Mathematics (MATH)

MATH800P
Number and Operation for K-3 Mathematics Specialists

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH800T
Mathematics as a Second Language

Prerequisites: 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.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH801P
Geometry, Measurement, and Algebraic Thinking for K-3 Mathematics Specialists

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH802P
Number, Geometry and Algebraic Thinking II for K-3 Math Specialists

Prerequisites: 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.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH802T
Functions, Algebra, and Geometry for Middle Level Teachers

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH803P
Algebraic Thinking in the Elementary Classroom

Prerequisites: A valid elementary or early childhood teaching certificate.

Not open to MA or MS students in mathematics or statistics.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH803T
Computational Thinking for Teachers

Prerequisites: Elementary or secondary teachers certification, or by permission.

As an 800-level course with a "T" designation, this course is intended for middle-level teachers pursuing the MAT degree from the Mathematics Department, the MA degree in Mathematics Education (CEHS) or simply taking graduate courses to further their education.

Description: This project-based course develops an understanding of computational thinking through engagement in problem-solving in a variety of real-world settings (some of them rather surprising) in our modern society and developing confidence and resources for implementing computational thinking activities in classrooms.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH804P
Problem Solving and Critical Thinking in the Elementary Classroom

Prerequisites: A valid elementary or early childhood teaching certificate.

Not open to MA or MS students in mathematics or statistics.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH804T
Experimentation, Conjecture and Reasoning

Prerequisites: 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.

Description: 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

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH805T
Discrete Mathematics for Middle Level Teachers

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

MATH 805T is intended for mid-level mathematics teachers.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH806T
Number Theory and Cryptology for Middle Level Teachers

Prerequisites: 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.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH807
Mathematics for High School Teaching ICrosslisted with MATH 407

Prerequisites: MATH 208/208H and MATH 309 or MATH 310.

Open only MATH majors with a declared Education option.

Description: Analysis of the connections between college mathematics and high school algebra and precalculus.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:SPRING

Credit Hours:3

ACE:

MATH807T
Using Mathematics to Understand Our World

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

MATH 807T is intended for middle-level mathematics teachers.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH808
Mathematics for High School Teaching IICrosslisted with MATH 408

Prerequisites: MATH 412 and MATH 309 or MATH 310.

Open only MATH majors with a declared Education option.

Description: Analysis of the connections between college mathematics and high school algebra and geometry.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH808T
Concepts of Calculus for Middle Level Teachers

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

MATH 808T is intended for middle-level mathematics teachers.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH810T
Algebra for Algebra Teachers

Prerequisites: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH811T
Functions for High School Teachers

Prerequisites: A valid secondary mathematics teaching certificate or by permission

Description: Course examines mathematics underlying pre-calculus material through problem solving. Connections to other topics in mathematics, including algebra, geometry and advanced mathematics are highlighted.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH812T
Geometry for Geometry Teachers

Prerequisites: A valid secondary mathematics teaching certificate

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH814
Linear Algebra

Prerequisites: A grade of P, C, or better in MATH 107 or MATH 107H

Not open to MA or MS students in mathematics or statistics.

Description: Fundamental concepts of linear algebra, including properties of matrix arithmetic, systems of linearequations, vector spaces, inner products, determinants, eigenvalues and eigenvectors, and diagonalization.

This course is a prerequisite for: MATH 415, MATH 815; MATH 842

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH814T
Linear Algebra for Teachers

Prerequisites: A valid secondary mathematics teaching certificate or by permission.

Description: Emphasis on connections between linear equations, linear transformations and the geometry of lines and planes. Applications to production planning, encryption methods, and analyzing data. Topics include methods of solving linear systems with an emphasis on solution behavior, along with behaviors exhibited by explicit linear transformations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Graded

Credit Hours:3

ACE:

MATH815
Theory of Linear TransformationsCrosslisted with MATH 415

Prerequisites: MATH 314/814; and MATH 309, MATH 310, or MATH 325.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH816T
Math in the City for Teachers

Prerequisites: An undergraduate course in at least one of statistics, differential equations or matrix algebra; a valid secondary mathematics teaching certificate

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH817
Introduction to Modern Algebra I

Prerequisites: MATH 417

Description: 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.

This course is a prerequisite for: MATH 818

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH818
Introduction to Modern Algebra II

Prerequisites: MATH 817

Description: 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.

This course is a prerequisite for: MATH 901; MATH 902; MATH 905; MATH 915; MATH 928; MATH 929

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH823
Complex AnalysisCrosslisted with MATH 423

Prerequisites: A grade of P, C, or better in MATH 208 or MATH 208H

Description: Complex numbers, functions of complex variables, analytic functions, complex integration, Cauchy's integral formulas, Taylor and Laurent series, calculus of residues and contour integration, conformal mappings, harmonic functions. Applications of these concepts in engineering, physical sciences, and mathematics.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH824
Introduction to Partial Differential EquationsCrosslisted with MATH 424

Prerequisites: A grade of P, C, or better in MATH 208/208H and MATH 221/221H.

Not open to MA or MS students in mathematics or statistics.

Description: 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.

This course is a prerequisite for: MECH 812

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH825
Mathematical Analysis I

Prerequisites: MATH 325

Description: 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.

This course is a prerequisite for: MATH 826

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH826
Mathematical Analysis II

Prerequisites: MATH 825

Description: 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.

This course is a prerequisite for: MATH 921; MATH 924; MATH 925; MATH 926; MATH 941

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH828
Principles of Operations ResearchCrosslisted with MATH 428

Prerequisites: MATH 314 or MATH 314H; and RAIK 270H, STAT 380, or MECH 321.

Description: Introduction to techniques and applications of operations research. Includes linear programming, queueing theory, decision analysis, network analysis, and simulation.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH830
Differential Equations I

Prerequisites: MATH 325

Description: Phase diagrams, bifurcation theory, linear systems, the matrix exponential function, Floquet theory, stability theory, existence (Poincare-Bendixson Theorem) and non-existence of periodic solutions for non-linear ordinary differential equations, self-adjoint equations, and Sturm-Liouville theory.

This course is a prerequisite for: MATH 831

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH831
Differential Equations II

Prerequisites: MATH 830

Description: Vector calculus, transport equations, Laplace's equation, the heat equation, the wave equation, maximum principles, mean-value formulae, finite speed of propagation, energy methods, solution representations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH833
Nonlinear OptimizationCrosslisted with MATH 433

Prerequisites: MATH 208/208H; MATH 314/314H; and MATH 309, MATH 310, or MATH 325.

Description: Mathematical theory of unconstrained and constrained optimization for nonlinear multivariate functions, particularly iterative methods, such as quasi-Newton methods, least squares optimization, and convex programming. Computer implementation of these methods.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:SPRING

Credit Hours:3

ACE:

MATH839
Mathematical BiologyCrosslisted with MATH 439

Prerequisites: MATH 221/221H & MATH 314/314H.

Description: Discrete and continuous models in ecology: population models, predation, food webs, the spread of infectious diseases, and life histories. Elementary biochemical reaction kinetics; random processes in nature. Use of software for computation and graphics.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH840
Numerical Analysis ICrosslisted with CSCE 440, CSCE 840, MATH 440

Credit toward the degree may be earned in only one of the following: CSCE/MATH 440/840 and MECH 480/880.

Description: Principles of numerical computing and error analysis covering numerical error, root finding, systems of equations, interpolation, numerical differentiation and integration, and differential equations. Modeling real-world engineering problems on digital computers. Effects of floating point arithmetic.

This course is a prerequisite for: CSCE 942

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Course and Laboratory Fee:$20

Credit Hours:3

ACE:

MATH842
Methods of Applied Mathematics I

Prerequisites: MATH 821 and 814, or their equivalents

Description: Interdependence between mathematics and the physical and applied sciences. Includes the calculus of variations, scaling and dimensional analysis, regular and singular perturbation methods.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH845
Number TheoryCrosslisted with MATH 445

Prerequisites: MATH 310.

Description: Fundamentals of number theory, including congruences, primality tests, factoring methods. Diophantine equations, quadratic reciprocity, continued fractions, and elliptic curves.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH847
Numerical Methods for Applied MathCrosslisted with MATH 447

Prerequisites: MATH 208/208H, MATH 221/221H & MATH 314/314H

Description: Numerical methods for approximate solutions of applied mathematics problems. Topics typically considered include numerical solution of linear systems of equations, approximation of eigenvalues and eigenvectors, numerical solution of nonlinear systems of equations, and numerical solution of initial value problems for ordinary differential equations. Given time, mathematical applications in optimization, machine learning, or data science may be considered.

This course is a prerequisite for: CSCE 942

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH850
Discrete Mathematics I

Prerequisites: MATH 310 or 325

Description: 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.

This course is a prerequisite for: MATH 852

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH852
Discrete Math II

Prerequisites: MATH 850

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH856
Differential Topology

Prerequisites: MATH 471/871

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH871
Topology I

Prerequisites: MATH 325 or MATH 417

Description: Topological spaces, continuous functions, product and quotient spaces, compactness and connectedness, homotopy, fundamental groups.

This course is a prerequisite for: MATH 856; MATH 872

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH872
Topology II

Prerequisites: MATH 871 and MATH 417

Description: Fundamental groups and the van Kampen theorem, covering spaces and the Galois correspondence, applications to groups, homology and the Mayer-Vietoris theorem.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH887
Probability TheoryCrosslisted with MATH 487

Prerequisites: MATH 314 or MATH 314H; and MATH 309, MATH 310, or MATH 325.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH889
Stochastic ProcessesCrosslisted with MATH 489

Prerequisites: MATH 314 or MATH 314H; and STAT 380 or RAIK 270H.

Description: Markov chains, continuous-time Markov processes, the Poisson process, Brownian motion, introduction to stochastic calculus.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH893
Seminar in MathematicsCrosslisted with MATH 493

Prerequisites: Permission.

Description: Topics in one or more branches of mathematics.

Course details
Credit Hours:1-4
Max credits per semester:4
Max credits per degree:8
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-4

ACE:

MATH894
Independent Study in Mathematics

Prerequisites: Permission.

Description: Directed reading or research with a faculty member.

Course details
Credit Hours:1-4
Max credits per semester:4
Max credits per degree:4
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-4

ACE:

MATH899
Masters Thesis

Prerequisites: Admission to masters degree program and permission of major adviser

Course details
Credit Hours:1-10
Max credits per semester:10
Max credits per degree:99
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-10

ACE:

MATH901
Algebra I

Prerequisites: MATH 818 or permission

Description: In-depth treatment of groups, rings, modules, algebraic field extensions, Galois theory, multilinear products, categories.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH902
Algebra II

Prerequisites: MATH 818 or permission

Description: In-depth treatment of groups, rings, modules, algebraic field extensions, Galois theory, multilinear products, categories.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH905
Commutative Algebra I

Prerequisites: MATH 818

Description: A first course in commutative algebra covering core topics in the field including noetherian rings, graded rings, localization, Nakayama's lemma, integral extensions, primary decomposition, Hilbert functions, and dimension theory.

This course is a prerequisite for: MATH 906; MATH 953

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH906
Commutative Algebra II

Prerequisites: MATH 905

Description: Continuation of Math 905, covering topics such as regular sequences, system of parameters, the Koszul complex, depth, Cohen-Macaulay rings, regular rings, and Gorenstein rings.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:SPRING

Credit Hours:3

ACE:

MATH911
Theory of Groups

Description: 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.

Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH915
Homological Algebra

Prerequisites: MATH 818

Description: Category theory, complexes and homology, Hom and tensor products, projective, injective and flat modules, resolutions, derived functors, and applications.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH918
Topics in Algebra
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH921
Measure and Integration

Prerequisites: MATH 826 or permission

Description: Rigorous treatment of integration and measure theory. General measures and measurable functions. Lebesgue measure and Lebesgue integral. Approximation of functions. Lebesgue's Monotone and Dominated Convergence Theorems. Signed measures and total variation of measures. Radon-Nikodym Theorem. Lebesgue-Stieltjes measures and integrals. Product measures and Fubini's theorem.

This course is a prerequisite for: MATH 928; MATH 929

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH923
Topics in Analysis
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH924
Theory of Analytic Functions I

Prerequisites: MATH 826 or permission

Description: Complex number field, elementary functions, analytic functions, conformal mapping, integration and calculus of residues, entire and meromorphic functions, higher transcendental functions, Riemann surfaces.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH925
Theory of Analytic Functions II

Prerequisites: MATH 826 or permission

Description: Complex number field, elementary functions, analytic functions, conformal mapping, integration and calculus of residues, entire and meromorphic functions, higher transcendental functions, Riemann surfaces.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH926
Spectral Theory

Prerequisites: MATH 826

Description: Geometry of Hilbert spaces, compact operators and applications, self-adjoint and normal bounded operators, unbounded operators, spectrum of an operator and its properties, continuous and Borel functional calculus, applications as time permits

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH928
Functional Analysis I

Prerequisites: MATH 818 and 921, or permission

Description: Banach and Hilbert Spaces, linear operators and functionals, completely continuous operators, spectral theory, integral equations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH929
Functional Analysis II

Prerequisites: MATH 818 and 921, or permission

Description: Banach and Hilbert Spaces, linear operators and functionals, completely continuous operators, spectral theory, integral equations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:3

ACE:

MATH934
Topics in Differential Equations
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH939
Topics in Applied Mathematics
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH941
Partial Differential Equations

Prerequisites: MATH 826

Description: Theory of distributions, Fourier transform, fundamental solutions, Sobolev space theory, weak formulation and solution of elliptic boundary value problems, elliptic regularity, Galerkin methods and other techniques of nonlinear analysis.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:FALL

Credit Hours:3

ACE:

MATH953
Algebraic Geometry

Prerequisites: MATH 905

Description: An introduction to algebraic geometry, including affine and projective varieties, coordinate rings, the Zariski topology, the Nullstellensatz, and dimensions of varieties.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option
Offered:SPRING

Credit Hours:3

ACE:

MATH958
Topics in Discrete Mathematics
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH990
Topics in Topology
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Grading Option:Grade Pass/No Pass Option

Credit Hours:3-6

ACE:

MATH993
Seminar in Mathematics

Description: Advanced topics in one or more branches of mathematics.

Course details
Credit Hours:1-3
Max credits per semester:3
Max credits per degree:3
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-3

ACE:

MATH994
Independent Study in Mathematics

Prerequisites: Permission.

Description: Independent reading or research directed by a faculty member.

Course details
Credit Hours:1-12
Max credits per semester:12
Max credits per degree:24
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-12

ACE:

MATH995
Research Seminar
Course details
Credit Hours:1-3
Max credits per semester:3
Max credits per degree:6
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-3

ACE:

MATH999
Doctoral Dissertation

Prerequisites: Admission to doctoral degree program and permission of supervisory committee chair

Course details
Credit Hours:1-24
Max credits per semester:24
Max credits per degree:99
Grading Option:Grade Pass/No Pass Option

Credit Hours:1-24

ACE: