singular value decomposition, determinant as an n-linear functional, Cayley-Hamilton theorem, nilpotent operators, and Jordan canonical form.
MATH
423/823
Introduction to Complex Variable Theory LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Advanced introductory course for engineering, physical sciences, and mathematics majors. Complex numbers, functions of complex variables, analytic functions, complex integration, Cauchy's integral formulas, Taylor and Laurant series, calculus of residues and contour integration, conformal mappings, harmonic functions, and some applications.
MATH
427/827
Mathematical Methods in the Physical Sciences LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Prereqs:
Not open to mathematics majors. Not open to MA or MS students in mathematics.
Matrix operations, transformations, inverses, orthogonal matrices, rotations in space. Eigenvalues and eigenvectors, diagonalization, applications of diagonalization. Curvilinear coordinate systems, differential operations in curvilinear coordinate systems, Jacobians, changes of variables in multiple integration. Scalar, vector and tensor fields, tensor operations, applications or tensors. Complex function theory, integration by residues, conformal mappings.
MATH
428/828
Principles of Operations Research LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| ACE Outcomes: | 10 |
| Groups: | Advanced Mathematics Courses |
Introduction to techniques and applications of operations research. Includes linear programming, queueing theory, decision analysis, network analysis, and simulation.
MATH
432/832
Linear Optimization LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Mathematical theory of linear optimization, convex sets, simplex algorithm, duality, multiple objective linear programs, formulation of mathematical models.
MATH
433/833
Nonlinear Optimization LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Mathematical theory of constrained and unconstrained optimization, conjugate direction and quasi-Newton methods, convex functions, Lagrange multiplier theory, constraint qualifications.
MATH
439/839
Mathematical Models in Biology LINK| Credit Hours: | 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Prereqs:
MATH 107 or permission.
Discrete and continuous models in ecology, population models, predation and food webs, the spread of infectious diseases and life histories. Probability and random processes in nature, elementary models for molecular events, and pharamacokinetics.
MATH
445/845
Introduction to the Theory of Numbers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Arithmetic functions, congruences, reciprocity theorem, primitive roots, Diophantine equations, and continued fractions.
MATH
465/865
Introduction to Mathematical Logic LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
| Groups: | Advanced Mathematics Courses |
Semantical and syntactical developments of propositional logic, discussion of several propositional calculi, applications to Boolean algebra and related topics, semantics and syntax of first-order predicate logic including Godel's completeness theorem, the compactness theorem.
MATH
487/887
Probability Theory LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
Math 314 and Math 325.
Probability, conditional probability, Bayes' theorem, independence, discrete and continuous random variables, density and distribution functions, multivariate distributions, probability and moment generating functions, the central limit theorem, convergence of sequences of random variables, random walks, Poisson processes. and applications.
MATH
489/889
Stochastic Processes and Advanced Mathematical Finance LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
| ACE Outcomes: | 10 |
| Groups: | Advanced Mathematics Courses |
Properties of stochastic processes and solutions of stochastic differential equations as a means of understanding modern financial instruments. Derivation and modeling of financial instruments, advanced financial models, advanced stochastic processes, partial differential equations, and numerical methods from a probabilistic point of view.
MATH
496/896
Seminar in Mathematics LINK| Credit Hours: | 1-3 |
| Max credits per degree: | 6 |
| Course Delivery: | Classroom |
| Groups: | Seminars, Independent Study, Topics and Reading Courses |
Prereqs:
Permission.
MATH
800P
Number and Operation for K-3 Mathematics Specialists LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
Number and operations. Place value and its role in arithmetic operations. Development of fractions and number systems. Develop the habits of mind of a mathematical thinker and to develop a depth of understanding of number and operations sufficient to enable the teacher to be a disciplinary resource for other K-3 teachers.
MATH
800T
Mathematics as a Second Language LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
MATH 800T is intended for mid-level mathematics teachers.
Numbers and operations. Careful reasoning, problem solving, and communicating mathematics both orally and in writing. Connections with other areas of mathematics. Development of mathematical thinking habits.
MATH
801P
Geometry, Measurement, and Algebraic Thinking for K-3 Mathematics Specialists LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
Polygons, polyhedra, rigid motions, symmetry, congruence, similarity, measurement in one, two and three dimensions, functions, mathematical expressions, solving equations, sequences. Develop the habits of mind of a mathematical thinker and to develop a depth of understanding of geometry, measurement and algebraic thinking to enable the teacher to be a disciplinary resource for other K-3 teachers.
MATH
802P
Number, Geometry and Algebraic Thinking II for K-3 Math Specialists LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.
MATH *802P will not count toward the MA or MS degree in mathematics or statistics.
Number sense and operations in the context of rational numbers, geometry and algebra in grades 4-6 curriculum, and how the mathematical content in grades K-3 (e.g., Taylor-Cox, 2003) lays a foundation for abstract thinking beginning in grades 4 and beyond. Designed to develop a depth of understanding sufficient to enable the teacher to be a disciplinary resource to other K-3 teachers.
MATH
802T
Functions, Algebra, and Geometry for Middle Level Teachers LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
MATH *802T is intended for mid-level mathematics teachers.
Variables and functions. Use of functions in problem solving. Theory of measurement, especially length, area, and volume. Geometric modeling in algebra. Graphs, inverse functions, linear and quadratic functions, the fundamental theorem of arithmetic, modular arithmetic, congruence and similarity. Ways these concepts develop across the middle level curriculum.
MATH
803P
Algebraic Thinking in the Elementary Classroom LINK| Credit Hours: | 3 |
| Course Format: | Lecture |
| Course Delivery: | Classroom |
Prereqs:
A valid elementary or early childhood teaching certificate, or permission.
Not open to MA or MS students in mathematics or statistics.
Course explores the mathematics supporting algebraic thinking in elementary mathematics. Develops a deeper understanding of algebraic properties and greater flexibility in mathematical reasoning. Case studies, video segments, and student work samples will be examined. Complex mathematical problems will be worked with connections made between participants' thinking and that of their students.
MATH
804P
Problem Solving and Critical Thinking in the Elementary Classroom LINK| Credit Hours: | 3 |
| Course Format: | Lecture |
| Course Delivery: | Classroom |
Prereqs:
A valid elementary or early childhood teaching certificate, or permission.
Not open to MA or MS students in mathematics or statistics.
Course uses problem-solving experiences to develop teachers' critical-thinking skills in order to build a strong foundation for teaching and communicating mathematical concepts. Provides a guided opportunity for the implementation of problem-solving instruction is aligned with the Mathematics Standards in both the primary (K-2) and intermediate (3-5) elementary classroom.
MATH
804T
Experimentation, Conjecture and Reasoning LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
MATH *804T is intended for middle-level mathematics teachers.
Problem solving, reasoning and proof, and communicating mathematics. Development of problem solving skills through the extensive resources of the American Mathematics Competitions. Concepts of logical reasoning in the context of geometry, number patterns, probability and statistics
MATH
805T
Discrete Mathematics for Middle Level Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences
MATH *805T is intended for mid-level mathematics teachers.
Concepts of discrete mathematics, as opposed to continuous mathematics, which extend in directions beyond, but related to, topics covered in middle-level curricula. Problems which build upon middle-level mathematics experiences. Logic, mathematical reasoning, induction, recursion, combinatorics, matrices, and graph theory.
MATH
806T
Number Theory and Cryptology for Middle Level Teachers LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
MATH *806T is intended for mid-level mathematics teachers.
Basic number theory results and the RSA cryptography algorithm. Primes, properties of congruences, divisibility tests, linear Diophantine equations, linear congruences, the Chinese Remainder Theorem, Wilson’s Theorem, Fermat’s Little Theorem, Euler’s Theorem, and Euler’s phi-function. Mathematical reasoning and integers’ connections to the middle school curriculum.
MATH
807
Mathematics for High School Teachers I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Analysis of the connections between college mathematics and high school algebra and precalculus.
MATH
807T
Using Mathematics to Understand Our World LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences
MATH *807T is intended for middle-level mathematics teachers.
The mathematics underlying several socially-relevant questions from a variety of academic disciplines. Construct mathematical models of the problems and study them using concepts developed from algebra, linear and exponential functions, statistics and probability. Original documentation, such as government data, reports and research papers, in order to provide a sense of the role mathematics plays in society, both past and present.
MATH
808
Mathematics for High School Teachers II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Analysis of the connections between college mathematics and high school algebra and geometry.
MATH
808T
Concepts of Calculus for Middle-Level Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences
MATH *808T is intended for middle-level mathematics teachers.
The processes of differentiation and integration, their applications and the relationship between the two processes. Rates of change, slopes of tangent lines, limits, derivatives, extrema, derivatives of products and quotients, anti-derivatives, areas, integrals, and the Fundamental Theorem of Calculus. Connections to concepts in the middle level curriculum.
MATH
810T
Algebra for Algebra Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences
The integers. The Euclidean algorithm, the Fundamental Theorem of Arithmetics, and the integers mod n. Polynomials with coefficients in a field. The division algorithm, the Euclidean algorithm, the unique factorization theorem, and its applications. Polynomials whose coefficients are rational, real or complex. Polynomial interpolation. The habits of mind of a mathematical thinker. The conceptual underpinnings of school algebra.
MATH
811T
Functions for High School Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
A valid secondary mathematics teaching certificate or by permission.
Course examines mathematics underlying pre-calculus material through problem solving. Connections to other topics in mathematics, including algebra, geometry and advanced mathematics are highlighted.
MATH
812T
Geometry for Geometry Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
A valid secondary mathematics teaching certificate.
Course examines mathematics underlying high school geometry through problem solving. Topics include Spherical, Euclidean and Hyperbolic geometry, introduction to Neutral geometry, Platonic and Archimedean solids and projective geometry.
MATH
816T
Math in the City for Teachers LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
An undergraduate course in at least one of statistics, differential equations or matrix algebra; a valid secondary mathematics teaching certificate.
A modeling course run in collaboration with area businesses or organizations in which real world problems are studied. Course emphasizes how mathematics is used outside academia.
MATH
817
Introduction to Modern Algebra I LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Topics from elementary group theory and ring theory, including fundamental isomorphism theorems, ideals, quotient rings, domains. Euclidean or principal ideal rings, unique factorization, modules and vector spaces including direct sum decompositions, bases, and dual spaces.
MATH
818
Introduction to Modern Algebra II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Topics from field theory including Galois theory and finite fields and from linear transformations including characteristic roots, matrices, canonical forms, trace and transpose, and determinants.
MATH
820
Elementary Analysis for the Sciences LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Course Delivery: | Classroom |
Prereqs:
Math 208 and evidence of adequate preparation.
A term paper and/or project is required for graduate credit. Not open to graduate students in Mathematics. Students in the sciences and Statistics cannot count MATH 820 toward a minor in Mathematics.
A mathematical introduction to elementary analysis (the calculus). Specifically, it is a demanding course that introduces concepts in abstraction: the axiomatic method, proofs, and mathematical thinking and writing in the context of elementary real analysis, or the theory underlying calculus. Specific topics include: logic, sets, functions; the real number system (field and order axioms, completeness axiom); mathematical induction; limits of sequences and functions, convergence, and continuity; the derivative and Riemann integral.
MATH
825
Mathematical Analysis I LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Real number system, topology of Euclidean space and metric spaces, continuous functions, derivatives and the mean value theorem, the Riemann and Riemann-Stieltjes integral, convergence, the uniformity concept, implicit functions, line and surface integrals.
MATH
826
Mathematical Analysis II LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Real number system, topology of Euclidean space and metric spaces, continuous functions, derivatives and the mean value theorem, the Riemann and Riemann-Stieltjes integral, convergence, the uniformity concept, implicit functions, line and surface integrals.
MATH
830
Ordinary Differential Equations I LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
The Picard existence theorem, linear equations and linear systems, Sturm separation theorems, boundary value problems, phase plane analysis, stability theory, limit cycles and periodic solutions.
MATH
831
Ordinary Differential Equations II LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
The Picard existence theorem, linear equations and linear systems, Sturm separation theorems, boundary value problems, phase plane analysis, stability theory, limit cycles and periodic solutions.
MATH
842
Methods of Applied Mathematics I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Interdependence between mathematics and the physical and applied sciences. Includes the calculus of variations, scaling and dimensional analysis, regular and singular perturbation methods.
MATH
843
Methods of Applied Mathematics II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 842 or permission
Application of partial differential equation models to problems in the physical and applied sciences. Includes derivation of partial differential equations, the theory of continuous media, linear and nonlinear wave propagation, diffusion, transform methods, and potential theory.
MATH
850
Discrete Mathematics I LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Enumeration of standard combinatorial objects (subsets, partitions, permutations). Structure and existence theorems for graphs and sub-graphs. Selected classes of error-correcting codes. Extremal combinatorics of graphs, codes, finite sets and posets.
MATH
852
Discrete Mathematics II LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH *850
Enumeration of standard combinatorial objects (subsets, partitions, permutations). Structure and existence theorems for graphs and sub-graphs. Selected classes of error-correcting codes. Extremal combinatorics of graphs, codes, finite sets and posets.
MATH
856
Differential Topology LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Introduction to a selection of topics in differentiable manifolds, smooth maps, vector fields and vector bundles, embeddings and immersions, differential forms, integration on manifolds, and applications.
MATH
858
Topics in Geometry LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Selected topics in some branch of geometry.
MATH
871
Topology I LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Topological spaces, continuous functions, product and quotient spaces, compactness and connectedness, homotopy, fundamental groups.
MATH
872
Topology II LINK| Credit Hours: | 3 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Fundamental groups and the van Kampen theorem, covering spaces and the Galois correspondence, applications to groups, homology and the Mayer-Vietoris theorem.
MATH
874M
Mathematics Integration LINK| Credit Hours: | 2-3 |
| Campus: | |
| Course Delivery: | Classroom |
MATH *874M may be counted towards the MAT and MScT degrees in mathematics and statistics, not the MA, MS, or PhD.
MATH
897
Reading Course LINK| Credit Hours: | 1-4 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
899
Masters Thesis LINK| Credit Hours: | 6-10 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to masters degree program and permission of major adviser
MATH
901
Algebra I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 818 or permission
In-depth treatment of groups, rings, modules, algebraic field extensions, Galois theory, multilinear products, categories.
MATH
902
Algebra II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 818 or permission
In-depth treatment of groups, rings, modules, algebraic field extensions, Galois theory, multilinear products, categories.
MATH
905
Commutative Algebra LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 818 or permission
Selected topics from classical ideal theory, Dedekind rings, completions, local rings, valvation theory.
MATH
909
Theory of Semigroups LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 818 or permission
Selected topics from semigroups of transformations, ideal structure and homomorphisms, free semigroups, inverse semigroups, matrix representation, decompositions and extensions.
MATH
911
Theory of Groups LINK| Credit Hours: | 3-6 |
| Max credits per degree: | 18 |
| Course Format: | Lecture 3 |
| Campus: | |
| Course Delivery: | Classroom |
Basic topics of infinite and finite group theory from among geometric, combinatorial, and algorithmic group theory, homology of groups, solvable and nilpotent groups and representation theory.
MATH
913
Introduction to the Theory of Rings LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Elementary ring theory and examples of rings, the Jacobson radical and the structure of semi-simple rings, rings with minimum condition, Wedderburn’s theorem, structure of modules.
MATH
915
Homological Algebra LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 902 or permission
Basic topics in homological algebra, including homology of complexes, extensions, tensor and torsion products and homological dimension, with application to rings and algebras.
MATH
918
Topics in Algebra LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
921
Real Analysis I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.
MATH
922
Real Analysis II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.
MATH
923
Topics in Analysis LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
924
Theory of Analytic Functions I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 826 or permission
Complex number field, elementary functions, analytic functions, conformal mapping, integration and calculus of residues, entire and meromorphic functions, higher transcendental functions, Riemann surfaces.
MATH
925
Theory of Analytic Functions II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 826 or permission
Complex number field, elementary functions, analytic functions, conformal mapping, integration and calculus of residues, entire and meromorphic functions, higher transcendental functions, Riemann surfaces.
MATH
927
Asymptotic Methods in Applied Mathematics LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Methods for approximating the solutions of differential equations, including local analysis near singular points, singular perturbation methods, boundary layer theory, WKB Theory, and multiple-scale methods. Asymptotic expansion of Laplace and Fourier integrals. Illustration of the use of asymptotics from journals in mathematics, science, and engineering.
MATH
928
Functional Analysis I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Banach and Hilbert Spaces, linear operators and functionals, completely continuous operators, spectral theory, integral equations.
MATH
929
Functional Analysis II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Banach and Hilbert Spaces, linear operators and functionals, completely continuous operators, spectral theory, integral equations.
MATH
932
Advanced Ordinary Differential Equations I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 826 or permission
Cauchy-Peano existence theorems, continuity and differentiability of solutions with respect to initial conditions, differential inequalities, uniqueness theorem, oscillation theory, Poincare-Bendixson theory, stability theory, almost periodic solutions.
MATH
933
Advanced Ordinary Differential Equations II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 826 or permission
Cauchy-Peano existence theorems, continuity and differentiability of solutions with respect to initial conditions, differential inequalities, uniqueness theorem, oscillation theory, Poincare-Bendixson theory, stability theory, almost periodic solutions.
MATH
934
Topics in Differential Equations LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
935
Advanced Methods in Applied Mathematics I LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Banach and Hilbert spaces, operator theory with application to differential and integral equations; spectral theory for compact, self-adjoint operators.
MATH
936
Advanced Methods in Applied Mathematics II LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 935 or permission
Distributions, Green’s functions and boundary value problems; integral transforms and spectral representations.
MATH
937
Nonlinear Partial Differential Equations LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Nonlinear wave propagation and shock structure with applications, dispersive waves, hyperbolic systems, group velocity and the method of stationary phase. WKB approximation and perturbation methods.
MATH
938
Mathematical Modeling LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Advanced course in mathematical modeling for students who desire experience in formulating and analyzing open-ended, real-world problems in the natural and applied sciences. Participation in a few group projects that require conceptualization and analytical, numerical, and graphical analysis with formal oral and written presentation of the results.
MATH
939
Topics in Applied Mathematics LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
941
Partial Differential Equations LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Theory of hyperbolic, elliptic, and parabolic equations. Classification, existence and uniqueness result, solution representations.
MATH
953
Algebraic Geometry LINK| Credit Hours: | 3 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
MATH 901-902
Affine geometry, coordinate rings, the Zariski topology, function fields and birational geometry, the Nullstellensatz, Krull dimension and transcendence degree, smoothness, projective geometry, divisors, curves.
MATH
958
Topics in Discrete Mathematics LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
990
Topics in Topology LINK| Credit Hours: | 3 |
| Max credits per degree: | 18 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
995
Research Seminar LINK| Credit Hours: | 1-3 |
| Max credits per degree: | 6 |
| Course Format: | Lecture |
| Campus: | |
| Course Delivery: | Classroom |
MATH
996
Seminar LINK| Credit Hours: | 1-3 |
| Max credits per degree: | 6 |
| Campus: | |
| Course Delivery: | Classroom |
Advanced topics in one or more branches of mathematics.
MATH
997
Reading course LINK| Credit Hours: | 1-24 |
| Campus: | |
| Course Delivery: | Classroom |
MATH
999
Doctoral Dissertation LINK| Credit Hours: | 1-24 |
| Campus: | |
| Course Delivery: | Classroom |
Prereqs:
Admission to doctoral degree program and permission of supervisory committee chair