MATHEMATICS (MATH) - 2020-2021 Curriculum and Catalog
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Mathematics (MATH) 1
MATHEMATICS (MATH)
MATH 1000 Special Problems (IND 0.0-6.0) MATH 1208 Calculus With Analytic Geometry I (LEC 5.0)
Problems or readings in specific subjects or projects in the department. A study of limits, continuity, differentiation and integration of algebraic
Consent of instructor required. and trigonometric functions. Applications of these concepts in physical
as well as mathematical settings are considered. Credit will only be given
for one of Math 1208 or Math 1214. Prerequisites: Math 1160; Math 1120
MATH 1001 Special Topics (LEC 0.0 and LAB 0.0)
or 1140, both with a grade of "C"; or better; or by placement exam.
This course is designed to give the department an opportunity to test a
new course. Variable title.
MATH 1212 Business Calculus (LEC 3.0 and LAB 1.0)
Calculus for Bus. & Mgt. Sys, Econ & Finance, or Info. Sci. & Tech; also
MATH 1101 Introduction To Mathematics (LEC 1.0)
possibly Bio. Sci, Soc. Sci. or Humanities. Derivatives, optimization,
Introduction to the department, program of study, methods of study, and
exponential and logarithmic functions, integration, multivariate functions,
an introduction of the various areas of mathematics. Required of fall
partial derivatives, Lagrange multipliers, applications. May not be used as
semester freshman mathematics majors.
a prerequisite for either Math 1215 or Math 1221. Prerequisite: A grade of
"C" or better in either 1120 or Math 1140; or by placement exam.
MATH 1103 Fundamentals Of Algebra (LEC 3.0)
Basic principles of algebra including the number line and an introduction
MATH 1214 Calculus For Engineers I (LAB 1.0 and LEC 3.0)
to equations and inequalities, polynomials, rational expressions,
Introduction to limits, continuity, differentiation and integration of
exponents and radicals, the quadratic formula and functions.
algebraic and elementary transcendental functions. Applications in
Prerequisite: Entrance requirements.
physical science and engineering. Credit will be given for only one of
Math 1208 or Math 1214. Math 1214 may be accompanied by Math 1160
MATH 1110 Mathematical Reasoning and Modeling (LEC 3.0) with Math department approval. Prerequisites: A grade of "C" or better
Designed for non-STEM majors, this course provides a comprehensive in both Math 1160 and one of Math 1120 or Math 1140; or by placement
overview of the reasoning skills required to process, reflect upon, and exam.
apply quantitative information in making decisions. Topics include ratios,
rates, percentages, units, descriptive statistics, linear and exponential
MATH 1215 Calculus For Engineers II (LAB 1.0 and LEC 3.0)
modeling, correlation, logic, and probability. Technology is emphasized.
Continuation of Math 1214. Transcendental functions, techniques of
Prerequisites: Entrance requirements.
integration, sequences, series including power series, polar coordinates,
polar and parametric equations. Applications in physical science and
MATH 1120 College Algebra (LEC 5.0) engineering. Credit will be given for only one of Math 1215 or Math 1221.
Contains the same topics as covered in Math 1140, and preceded by Prerequisites: Math 1160 and either Math 1208 or Math 1214 both with a
a thorough review of the basic principles of algebra. Prerequisite: By grade of "C" or better; or by placement exam.
placement examination.
MATH 1120 - MOTR MATH 130: Pre-Calculus Algebra
MATH 1221 Calculus With Analytic Geometry II (LEC 5.0)
A continuation of Math 8; differentiation and integration of elementary
MATH 1140 College Algebra (LEC 3.0) transcendental functions, integration techniques, improper integrals,
A study of linear equations, rational functions, radicals, quadratic conic sections, polar coordinates, introduction to sequences and
equations, inequalities, determinants, progressions, theory of equations, series. Credit will only be given for one of Math 1221 or Math 1215.
permutations, combinations, and the binomial theorem. Prerequisite: By Prerequisites: Math 1160 and either Math 1208 or Math 1214 both with a
placement examination. grade of "C" or better; or by placement exam.
MATH 1140 - MOTR MATH 130: Pre-Calculus Algebra
MATH 1140 - MOTR MATH 150: Pre-Calculus
MATH 2002 Cooperative Work Training (IND 0.0-6.0)
On-the-job experience gained through cooperative education with
MATH 1160 Trigonometry (LEC 2.0) industry. Variable credit arranged with the advisor. P/F grading option is
A study of the trigonometric functions, radian measure, graphing required and maximum credit per semester is 3 hrs., maximum for entire
trigonometric functions, identities, trigonometric equations and inverse program is 6 hrs.
trigonometric functions. Solutions of general triangles and trigonometric
representation of complex numbers are included. Prerequisite: Math 1120
MATH 2222 Calculus with Analytic Geometry III (LEC 3.0 and LAB 1.0)
or 1140 with a grade of "C" or better; or by placement exam.
An introduction to multivariable calculus. Vector valued functions, curves
MATH 1160 - MOTR MATH 150: Pre-Calculus
and surfaces in two and three dimensions, partial differentiation, multiple
integration, line and surface integrals, the major theorems of vector
MATH 1190 Success for Calculus (LEC 3.0 and LAB 1.0) calculus, and applications of these ideas are studied. Prerequisites: Math
This course focuses on the use of college algebra and trigonometry skills 1215 or Math 1221 with a grade of "C" or better.
within the context of calculus, providing students with the opportunity
to improve their preparedness for future calculus coursework. Pass/Fail
only. Prerequisites: Consent of instructor.
2020-20212 Mathematics (MATH)
MATH 3000 Special Problems (IND 0.0-6.0) MATH 4096 Problem Solving In Pure Mathematics (LEC 1.0)
Problems or readings in specific subjects or projects in the department. Problems from pure mathematics, including analysis, algebra, number
Consent of instructor required. theory, set theory, finite mathematics, probability and statistics. Emphasis
on identifying or inventing ways to solve problems based on the student's
entire mathematics background. Prerequisites: Corequisite Math 4209
MATH 3001 Special Topics (IND 0.0-6.0)
and Senior standing.
This course is designed to give the department an opportunity to test a
new course. Variable title.
MATH 4097 Problem Solving In Applied Mathematics (LEC 1.0)
Problems from applied mathematics which are open-ended, and do
MATH 3010 Undergraduate Seminar (SEM 1.0-3.0)
not always have a unique correct solution. Emphasis on developing
Discussion of advanced or current topics. (Course cannot be used for
mathematical models and writing solution narratives, including clarity,
graduate credit).
analysis, and design. Prerequisites: Math 3109 and Senior standing.
MATH 3108 Linear Algebra I (LEC 3.0)
MATH 4098 Explorations in Pure Mathematics (LEC 3.0)
Systems of linear equations, matrices, vector spaces, inner products,
Students interested in pure mathematics will be encouraged to use their
linear transformations, determinants, and eigenvalues are studied.
entire mathematics background as a context for learning about some of
Prerequisite: Math 1215 or 1221 or 2222 with a grade of "C" or better.
the great theorems which have shaped the development of mathematics
and solving novel problems in areas such as, but not limited to, analysis,
MATH 3109 Foundations Of Mathematics (LEC 3.0) algebra, number theory, set theory, topology, and finite mathematics.
Introduction to mathematical reasoning through an axiomatic Prerequisites: Senior standing; preceded or accompanied by Math 4209.
development of mathematical systems. Strong emphasis is placed
on learning to understand what constitutes a sound mathematical
MATH 4099 Undergraduate Research (IND 0.0-6.0)
argument. Communication, both written and spoken, is emphasized.
This course is designed for the undergraduate student who wishes to
Prerequisite: Math 1215 or 1221 with a grade of "C" or better.
engage in research. It is not to be used for graduate credit nor for more
than six credit hours of undergraduate credit. The subject and credit are
MATH 3304 Elementary Differential Equations (LEC 3.0) to be arranged with the instructor. Prerequisite: Consent of instructor.
First order differential equations and linear differential equations of
higher order are studied. The Laplace transform and systems of linear
MATH 4209 Advanced Calculus I (LEC 3.0)
equations as well as selected physical applications are covered. Credit
Completeness of the set of real numbers, sequences and series of real
will not be given for both Math 3329 and Math 3304. Prerequisite: Math
numbers, limits, continuity and differentiability, uniform convergence,
2222 with a grade of "C" or better.
Taylor series, Heine-Borel theorem, Riemann integral, fundamental
theorem of calculus, Cauchy-Riemann integral. Prerequisite: Math
MATH 3921 Teaching Math in Elementary and Middle Schools (LEC 3.0) 2222 and Math 3109, or a 4000-level or higher mathematics course, or
The course presents an overview of how children learn mathematics, graduate standing.
various techniques in teaching mathematics, and examples of applying
these techniques to specific mathematical concepts (such as geometry,
MATH 4211 Advanced Calculus II (LEC 3.0)
measurement, basic operations, statistics and probability, etc.).
Euclidean n-space, differentiation and integration of scalar functions
Prerequisite: Math 1120 or Math 1140; Educ 1040. (Co-listed with Educ
of several variables, maxima and minima theory, change of variables,
3221).
differentiation and integration of vector functions of several variables,
Divergence theorem, Stokes' theorem. Prerequisite: Math 4209.
MATH 3922 Geometric Concepts for Elementary Teachers (LEC 3.0)
The course covers methods of teaching the study of points, lines,
MATH 4530 Topics In Geometry (LEC 3.0)
polygons, similarity, congruence, constructions, and proof in Euclidean
A survey of non-Euclidean geometries, finite geometries, affine and
Plane Geometry. Transformational geometry and trigonometry are
projective planes, metric postulates for the Euclidean plane, and selected
introduced to elementary teachers. Prerequisites: Math 1120 or Math
topics. Credit will not be given for both Math 4530 and Math 5530.
1140. (Co-listed with Educ 3222).
Prerequisites: MATH 3108.
MATH 4000 Special Problems (IND 0.0-6.0)
MATH 5000 Special Problems (IND 0.0-6.0)
Problems or readings on specific subjects or projects in the department.
Problems or readings on specific subjects or projects in the department.
Consent of instructor required.
Consent of instructor required.
MATH 4001 Special Topics (LEC 0.0-6.0)
MATH 5001 Special Topics (LEC 0.0-6.0)
This course is designed to give the department an opportunity to test a
This course is designed to give the department an opportunity to test a
new course. Variable title.
new course. Variable title.
MATH 4010 Undergraduate Seminar (SEM 1.0-3.0)
MATH 5010 Graduate Seminar (SEM 1.0)
Discussion of advanced or current topics. (Course cannot be used for
Discussion of advanced or current topics.
graduate credit).
2020-2021Mathematics (MATH) 3
MATH 5040 Oral Examination (IND 0.0) MATH 5222 Vector And Tensor Analysis (LEC 3.0)
After completion of all other program requirements, oral examinations for Vector algebra, vector differential and integral calculus, line and surface
on-campus M.S./Ph.D. students may be processed during intersession. integrals, theorems of Stokes and Gauss, tensor algebra and tensor
Off-campus M.S. students must be enrolled in oral examination and analysis, applications to problems in kinematics, elasticity theory, fluid
must have paid an oral examination fee at the time of the defense/ mechanics, electromagnetic theory, relativity theory. Prerequisite: Math
comprehensive examination (oral/ written). All other students must enroll 2222; Math 3103 or Math 3108.
for credit commensurate with uses made of facilities and/or faculties. In
no case shall this be for less than three (3) semester hours for resident MATH 5302 Intermediate Differential Equations (LEC 3.0)
students. Linear differential equations, vector-matrix systems, existence and
uniqueness theory, nonlinear systems, phase-plane analysis, introduction
MATH 5099 Graduate Research (IND 0.0-6.0) to stability theory. Prerequisite: Math 3304 or Math 3329.
Investigation of an advanced nature leading to the preparation of a MS
thesis or dissertation. MATH 5325 Partial Differential Equations (LEC 3.0)
Linear equations, heat equation, eigenfunction expansions, Green's
MATH 5105 Modern Algebra I (LEC 3.0) formula, inhomogeneous problems, Fourier series, wave equation.
Equivalence relations and functions, basic properties of groups, Prerequisite: Math 3304 with a grade of "C" or better.
subgroups, permutations, cosets and Lagrange's Theorem,
homomorphisms and isomorphisms, factor groups. Prerequisite: Math MATH 5351 Introduction To Complex Variables (LEC 3.0)
3109 or graduate standing; preceded or accompanied by Math 3108. The basic tools of complex variables are studied. These include the
Cauchy-Riemann equations, complex contour integration, the Cauchy-
MATH 5106 Modern Algebra II (LEC 3.0) Goursat theorem, conformal mappings, the calculus of residues and
This course is a continuation of Math 5105. Rings and fields are applications to boundary value problems. Prerequisite: Math 3304.
discussed. Euclidean domains, principal ideal domains, unique
factorization domains, vector spaces, finite fields and field extensions are MATH 5483 Operational Calculus (LEC 3.0)
studied. Prerequisite: Math 5105. The Laplace transformation, properties of the transformation, various
applications to ordinary and partial differential equations, systems
MATH 5107 Combinatorics And Graph Theory (LEC 3.0) with step and Dirac functions as driving forces, various non-elementary
Covers some basics of enumeration and graph theory. Topics are functions and their transforms, problems in heat conduction and wave
selected from the following: permutations combinations, the inclusion/ motion, Fourier transforms and their operational properties. Prerequisite:
exclusion principle, generating functions, recurrence relations, trees, Math 3304.
networks, graph connectivity and graph coloring. Prerequisite: Comp Sci
1200 or Math 3109. MATH 5512 Introduction To Differential Geometry (LEC 3.0)
Elements of the geometry of curves and surfaces in Euclidean three-
MATH 5108 Linear Algebra II (LEC 3.0) space using methods of advanced calculus and vectors. Prerequisite:
Eigenvalue problems, Cayley-Hamilton theorem, Jordan normal form, Math 4209 or Math 5222.
linear functionals, bilinear forms, quadratic forms, orthogonal and unitary
transformations, selected applications of linear algebra. Prerequisite: MATH 5530 Topics in Geometry - Graduate Option (LEC 3.0)
Math 3108. A survey of non-Euclidean geometries, finite geometries, affine and
projective planes, metric postulates for the Euclidean plane, and selected
MATH 5154 Mathematical Logic I (LEC 3.0) topics. Students will demonstrate graduate-level mastery of the subject
A mathematical introduction to logic with some applications. Functional matter. Credit will not be given for both Math 4530 and Math 5530.
and relational languages, satisfaction, soundness and completeness Prerequisites: MATH 3108.
theorems, compactness theorems. Examples from Mathematics,
Philosophy, Computer Science, and/or Computer Engineering. MATH 5585 Introduction To Topology (LEC 3.0)
Prerequisite: Philos 3254 or Math 5105 or Comp Sci 2500 or Comp Eng Metric spaces; general topological spaces; connectedness, compactness,
2210. (Co-listed with Comp Eng 5803, Comp Sci 5203 and Philos 4354). separation properties, functions and continuity. Prerequisite: Math 4209.
MATH 5215 Introduction To Real Analysis (LEC 3.0) MATH 5603 Methods of Applied Mathematics (LEC 3.0)
Riemann-Stieltjes integration, sequences and series of functions, Methods to develop and analyze mathematical models. Topics
uniform approximation, the Banach Space C(a,b), Lebesgue measure and include dimensional analysis and scaling, perturbation methods,
integration, the space LP(a,b), Fourier series. Prerequisite: Math 4209. and the construction of ordinary and partial differential equation
models. Prerequisites: Math 3304 or 3329 with a grade of "C" or better,
programming competency.
2020-20214 Mathematics (MATH)
MATH 5604 Introduction to Numerical Methods for Differential Equations MATH 6050 Continuous Registration (IND 1.0)
(LEC 3.0) Doctoral candidates who have completed all requirements for the degree
An introduction to finite difference methods for ordinary and partial except the dissertation, and are away from the campus must continue
differential equations, including (1) the derivation of the numerical to enroll for at least one hour of credit each registration period until the
methods, (2) implementation of the methods in Matlab, and (3) degree is completed. Failure to do so may invalidate the candidacy. Billing
the mathematical accuracy and stability analysis of the methods. will be automatic as will registration upon payment.
Prerequisites: MATH 3304 and programming competency (preferably
Matlab). MATH 6099 Research (IND 0.0-15)
Investigation of an advanced nature leading to the preparation of a thesis
MATH 5737 Financial Mathematics (LEC 3.0) or dissertation.
The course objective is to provide an understanding of the fundamental
concepts of financial mathematics. Topics include pricing, assets-liability MATH 6105 Finite Fields And Applications (LEC 3.0)
management, capital budgeting, valuing cash flow, bonds, futures, swaps, After reviewing basic group theory and introducing basic properties of
options. Preparation for the financial mathematics actuarial exam will commutative rings, the main focus of the course will be on topics such
be provided. Prerequisites: Math 1215 or Math 1221, Econ 1100 or Econ as structure of finite fields, polynomials over finite fields, and applications
1200, and one of the following: Stat 3111, Stat 3113, Stat 3115, Stat 3117 such as coding theory and cryptography. Prerequisite: Math 5105.
or Stat 5643. (Co-listed with Econ 5337).
MATH 6106 Introduction to Ring Theory (LEC 3.0)
MATH 5940 Mathematical Analysis For Secondary Teachers (LEC 3.0) Properties of rings with an emphasis on commutative rings. Ideals, factor
Designed to help teachers gain a deeper understanding of the rings, ring homomorphisms, polynomial rings; factorization, divisibility,
fundamental idea in analysis, that of a limit. A discovery method is used and irreducibility. Introduction to extension fields and Galois theory.
which includes both individual and group work. Students will present their Applications may be chosen based on the interests of the students.
results in written and oral format. Prerequisite: Math 2222 or equivalent. Prerequisite: Math 5105.
MATH 5948 Mathematical Analysis For Secondary Teachers Practicum (LEC MATH 6107 Group Theory (LEC 3.0)
1.0) Groups, subgroups, and factor groups; homomorphisms, isomorphisms,
An instructional unit based on the discovery method used in Math 340 and associated theorems; abelian groups; Sylow theorems and p-groups;
will be designed by each student. These units will be class tested. The permutation groups; free groups and generators; representation theory;
unit and results of class testing will be presented both in written and oral cohomology theory. Prerequisite: Math 5106.
format. Prerequisite: Math 5940.
MATH 6108 Applied Matrix Theory (LEC 3.0)
MATH 6000 Special Problems (IND 0.0-6.0) A second course in matrix theory directed toward applications. Linear
Problems or readings on specific subjects or projects in the department. spaces, linear operators, equivalence and similarity, spectral theorem,
Consent of instructor required. canonical forms, congruence, inertia theorem, quadratic forms,
singular value decomposition and other factorizations, generalized
MATH 6001 Special Topics (LEC 0.0-6.0) inverses. Applications to optimization, differential equations, stability.
This course is designed to give the department an opportunity to test a Prerequisites: Math 3103, 3108, or 5302.
new course. Variable title.
MATH 6215 Functions Of A Real Variable I (LEC 3.0)
MATH 6010 Graduate Seminar (RSD 1.0-3.0) Measure spaces, extensions of measures, probability spaces,
Discussion of topics of current interest. Prerequisite: Graduate standing. measures and distributions in normed linear spaces, product measures,
independence, integral and expectation, convergence theorems,
Radon-Nikodyn theorem and applications. Lp spaces, selected topics.
MATH 6040 Oral Examination (IND 0.0)
Prerequisite: Math 5215.
After completion of all other program requirements, oral examinations for
on-campus M.S./Ph.D. students may be processed during intersession.
Off-campus M.S. students must be enrolled in oral examination and MATH 6216 Functions Of A Real Variable II (LEC 3.0)
must have paid an oral examination fee at the time of the defense/ Abstract measures and integrals, the Daniell integration theory,
comprehensive examination (oral/ written). All other students must enroll integration on locally compact Hausdorff spaces, integration in function
for credit commensurate with uses made of facilities and/or faculties. In spaces, selected topics. Prerequisite: Must be preceded by Math 6215.
no case shall this be for less than three (3) semester hours for resident
students. MATH 6330 Theory Of Differential Equations I (LEC 3.0)
Stability theory, Liapunov's direct method, periodic solutions, Poincare-
Bendixson theory, applications. Prerequisite: Math 5302.
2020-2021Mathematics (MATH) 5
MATH 6331 Theory Of Differential Equations II (LEC 3.0) MATH 6540 Geometric Structures (LEC 3.0)
Continuation of Math 6330. Nonlinear oscillations, solutions near Selected topics in non-Euclidean, solid, projective, and fractal geometry.
singular points, asymptotic methods, differential equations on manifolds, Prerequisite: Math 4530.
boundary-value problems. Prerequisite: Math 5302.
MATH 6548 Geometric Structures Practicum (LEC 1.0)
MATH 6351 Functions Of A Complex Variable I (LEC 3.0) An instructional unit based on material learned in Math 6540 will be
Complex plane, complex function theory, elementary Riemann surfaces, designed by each student. These units will be class tested. The unit and
conformal mapping, complex integration, infinite complex series and results of class testing will be presented both in written and oral format.
sequences, calculus of residues with applications. Prerequisite: Math Prerequisite: Math 6540.
4211.
MATH 6585 Topology I (LEC 3.0)
MATH 6352 Functions Of A Complex Variable II (LEC 3.0) Topological spaces, uniform and quasi-uniform spaces, product
Argument principle and consequences; harmonic functions and and quotient spaces, separation properties and connected spaces,
Dirichlet's problem; infinite products; entire, meromorphic and rational compactness. Prerequisite: Math 5585.
functions; analytic continuation; symmetry principle; conformal mapping;
functions of several complex variables. Prerequisite: Preceded by Math MATH 6586 Topology II (LEC 3.0)
6351. Metrizability conditions, the theory of convergence using both filters and
nets, completions and compactifications, and papers from the recent
MATH 6375 Theory Of Partial Differential Equations (LEC 3.0) literature. Prerequisite: Math 6585.
Sobolev spaces; existence, uniqueness, and regularity of weak solutions
to linear elliptic, parabolic, and hyperbolic PDEs; selected topics. MATH 6601 Numerical Analysis (LEC 3.0)
Prerequisite: Math 6417. A proof based course emphasizing theoretical analysis of convergence
and accuracy of various numerical methods including approximate
MATH 6383 Special Functions (LEC 3.0) solutions of linear and nonlinear equations, numerical integration, and
Infinite products, gamma and beta functions, asymptotic series, the function approximation, with implementation to validate results and
hypergeometric function, generalized hypergeometric functions, Bessel illustrate the methods. Prerequisites: Any 4000 or higher level MATH
functions, generating functions; polynomials of legendre, Hermite, course, or any instructor approved 4000 or higher level course from
Laguerre, and Jacobi; elliptic functions, theta functions, Jacobian elliptic another discipline with a significant computational component.
functions. Prerequisites: Math 4209 and 5351.
MATH 6602 Mathematical Foundation of Finite Element Methods (LEC 3.0)
MATH 6417 Functional Analysis I (LEC 3.0) Implementation and theoretical analysis of the finite element method for
Banach spaces, Hilbert spaces, linear transformations, Hahn-Banach the approximate solution of partial differential equations. Implementation
theorem, duality, uniform boundedness principle, weak topologies, of finite element methods for elliptic and parabolic equations. Theoretical
convexity, bounded linear maps, compact operators, and spectral theory. analysis of convergence, accuracy, and stability of approximate solutions.
Prerequisites: Math 5215; Math 5108 or Math 5585. Prerequisites: Any 4000 or higher level Mathematics course, or any
instructor approved 4000 or higher level course from another discipline
with a significant computational component.
MATH 6418 Functional Analysis II (LEC 3.0)
A continuation of Math 6417 with additional topics related to bounded
and unbounded operators and their applications. Prerequisites: Math MATH 6665 Mathematical Programming (LEC 3.0)
6215 and Math 6417. Linear optimization and its engineering applications; problem modeling,
search-based optimization, the simplex method for solving linear
problems, multi-objective optimization, discrete dynamic programming.
MATH 6461 Harmonic Analysis I (LEC 3.0)
Applications of optimization in the fields such as transportation, project
Fourier series, norm and pointwise convergence of Fourier series, the
management, manufacturing and facility location will be discussed.
conjugate and maximal functions, analytic functions in the unit disk and
Prerequisites: One of the following:Stat 3113, Stat 3115, or Stat 3117;
Hardy spaces, interpolation of linear operators and the Hausdorff-Young-
Math 3108. (Co-listed with Eng Mgt 6412 and Sys Eng 6412).
Riesz Theorem, Sidon sets. Prerequisites: Math 5215 and Math 5351.
MATH 6737 Financial Mathematics II (LEC 3.0)
MATH 6462 Harmonic Analysis II (LEC 3.0)
Continuation of Math 5737/Econ 5337. Topics include martingales
Fourier integrals, almost-periodic functions on the real line, Banach
and measures, stopping times, discrete and continuous time finance,
algebras, Wiener's Tauberian Theorem and the prime number theorem,
Brownian motion, Ito calculus, stochastic differential equations, Black-
the Paley-Wiener Theorems, band-limited functions and Shannon's
Scholes-Merton formula, numerical procedures. Prerequisite: Math 5737
Theorem, the continuous wavelet transform, discrete wavelet transforms
or Econ 5337. (Co-listed with Econ 6337).
and frames, orthonormal bases of wavelets and multi-resolution analysis.
Prerequisite: Must be preceded by Math 6461.
2020-20216 Mathematics (MATH) MATH 6802 Mathematical Physics I (LEC 3.0) Vector spaces, generalized coordinate transformations, vector analysis, tensors, partial differential equations in physics and boundary value problems, orthogonal functions and solutions to ordinary differential equations, hypergeometric, confluent hypergeometric, Legendre, Laguerre, and Bessel functions, Hermite polynomials, Green's functions in one dimension. (Co-listed with Physics 6403). MATH 6803 Mathematical Physics II (LEC 3.0) Green's functions in three dimensions, integral equations, complex variable theory and contour integration, group theory with applications to quantum mechanics, solid state and molecular physics. Prerequisite: Math 6802 or Physics 6403. (Co-listed with Physics 6413). 2020-2021
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