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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH803P
Algebraic Thinking in the Elementary Classroom

Prerequisites: A valid elementary or early childhood teaching certificate, or permission

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
Course Format:LEC

Credit Hours:3

ACE:

MATH804P
Problem Solving and Critical Thinking in the Elementary Classroom

Prerequisites: A valid elementary or early childhood teaching certificate, or permission

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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH807
Mathematics for High School Teachers I

Prerequisites: MATH 208 and 310.

Not open to graduate students in mathematics.

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH808
Mathematics for High School Teachers II

Prerequisites: MATH 310 and 350.

Not open to graduate students in mathematics.

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

Course details
Credit Hours:0
Max credits per semester:
Max credits per degree:
Course Format:LEC

Credit Hours:0

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
Course Format:LEC

Credit Hours:3

ACE:

MATH809
Math for High School Teachers II, Using Math to Understand Our WorldCrosslisted with MATH 409

Prerequisites: 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.

Description: Designed around a series of projects in which students create mathematical models to examine the mathematics underlying several socially-relevant questions.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH814
Linear AlgebraCrosslisted with MATH 314

Prerequisites: MATH 208.

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 405; MATH 442; MATH 471; MATH 809, MATH 409; MECH 350

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

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
Course Format:LEC

Credit Hours:3

ACE:

MATH815
Theory of Linear TransformationsCrosslisted with MATH 415

Prerequisites: Math 314/814 and either Math 325 or Math 310.

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
Course Format:LEC

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
Course Format:LEC

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH820
Elementary Analysis for the Sciences

Prerequisites: Math 208 and evidence of adequate preparation

Students in the sciences and Statistics cannot count MATH 820 toward a minor in Mathematics. A term paper and/or project is required for graduate credit. Not open to graduate students in Mathematics.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH821
Differential EquationsCrosslisted with MATH 221

Prerequisites: A grade of "P" or "C" or better in MATH 208/208H.

Description: First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH822
Advanced CalculusCrosslisted with MATH 322

Description: 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.

This course is a prerequisite for: METR 965

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH823
Complex AnalysisCrosslisted with MATH 423

Prerequisites: Math 221 or Math 325.

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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH824
Introduction to Partial Differential EquationsCrosslisted with MATH 424

Prerequisites: MATH 221.

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH827
Mathematical Methods in the Physical SciencesCrosslisted with MATH 427

Prerequisites: MATH 221.

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH828
Principles of Operations ResearchCrosslisted with MATH 428

Prerequisites: MATH 314 and either 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
Course Format:LEC
Groups:Advanced Mathematics Courses

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH832
Linear OptimizationCrosslisted with MATH 432

Prerequisites: MATH 314/814 and MATH 310 or MATH 325.

Description: Mathematical theory of linear optimization, convex sets, simplex algorithm, duality, multiple objective linear programs, formulation of mathematical models.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH833
Nonlinear OptimizationCrosslisted with MATH 433

Prerequisites: MATH 314/814 and 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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH838
Mathematical Methods for Biology and MedicineCrosslisted with MATH 238

Prerequisites: Grade of P, C, or better in MATH 106/106B or MATH 108H.

MATH 838 will not count toward a MA or MS degree in MATH or STAT. Some computation and visualizations in MATH 238/838 will be done with Matlab.

Description: 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.

Course details
Credit Hours:5
Max credits per semester:5
Max credits per degree:5
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:5

ACE:

MATH839
Mathematical Models in BiologyCrosslisted with MATH 439

Prerequisites: MATH 107 or permission.

MATH 439/839 has a small laboratory component.

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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

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

Prerequisites: CSCE 155A, CSCE 155E, CSCE 155H, CSCE 155N, or CSCE 155T; Math 107.

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH841
Approximation of FunctionsCrosslisted with CSCE 441, CSCE 841, MATH 441

Prerequisites: A programming language, MATH 221 and 314.

Description: Polynomial interpolation, uniform approximation, orthogonal polynomials, least-first-power approximation, polynomial and spline interpolation, approximation and interpolation by rational functions.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

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
Course Format:LEC

Credit Hours:3

ACE:

MATH843
Methods of Applied Mathematics II

Prerequisites: MATH 842 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH845
Number TheoryCrosslisted with MATH 445

Prerequisites: MATH 310 or 310H.

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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH847
Numerical Linear AlgebraCrosslisted with CSCE 447, CSCE 847, MATH 447

Prerequisites: MATH 314

Description: Mathematics and algorithms for numerically stable matrix and linear algebra computations, including solution of linear systems, computation of eigenvalues and eigenvectors, singular value decomposition, and QR decomposition.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH865
Introduction to Mathematical LogicCrosslisted with MATH 465

Description: Semantical and syntactical developments of propositional logic, discussion of several propositional calculi, application of Boolean algebra and related topics, semantics and syntax of first order predicate logic including Godel's completeness theorem, the compactness theorem.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC
Groups:Advanced Mathematics Courses

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH874M
Topics in Chemical Pedagogy - Mathematics IntegrationCrosslisted with CHEM 874M, TEAC 874M

Description: Topical chemistry content for high school teachers organized according to the National Science Education Standards. A maximum combined total of 12 hours from TEAC *869 and/or *874 may be counted toward a masters degree. Credit in this course will not count towards a graduate degree in chemistry. May be counted towards the MAT and MScT degrees in mathematics and statistics, not the MA, MS, or PhD. Courses are Web-based.

Course details
Credit Hours:2-3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:2-3

ACE:

MATH887
Probability TheoryCrosslisted with MATH 487

Prerequisites: Math 314 and 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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH889
Stochastic ProcessesCrosslisted with MATH 489

Prerequisites: MATH 314 and STAT/MATH 380 (or STAT 880).

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
Course Format:LEC
Groups:Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH896
Seminar in MathematicsCrosslisted with MATH 496

Prerequisites: Permission.

Course details
Credit Hours:1-3
Max credits per semester:3
Max credits per degree:6
Course Format:LEC
Groups:Seminars,Ind Study, Topics

Credit Hours:1-3

ACE:

MATH897
Reading Course
Course details
Credit Hours:1-4
Max credits per semester:4
Max credits per degree:4
Course Format:IND

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
Course Format:IND

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH905
Commutative Algebra

Prerequisites: MATH 818 or permission

Description: Selected topics from classical ideal theory, Dedekind rings, completions, local rings, valvation theory.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH909
Theory of Semigroups

Prerequisites: MATH 818 or permission

Description: Selected topics from semigroups of transformations, ideal structure and homomorphisms, free semigroups, inverse semigroups, matrix representation, decompositions and extensions.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

Credit Hours:3-6

ACE:

MATH913
Introduction to the Theory of Rings

Prerequisites: MATH 818

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH915
Homological Algebra

Prerequisites: MATH 902 or permission

Description: Basic topics in homological algebra, including homology of complexes, extensions, tensor and torsion products and homological dimension, with application to rings and algebras.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH918
Topics in Algebra
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Course Format:LEC

Credit Hours:3-6

ACE:

MATH921
Real Analysis I

Prerequisites: MATH 818, 826, and 871 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH922
Real Analysis II

Prerequisites: MATH 818, 826, and 871 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH923
Topics in Analysis
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH927
Asymptotic Methods in Applied Mathematics

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3

ACE:

MATH932
Advanced Ordinary Differential Equations I

Prerequisites: MATH 826 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH933
Advanced Ordinary Differential Equations II

Prerequisites: MATH 826 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

Credit Hours:3-6

ACE:

MATH935
Advanced Methods in Applied Mathematics I

Prerequisites: MATH 821 and 826

Description: Banach and Hilbert spaces, operator theory with application to differential and integral equations; spectral theory for compact, self-adjoint operators.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH936
Advanced Methods in Applied Mathematics II

Prerequisites: MATH 935 or permission

Description: Distributions, Green's functions and boundary value problems; integral transforms and spectral representations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH937
Nonlinear Partial Differential Equations

Prerequisites: MATH 843 or 941 or permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH938
Mathematical Modeling

Prerequisites: MATH 842, 843 and permission

Description: 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.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH939
Topics in Applied Mathematics
Course details
Credit Hours:3-6
Max credits per semester:6
Max credits per degree:18
Course Format:LEC

Credit Hours:3-6

ACE:

MATH941
Partial Differential Equations

Prerequisites: MATH 826

Description: Theory of hyperbolic, elliptic, and parabolic equations. Classification, existence and uniqueness result, solution representations.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH942
Numerical Analysis IIICrosslisted with CSCE 942

Prerequisites: CSCE/MATH 840 or 841 or 847 or permission

Description: Advanced topics in numerical analysis.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

Credit Hours:3

ACE:

MATH953
Algebraic Geometry

Prerequisites: MATH 901-902

Description: Affine geometry, coordinate rings, the Zariski topology, function fields and birational geometry, the Nullstellensatz, Krull dimension and transcendence degree, smoothness, projective geometry, divisors, curves.

Course details
Credit Hours:3
Max credits per semester:3
Max credits per degree:3
Course Format:LEC

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
Course Format:LEC

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
Course Format:LEC

Credit Hours:3-6

ACE:

MATH995
Research Seminar
Course details
Credit Hours:1-3
Max credits per semester:3
Max credits per degree:6
Course Format:LEC

Credit Hours:1-3

ACE:

MATH996
Seminar

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
Course Format:LEC

Credit Hours:1-3

ACE:

MATH997
Reading Course
Course details
Credit Hours:1-24
Max credits per semester:24
Max credits per degree:24
Course Format:IND

Credit Hours:1-24

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
Course Format:IND

Credit Hours:1-24

ACE: