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Rensselaer Catalog 2014-2015 [Archived Catalog]
Courses
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MANE 6770 - Multiscale Computational Modeling
This course will introduce a unified approach of modeling in science and engineering across spatial and temporal scales using particles as well as continuum fields, specifically focusing on methods and algorithms that will facilitate this bridging. Topics include two categories of multiscale approaches: information-passing and concurrent-bridging approaches. Our goal is to algorithmically develop these methods, and in the process teach the underlying simulation techniques. Applications to realistic problems will highlight the strengths of these approaches, while stressing the challenges that still need to be surmounted.
Prerequisites/Corequisites: Prerequisite: MANE 4240 or equivalent.
When Offered: Spring term even-numbered years.
Credit Hours: 3
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MANE 6780 - Numerical Modeling of Failure Processes in Materials
State of the art in computational modeling of failure processes in materials. Topics include numerical modeling of discrete defects, distributed damage and multiscale computational techniques including multiple scale perturbation techniques, boundary layer techniques, and various global-local approaches.
Prerequisites/Corequisites: Prerequisite: CIVL 6660 or MANE 6660.
When Offered: Spring term even-numbered years.
Cross Listed: Cross listed as CIVL 6780. Students cannot obtain credit for both this course and CIVL 6780.
Credit Hours: 3
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MANE 6800 - Manufacturing Systems Integration
Examination of the basic elements that are used to integrate the design and manufacture of capital and consumer products; manufacturing information systems, CAD/CAM systems, and manufacturability considerations when integrating unit process operations.
When Offered: Fall term annually.
Credit Hours: 3
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MANE 6820 - Finite Deformation Plasticity: Theory and Applications Kinematics of Finite Deformation
Elastic-plastic and elasto-viscoplastic constitutive behavior for isotropic and strain-induced anisotropic materials. Integration algorithms and finite element formulations for solving practical problems.
Prerequisites/Corequisites: Prerequisite: MANE 6170 or equivalent.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6830 - Combustion
Review of fundamentals of thermodynamics, chemical kinetics, fluid mechanics, and modern diagnostics. Discussion of flame propagation, thermal and chain explosions, stirred reactors, detonations, droplet combustion, and turbulent jet flames. Introduction to computational tools for complex equilibrium and kinetic calculations. Application to problems such as pollutant formation.
Prerequisites/Corequisites: Prerequisite: Permission of instructor.
When Offered: Spring term odd-numbered years.
Cross Listed: Cross listed as CHME 6830. Students cannot obtain credit for both this course and CHME 6830.
Credit Hours: 3
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MANE 6840 - An Introduction to Multiphase Flow and Heat Transfer I
This course is intended to give students a state-of-the-art understanding about single and multicomponent boiling and condensation heat transfer phenomena. Applications include the analysis of nuclear reactors, oil wells, and chemical process equipment. Students satisfactorily completing this course are expected to thoroughly understand the current thermal-hydraulics literature on multiphase heat and mass transfer and be able to conduct independent research in this field.
Prerequisites/Corequisites: Prerequisite: A working knowledge of fluid mechanics and heat transfer.
When Offered: Fall term annually.
Credit Hours: 3
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MANE 6850 - An Introduction to Multiphase Flow and Heat Transfer II
This course is intended to give students a state-of-the-art understanding in multicomponent flow phenomena. Applications in the chemical process, petroleum recovery, and fossil/nuclear power industries are given. Specific areas of coverage include two-phase: fluid mechanics, pressure drop, modeling and analysis, stability analysis, critical flow and dynamic waves, flow regime analysis, and phase separation and distribution phenomena.
Prerequisites/Corequisites: Prerequisite: CHME 6840 or MANE 6840.
When Offered: Spring term annually.
Cross Listed: Cross listed as CHME 6850. Students cannot obtain credit for both this course and CHME 6850.
Credit Hours: 3
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MANE 6880 - Product Realization
Concepts and tools that enable engineers and business leaders to jointly make sound business/technology decisions in moving from ideas and designs to real products will be taught using lectures, cases, and a major project that will enhance the change of success of a new venture business. Topics: Disciplined Toll-Gate Processes, Customer Contract, Technical Risk Management, Design Decisions, Quality Management, Sourcing, Product Launch.
Prerequisites/Corequisites: Prerequisites: Engineering B.S. or MGMT 6040 and MGMT 6050 or MGMT 6620 or permission of the instructor.
When Offered: Spring term annually.
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MANE 6900 - Seminar
When Offered: Fall and spring terms annually.
Credit Hours: 0
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MANE 6940 - Individual Projects in Mechanical Engineering, Aeronautical Engineering, Nuclear Engineering, or Engineering Physics
Prerequisites/Corequisites: Prerequisite: permission of instructor.
When Offered: Fall and spring terms annually.
Credit Hours: 3 to 6
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MANE 6960 - Topics in Mechanical Engineering, Aeronautical Engineering, Nuclear Engineering, or Engineering Physics
When Offered: Fall and spring terms annually.
Credit Hours: 3
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MANE 6970 - Professional Project
Active participation in a semester-long project, under the supervision of a faculty adviser. A Professional Project often serves as a culminating experience for a Professional Master’s program but, with departmental or school approval, can be used to fulfill other program requirements. With approval, students may register for more than one Professional Project. Professional Projects must result in documentation established by each department or school, but are not submitted to the Office of Graduate Education and are not archived in the library. Grades of A,B,C, or F are assigned by the faculty adviser at the end of the semester. If not completed on time, a formal Incomplete grade may be assigned by the faculty adviser, listing the work remaining to be completed and the time limit for completing this work.
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MANE 6980 - Master’s Project
Active participation in a Master’s-level project under the supervision of a faculty adviser, leading to a master’s project report. Grades of IP are assigned until the master’s project has been approved by the faculty adviser. If recommended by the adviser, the master’s project may be accepted by the Office of Graduate Education to be archived in the library. Grades will then be listed as S.
Credit Hours: 1 to 9
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MANE 6990 - Master’s Thesis
Active participation in research, under the supervision of a faculty adviser, leading to a master’s thesis. Grades of S or U are assigned by the adviser each term to reflect the student’s research progress for the given semester. Once the thesis has been presentend, approved by the adviser, and accepted by the Office of Graduate Education, it will be archived in a standard format in the library.
Credit Hours: 1 to 9
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MANE 7000 - Advanced Engineering Mathematics II
A continuation of the advanced presentation of mathematical methods useful in engineering practice. The course covers the Frobenius method for the solution of boundary value problems; the representation of arbitrary functions by characteristic functions; calculus of functions of more than one variable including the study of extreme; overview of calculus of variations; principles of vector and tensor analysis; analytical and numerical techniques for the solution of initial and boundary value problems in partial differential equations. Symbolic manipulation and scientific computation software used extensively. Emphasis on reliable computing is made throughout.
Credit Hours: 3
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MANE 7100 - Mechanical Engineering Foundations II
A presentation of the most common physical and mathematical modes used in the description of the mechanical behavior of materials. The course covers the microstructural and thermodynamic foundations of constitutive material behavior of interest in mechanical engineering applications; overview of elasticity and plasticity and their relationship to microstructural features; principles of rheology; viscoelasticity and creep; failure mechanisms including fracture crack propagation and fatigue crack growth. Particular attention throughout is given to the development of the ability to utilize the mathematical models to assess the reliability and life of mechanical engineering components at the design state.
Credit Hours: 3
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MANE 9990 - Dissertation
Active participation in research, under the supervision of a faculty adviser, leading to a doctoral dissertation. Grades of IP are assigned until the dissertation has been publicly defended, approved by the doctoral committee, and accepted by the Office of Graduate Education to be archived in a standard format in the library. Grades will then be listed as S.
Credit Hours: 1 to 15
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MATH 1010 - Calculus I
Functions, limits, continuity, derivatives, implicit differentiation, related rates, maxima and minima, elementary transcendental functions, introduction to definite integral with applications to area and volumes of revolution.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 1020 - Calculus II
Techniques and applications of integration, polar coordinates, parametric equations, infinite sequences and series, vector functions and curves in space, functions of several variables, and partial derivatives.
Prerequisites/Corequisites: Prerequisite: MATH 1010.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 1500 - Calculus for Architecture, Management, and HASS
Basic concepts in differential and integral calculus for functions of one variable. Topics will include functions, limits, continuity, derivatives, integration, exponential and logarithmic functions, and techniques of integration. Application areas will include topics in Management, Architecture, and Social Sciences with special emphasis on the role of calculus in introductory probability.
Prerequisites/Corequisites: Prerequisite: Major in Management, Architecture, or HASS.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 1520 - Mathematical Methods in Management and Economics
Functions of several variables, introductory linear algebra, and other analytical techniques needed for further study in probability, statistics, and operations research. Topics covered include improper integrals, probability density functions, partial derivatives and optimization techniques for functions of several variables, matrix algebra, linear systems, lines and planes in 3-space, linear inequalities, introductory linear programming, introductory combinatorics, and some probability.
Prerequisites/Corequisites: Prerequisites: MATH 1010 or MATH 1500 and major in Management or Economics, or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 1620 - Contemporary Mathematical Ideas in Society
An application-oriented course introducing contemporary mathematical concepts that pertain to areas of Architecture and Humanities, Arts, and Social Sciences. The course will cover growth and form, symmetry, patterns, tilings, linear programming, information coding, voting systems, game theory, logic, probability and statistics.
Prerequisites/Corequisites: Prerequisites: Major in Architecture or Humanities, Arts, and Social Sciences and MATH 1010 or MATH 1500 or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 1900 - Art and Science of Mathematics I
A seminar for first-year math majors. The weekly student-faculty discussions will vary but examples of topics are: unsolved math problems, countability and the arithmetic of the infinite, topology and the concept of dimension, geometry and one-sided surfaces, and the theory underlying topics currently covered in calculus.
Prerequisites/Corequisites: Prerequisite: First-year math majors.
When Offered: Fall term annually.
Credit Hours: 1
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MATH 1910 - Art and Science of Mathematics II
A seminar for first-year math majors. The weekly student-faculty discussions will vary but examples of topics are: unsolved math problems, countability and the arithmetic of the infinite, topology and the concept of dimension, geometry and one-sided surfaces, and the theory underlying topics currently covered in calculus.
Prerequisites/Corequisites: Prerequisite: First-year math majors.
When Offered: Spring term annually.
Credit Hours: 1
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MATH 2010 - Multivariable Calculus and Matrix Algebra
Directional derivatives, maxima and minima, double integrals, line integrals, div and curl, and Green’s Theorem; matrix algebra and systems of linear equations, vectors and linear transformations in R^n, eigenvectors and eigenvalues, applications in engineering and science.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 2400 - Introduction to Differential Equations
First-order differential equations, second-order linear equations, eigenvalues and eigenvectors of matrices, systems of first-order equations, stability and qualitative properties of nonlinear autonomous systems in the plane, Fourier series, separation of variables for partial differential equations.
Prerequisites/Corequisites: Prerequisites: MATH 1020 and some knowledge of matrices.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 2800 - Introduction to Discrete Structures
Introduction to the mathematical foundation of computer science. Topics include logic and set theory; methods of proof; mathematical induction and wellordering; principles of counting; relations and graphs; recurrences; discrete probability.
Prerequisites/Corequisites: Prerequisite: MATH 1010 or MATH 1500 or equivalent.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 2940 - Readings in Mathematics
Credit Hours: 1 to 4
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MATH 2960 - Topics in Mathematics
Credit Hours: 1 to 4
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MATH 4010 - Abstract Algebra
Groups, rings, polynomial rings, fields, integral domains, with emphasis on group theory; homomorphisms and isomorphisms; normal subgroups, cosets, ideals, modules; quotient groups and quotient rings; other topics chosen from number theory, polynomials and Galois Theory.
Prerequisites/Corequisites: Prerequisite: MATH 4090 or graduate standing or permission of the instructor. MATH 4100 is desirable but not required.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4020 - Introduction to Number Theory
Topics include the history of number representation systems, divisibility, greatest common divisor and prime factorization, linear Diophantine equations, congruences, and condition congruences. Additional topics may be chosen from cryptology, the perpetual calendar, hashing functions, computer operations and complexity, continued fractions, multiplicative functions, primitive roots, pseudo-random numbers, nonlinear Diophantine equations, Fermat’s last theorem, algebraic numbers, and approximation of numbers by rationals.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 4030 - Computability and Logic
A team-based, project-oriented, hands-on introduction to great concepts and discoveries in logic and computability, including Turing Machines, first order logic, the limitations of computing machines, Godel’s incompleteness results and so forth. A hands-on laboratory component is included.
Prerequisites/Corequisites: Prerequisite: PHIL 2140.
When Offered: Spring term annually.
Cross Listed: Cross listed as PHIL 4420. Students cannot obtain credit for both this course and PHIL 4420.
Credit Hours: 4
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MATH 4040 - Introduction to Topology
Topics include general topological spaces, connectedness, compactness, continuity, and product spaces. Additional topics may be chosen from identification spaces, homotopy, the fundamental group, covering maps, lifts, classification of surfaces, Baire category, dimension, and the Jordan curve theorem.
Prerequisites/Corequisites: Prerequisite: MATH 4090 or graduate standing or permission of the instructor.
When Offered: Fall term even-numbered years.
Credit Hours: 4
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MATH 4090 - Foundation of Analysis
The course provides an opportunity for the development of theorem-proving skills in the field of mathematical analysis. Expansion of a knowledge base comes as a by-product of energy expended in theorem proving and subsequent exposition. Analysis topics included are: sets, functions, the real numbers, cardinality, induction, decimal representations of real numbers, Euclidean spaces, abstract vector spaces, and metric spaces. This is a communication-intensive course.
Prerequisites/Corequisites: Prerequisite: Mathematics major; corequisite: MATH 2010 or permission of instructor.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 4100 - Linear Algebra
The theory underlying vector spaces, algebra of subspaces, bases; linear transformations, dual spaces; eigenvectors, eigenvalues, minimal polynomials, canonical forms of linear transformations; inner products, adjoints, orthogonal projections and complements.
Prerequisites/Corequisites: Prerequisite: MATH 2010.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4120 - Fundamentals of Geometry
Topics may be chosen from differential geometry of curves and surfaces, involutes and evolutes, order of contact, developable surfaces, Euler’s and Meusnier’s Theorem, mean and Gaussian curvatures, geodesics and parallel transport, The Theorem Egregium of Gauss, Gauss-Bonnet Theorem, computer-aided geometric design, computational geometry, tessellations, tiling and patterns, projective and non-Euclidean geometries, postulates and axiomatic systems, advanced Euclidean geometry, and the history of geometry.
Prerequisites/Corequisites: Prerequisites: MATH 2010 and MATH 4600 or permission of the instructor.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 4150 - Graph Theory
Fundamental concepts and methods of graph theory and its applications in various areas of computing and the social and natural sciences. Topics include graphs as models, representation of graphs, trees, distances, matchings, connectivity, flows in networks, graph colorings, Hamiltonian cycles, traveling salesman problem, planarity. All concepts, methods, and applications are presented through a sequence of exercises and problems, many of which are done with the help of novel software systems for combinatorial computing.
Prerequisites/Corequisites: Prerequisite: MATH 2800 and CSCI 1100. Spring term even-numbered years.
When Offered: Spring term even-numbered years.
Cross Listed: Cross listed as CSCI 4260. Students cannot obtain credit for both this course and CSCI 4260.
Credit Hours: 4
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MATH 4200 - Mathematical Analysis I
Fundamental concepts of mathematical analysis. This is the first course in a two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem.
Prerequisites/Corequisites: Prerequisites: MATH 1020 and MATH 4090 or graduate standing or permission of the instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4210 - Mathematical Analysis II
Fundamental concepts of mathematical analysis. This is the second course in a two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem.
Prerequisites/Corequisites: Prerequisites: MATH 4200 or graduate standing or permission of the instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4300 - Introduction to Complex Variables: Theory and Applications
An introduction to the theory and applications of complex variables. Topics include analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residues, conformal mapping, harmonic functions, and Laplace transforms. Applications will be to problems in science and engineering such as fluid and heat flow, dynamical systems, and electrostatics.
Prerequisites/Corequisites: Prerequisite: MATH 2010 or equivalent.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4400 - Ordinary Differential Equations and Dynamical Systems
An intermediate course emphasizing a modern geometric approach and applications in science and engineering. Topics include first-order equations, linear systems, phase plane, linearization and stability, calculus of variations, Lagrangian and Hamiltonian mechanics, oscillations, basic bifurcation theory, chaotic dynamics, and existence and uniqueness.
Prerequisites/Corequisites: Prerequisite: MATH 2400 or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4500 - Methods of Partial Differential Equations of Mathematical Physics
An intermediate course serving to introduce both the qualitative properties of solutions of partial differential equations and methods of solution, including separation of variables. Topics include first-order equations, derivation of the classical equations of mathematical physics (wave, potential, and heat equations), method of characteristics, construction and behavior of solutions, maximum principles, energy integrals.
Prerequisites/Corequisites: Prerequisite: MATH 4600 or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4600 - Advanced Calculus
Topics include differentials and derivatives of functions of several variables, Jacobians, Lagrange multipliers, line, surface and volume integrals, independence of path, curvilinear coordinates, vector calculus, calculus of variations, theorems of Green, Gauss, and Stokes.
Prerequisites/Corequisites: Prerequisites: MATH 2010.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 4700 - Foundations of Applied Mathematics
Mathematical formulation of models for various processes. Derivation of relevant differential equations from conservation laws and constitutive relations. Use of dimensional analysis, scaling, and elementary perturbation methods. Description of basic wave motion. Examples from areas including biology, elasticity, fluid dynamics, particle mechanics, chemistry, geophysics, and finance.
Prerequisites/Corequisites: Prerequisite: MATH 2400 or equivalent.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4720 - Mathematics in Medicine and Biology
An introduction to mathematics used in biology, biophysics, biomedical engineering, and medicine. The mathematical topics covered are selected from calculus, linear algebra, differential equations, numerical methods, and Fourier analysis. The biological applications covered are selected from human physiology (heart, lung, brain), population models (microorganisms, cells, animals), and the diagnosis and treatment of disease (heart, cancer).
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4740 - Introduction to Financial Mathematics and Engineering
This course is designed to introduce students to mathematical and computational finance. Topics include a mathematical approach to risk analysis, portfolio selection theory, futures, options, and other derivative investment instruments. Finite difference and finite element methods for computing American option prices are discussed. A working knowledge of MAPLE or MATLAB is required to compute optimal portfolios.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4800 - Numerical Computing
A survey of numerical methods for scientific and engineering problems. Topics include numerical solution of linear and nonlinear algebraic equations, interpolation and least squares approximations, numerical integration and differentiation, eigenvalue problems, and an introduction to the numerical solution of ordinary differential equations. Emphasis placed on efficient computational procedures including the use of library and student written procedures using high-level software such as MATLAB.
Prerequisites/Corequisites: Prerequisites: CSCI 1100 and MATH 2010 or ENGR 1100. Corequisite: MATH 2400.
When Offered: Fall and spring terms annually.
Cross Listed: Cross listed as CSCI 4800. Students cannot obtain credit for both this course and CSCI 4800.
Credit Hours: 4
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MATH 4820 - Introduction to Numerical Methods for Differential Equations
Derivation, analysis, and use of computational procedures for solving differential equations. Topics covered include ordinary differential equations (both initial value and boundary value problems) and partial differential equations. Runge-Kutta and multistep methods for initial value problems. Finite difference methods for partial differential equations including techniques for heat conduction, wave propagation, and potential problems. Basic convergence and stability theory.
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800.
When Offered: Spring term annually.
Cross Listed: Cross listed as CSCI 4820. Students cannot obtain credit for both this course and CSCI 4820.
Credit Hours: 4
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MATH 4940 - Readings in Mathematics
Credit Hours: 1 to 4
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MATH 4950 - Senior Research
Undergraduate mathematics projects that utilize students’ mathematical knowledge will result in formal reports and final presentations. Examples are research projects or critical in-depth mathematical literature reviews. Information about projects will be exchanged in weekly meetings. Students wishing to work on research should make arrangements with faculty in advance. Students already engaged in research may extend and present their results. This is a communication-intensive course. To be graded S/U.
Prerequisites/Corequisites: Prerequisite: Open to mathematics seniors only.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4960 - Topics in Mathematics
Credit Hours: 1 to 4
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MATH 4980 - Undergraduate Project in Mathematics
Credit Hours: 1 to 4
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MATH 6190 - Topics from Pure Mathematics
The course is intended to provide a mathematical perspective on one or more topics chosen from algebra, geometry, and/or topology. Topics may include combinatorial matrix theory, classification of surfaces, Lie groups, Galois theory, geometric analysis, computational geometry, homology, and/or fixed point theorems.
Prerequisites/Corequisites: Prerequisites: Vary with topic.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6200 - Real Analysis
A careful study of measure theory, including abstract and Lebesgue measures and integration, absolute continuity and differentiation, L^p spaces, Fourier transforms and Fourier series, Hilbert spaces and normed linear spaces.
Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6220 - Introduction to Functional Analysis
A basic course in the concepts of linear functional analysis, including such topics as linear functionals, bounded linear operators, unbounded linear operators, graphs, adjoints, spectral theory of linear operators, and applications to differential equations and mathematical physics.
Prerequisites/Corequisites: Prerequisites: MATH 4210, MATH 4300, or permission of instructor; MATH 6200 or equivalent also desirable.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 6240 - Functional Analysis and Analysis for Nonlinear Operators
A continuation of material presented in MATH 6220. Covers such topics as inverse and implicit function theorems, fixed point theorems, Riesz bases, distributions and Sobolev spaces, variational methods, degree theory, and applications to differential equations.
Prerequisites/Corequisites: Prerequisite: MATH 6220 or equivalent or permission of instructor.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 6300 - Complex Analysis
A basic graduate course covering Cauchy’s Theorem, residues, infinite series and products, partial fractions, conformal mapping and the Riemann mapping theorem, analytic continuation, zeros and growth of analytic functions, approximation by rational functions, Phragmen-Lindelof Theorems, inverse-scattering theory, elliptic functions, and Riemann Surfaces.
Prerequisites/Corequisites: Prerequisites: MATH 4210 and MATH 4300 or equivalent or permission of instructor.
When Offered: Fall term odd-numbered years.
Credit Hours: 4
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MATH 6400 - Ordinary Differential Equations
A basic graduate course introducing the fundamental concepts of modern evolution equations theory in the setting of ordinary differential equations. Topics include existence and uniqueness, integral equations, stability of equilibria, stable manifolds, Floquet theory, Poincare-Bendixson theory, bifurcation theory, center manifolds, normal forms, averaging theory, Hamiltonian mechanics and calculus of variations, chaotic dynamics, KAM theory, and soliton theory.
Prerequisites/Corequisites: Prerequisite: MATH 4400 or permission of instructor.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6490 - Topics in Ordinary Differential Equations
Mathematical foundations and/or applications of ordinary differential equations. Possible topics include: stability and chaos in dynamics, mathematical methods of classical mechanics, stochastic differential equations, and soliton equations. Listing of topics offered to date.
Prerequisites/Corequisites: Prerequisites: Vary with topic.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 6500 - Partial Differential Equations
A course dealing with the basic theory of partial differential equations. It includes such topics as properties of solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables; linear and nonlinear first order equations; existence and uniqueness theory for general higher order equations; potential theory and integral equations.
Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 6590 - Topics in Partial Differential Equations
Mathematical foundation and/or applications of partial differential equations. Possible topics include soliton theory and applications, wavelets and PDEs, scattering theory, hyperbolic conservation laws.
Prerequisites/Corequisites: Prerequisites: Vary with topic.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 6600 - Methods of Applied Mathematics
Linear vector spaces; eigenvalues and eigenvectors in discrete systems; eigenvalues and eigenvectors in continuous systems including Sturm-Liouville theory, orthogonal expansions and Fourier series, Green’s functions; elementary theory of nonlinear ODEs including phase plane, stability and bifurcation; calculus of variations. Applications will be drawn from equilibrium and dynamic phenomena in science and engineering.
Prerequisites/Corequisites: Prerequisites: MATH 2400 and MATH 4600.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 6620 - Perturbation Methods
This course is devoted to advanced methods rather than theory. Content includes such topics as matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations. The methods are illustrated using currently interesting scientific and engineering problems that involve such phenomena as boundary or shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.
Prerequisites/Corequisites: Prerequisites: MATH 2400 and MATH 4600 or equivalent.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6640 - Complex Variables and Integral Transforms with Applications
Review of basic complex variables theory; power series, analytic functions, singularities, and integration in the complex plane. Integral transforms (Laplace, Fourier, etc.) in the complex plane, with application to solution of PDEs and integral equations. Asymptotic expansions of integrals (Laplace method, methods of steepest descent and stationary phase), with emphasis on extraction of useful information from inversion integrals of transforms. Problems to be drawn from linear models in science and engineering.
Prerequisites/Corequisites: Prerequisites: MATH 4600 and familiarity with elementary ordinary and partial differential equations.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 6660 - Stochastic Processes and Modeling
A course which will introduce methods and concepts to model and analyze the dynamics of system with uncertain inputs or too many variables to track explicitly. Topics may include Markov processes, point processes, renewal processes, and/or stochastic differential equations. Applications will be developed and illustrated on examples drawn from physics, biology, chemistry, industry, and finance.
Prerequisites/Corequisites: Prerequisites: MATH 2400
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6740 - Financial Mathematics and Simulation
This course is the second mathematical and computational finance course in a new one-year sequence for mathematics, DSES and engineering majors, and graduate students. It will cover the basics of stochastic processes, and current methods in the simulation of stochastic problems such as Monte Carlo algorithms and variance reduction tools. It will also focus on teaching the application of these stochastic simulation methods to finance.
Prerequisites/Corequisites: Prerequisite: MATH 4740.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 6790 - Topics in Applied Mathematics
Advanced methods and/or applications of mathematics. Possible topics include: nonlinear continuum mechanics, nonlinear waves, inverse problems, nonlinear optics, combustion, acoustic wave propagation, similarity methods for differential equations, quantum field theory and statistical mechanics, stability of fluid flows, biomathematics, and finance.
Prerequisites/Corequisites: Prerequisites: Vary with topic.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 6800 - Computational Linear Algebra
Gaussian elimination, special linear systems (such as positive definite, banded, or sparse), introduction to parallel computing, iterative methods for linear systems (such as conjugate gradient and preconditioning), QR factorization and least squares problems, and eigenvalue problems.
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800 or permission of instructor.
When Offered: Fall term annually.
Cross Listed: Cross listed as CSCI 6800. Students cannot obtain credit for both this course and CSCI 6800.
Credit Hours: 4
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MATH 6820 - Numerical Solution of Ordinary Differential Equations
Numerical methods and analysis for ODEs with applications from mechanics, optics, and chaotic dynamics. Numerical methods for dynamical systems include Runge-Kutta, multistep and extrapolation techniques, methods for conservative and Hamiltonian systems, methods for stiff differential equations and for differential-algebraic systems. Methods for boundary value problems include shooting and orthogonalization, finite difference and collocation techniques, and special methods for problems with boundary or shock layers.
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800 or permission of instructor.
When Offered: Spring term odd-numbered years.
Cross Listed: Cross listed as CSCI 6820. Students cannot obtain credit for both this course and CSCI 6820.
Credit Hours: 4
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MATH 6840 - Numerical Solution of Partial Differential Equations
Numerical methods and analysis for linear and nonlinear PDEs with applications from heat conduction, wave propagation, solid and fluid mechanics, and other areas. Basic concepts of stability and convergence (Lax equivalence theorem, CFL condition, energy methods). Methods for parabolic problems (finite differences, method of lines, ADI, operator splitting), methods for hyperbolic problems (vector systems and characteristics, dissipation and dispersion, shock capturing and tracking schemes), methods for elliptic problems (finite difference and finite volume methods).
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800 or permission of Instructor.
When Offered: Fall term odd-numbered years.
Cross Listed: Cross listed as CSCI 6840. Students cannot obtain credit for both this course and CSCI 6840.
Credit Hours: 4
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MATH 6860 - Finite Element Analysis
Galerkin’s method and extremal principles, finite element approximations (Lagrange, hierarchical and 3-D approximations, interpolation errors), mesh generation and assembly, adaptivity (h-, p-, hp-refinement). Error analysis and convergence rates. Perturbations resulting from boundary approximation, numerical integration, etc. Time dependent problems including parabolic and hyperbolic PDEs. Applications will be selected from several areas including heat conduction, wave propagation, potential theory, and solid and fluid mechanics.
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800 or permission of instructor.
When Offered: Spring term even-numbered years.
Cross Listed: Cross listed as CSCI 6860. Students cannot obtain credit for both this course and CSCI 6860.
Credit Hours: 4
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MATH 6890 - Topics in Computational Mathematics
Advanced methods and/or applications in scientific computing. Possible topics include computational fluid dynamics, parallel computing, computational acoustics, and computer applications in medicine and biology.
Prerequisites/Corequisites: Prerequisites: Vary with topic.
When Offered: Fall term even-numbered years.
Credit Hours: 4
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MATH 6940 - Readings in Mathematics
Credit Hours: 1 to 4
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MATH 6950 - Teaching Seminar for Teaching Assistants
A seminar required for first-year TAs in mathematics.
Prerequisites/Corequisites: Prerequisite: first-year math TA.
When Offered: Fall term annually.
Credit Hours: 1
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MATH 6951 - Introduction to Research in Mathematics
This seminar introduces first-year graduate students in mathematics to the faculty and their research. Each week a different faculty member from math will give introductory presentations of their current research areas in a setting that is conducive for significant student-faculty discussions of the material.
Prerequisites/Corequisites: Prerequisite: Graduate student in mathematics.
When Offered: Spring term annually.
Credit Hours: 1
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MATH 6960 - Topics in Mathematics
Credit Hours: 1 to 4
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MATH 6970 - Master’s Practicum in Mathematics
Active participation in a professional experience in mathematics, under the supervision of a faculty adviser. A Master’s Practicum may serve as the capstone professional experience for the M.S. degree. A Master’s Practicum may result in documentation as required by the adviser, but is not submitted to the Office of Graduate Education and is not archived in the library. Grades of A, B, C, or F are assigned if credit is awarded for the Master’s Practicum.
Credit Hours: 0 to 6
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MATH 6980 - Master’s Project
Active participation in a master’s-level project under the supervision of a faculty adviser, leading to a master’s project report. Grades of IP are assigned until the master’s project has been approved by the faculty adviser. If recommended by the adviser, the master’s project may be accepted by the Office of Graduate Education to be archived in the Library. Grades will then be listed as S.
Credit Hours: 1 to 6
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MATH 9990 - Dissertation
Active participation in research, under the supervision of a faculty adviser, leading to a doctoral dissertation. Grades of IP are assigned until the dissertation has been publicly defended, approved by the doctoral committee, and accepted by the Office of Graduate Educationl to be archived in a standard format in the library. Grades will then be listed as S.
Credit Hours: Variable
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MATP 4600 - Probability Theory and Applications
Axioms of probability, joint and conditional probability, random variables, probability density and distribution functions, expectation, functions of random variables, and limit theorems. Applications of probability to models in operations research, including queuing theory and Markov chains.
Prerequisites/Corequisites: Prerequisite: MATH 1020 or equivalent or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATP 4620 - Mathematical Statistics
A course in the theory of statistics that will provide students with a basic foundation for more specialized statistical methodology courses. Topics include sampling and sampling distributions; point estimation including method of moments, maximum likelihood estimation, uniform minimum variance estimation, and properties of the associated estimators; hypothesis testing including uniformly most powerful, likelihood ratio, chi-square goodness-of-fit tests, and tests for independence. The course concludes with an introduction to linear statistical models.
Prerequisites/Corequisites: Prerequisite: MATP 4600 or equivalent calculus-based course.
When Offered: Spring term annually.
Cross Listed: Cross listed as ISYE 4760. Students cannot obtain credit for both this course and ISYE 4760.
Credit Hours: 4
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MATP 4700 - Mathematical Models of Operations Research
Introduction to deterministic models of operations research including linear programming formulations, the simplex algorithm, degeneracy, geometry of convex polyhedra, duality theory, and sensitivity analysis. Special linear programming models for assignment, transportation, and network problems. Integer programming formulations along with branch and bound solution. Dynamic programming.
Prerequisites/Corequisites: Prerequisites: MATH 1020, and MATH 2010 or ENGR 1100, or equivalent, or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATP 4820 - Computational Optimization
An introduction to nonlinear programming. Models, methods, algorithms, and computer techniques for nonlinear optimization are studied. Students investigate contemporary optimization methods both by implementing these methods and through experimentation with commercial software. Nonmajors wishing to gain practical optimization skills are welcomed in this course. A course project will allow students to explore optimization methods and practical problems directly related to their interests.
Prerequisites/Corequisites: Prerequisites: MATH 2010 or ENGR 1100, and CSCI 1100 or permission of instructor.
When Offered: Spring term annually.
Cross Listed: Students cannot obtain credit for both this course and MATP 6610.
Credit Hours: 4
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MATP 4940 - Readings in Mathematical Programming, Probability, and Mathematical Statistics
Credit Hours: 1 to 4
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MATP 4960 - Topics in Mathematical Programming, Probability, and Mathematical Statistics
Credit Hours: 1 to 4
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MATP 4980 - Undergraduate Project in Mathematical Programming, Probability, and Mathematical Statistics
Credit Hours: 1 to 4
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MATP 6600 - Nonlinear Programming
Convex sets and functions, optimality conditions in nonlinear programming, Lagrangian duality, quadratic programming; algorithms for nonlinear programming including Newton’s method, quasi-Newton methods, conjugate gradient methods, together with proofs of convergence.
Prerequisites/Corequisites: Prerequisite: MATH 4200 or equivalent or permission of instructor.
When Offered: Fall term annually.
Cross Listed: Cross listed as ISYE 6780. Students cannot obtain credit for both this course and ISYE 6780.
Credit Hours: 4
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MATP 6610 - Computational Optimization
An introduction to nonlinear programming. Models, methods, algorithms, and computer techniques for nonlinear optimization are studied. Students investigate contemporary optimization methods both by implementing these methods and through experimentation with commercial software. Nonmajors wishing to gain practical optimization skills are welcomed in this course. A course project will allow students to explore optimization methods and practical problems directly related to their interests. A computer implementation and a research presentation will be required. Students cannot obtain credit for both this course and MATP 4820.
When Offered: Spring term annually.
Credit Hours: 4
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MATP 6620 - Combinatorial Optimization and Integer Programming
Exact and heuristic methods for solving discrete problems, including the traveling salesman problem, the knapsack problem, packing and covering problems. Algorithm complexity and NP-completeness, cutting plane methods and polyhedral theory, branch and bound, simulated annealing, tabu search, Lagrangian duality.
Prerequisites/Corequisites: Prerequisite: MATP 4700.
When Offered: Spring term odd-numbered years.
Cross Listed: Cross listed as ISYE 6760. Students cannot obtain credit for both this course and ISYE 6760.
Credit Hours: 4
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MATP 6640 - Linear Programming
A unified development of linear systems and linear programming, polyhedral theory, the simplex method, interior point methods, decomposition methods for large-scale linear programming problems, the ellipsoid method, column generation algorithms for stochastic programming, and other problems.
Prerequisites/Corequisites: Prerequisite: MATP 4700.
When Offered: Spring term even-numbered years.
Cross Listed: Cross listed as ISYE 6770. Students cannot obtain credit for both this course and ISYE 6770.
Credit Hours: 4
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MATP 6940 - Readings in Mathematical Programming, Probability, and Mathematical Statistics
Credit Hours: 1 to 4
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MATP 6960 - Topics in Optimization
Advanced methods and/or applications in optimization. Possible topics include stochastic programming, learning theory, cone programming, optimization of medical treatment, and network flows.
Prerequisites/Corequisites: Prerequisites: Vary with topics and/or instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATP 6980 - Master’s Project
Active participation in a master’s-level project under the supervision of a faculty adviser, leading to a master’s project report. Grades of IP are assigned until the master’s project has been approved by the faculty adviser. If recommended by the adviser, the master’s project may be accepted by the Office of Graduate Education to be archived in the Library.
Graded: Grades will then be listed as S.
Credit Hours: 1 to 6
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MGMT 69xx - Organizational Design and Change
This course is focused on developing, evolving, and managing organizations during high impact change involving advanced and disruptive technology. The primary focus is on managing change, reimagining business processes, and designing organizational structures that can compete in the era of globalization. This includes understanding the importance of cultural differences, an entrepreneurial mindset, and the role of innovation.
When Offered: Spring term annually.
Credit Hours: 3
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MGMT 696X - Craig Professional Development Seminar
This course assists students in developing those skills and techniques needed to be an effective manager. Topics include business writing and communication, presentation skills, agenda setting and meeting skills, stress management, and time management.
Credit Hours: 0
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MGMT 1100 - Introduction to Management
This is a required first course for management majors and minors. In a case-based format, it emphasizes broad, basic principles of managerial functions and processes using an interdisciplinary approach to goal-oriented situations of private and public organizations. This is a communication-intensive course.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MGMT 1240 - Management Leadership I
The overall content focuses on skills, body of knowledge, and theories of leadership development. It involves discussion and practice to give students well-rounded skills necessary for personal and professional success. The course emphasizes the following themes: communication, ethics, values and self-awareness, leadership and followership.
When Offered: Fall and spring sequences annually.
Credit Hours: 2
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MGMT 1250 - Management Leadership II
The overall content focuses on skills, body of knowledge, and theories of leadership development. It involves discussion and practice to give students well-rounded skills necessary for personal and professional success. The course emphasizes the following themes: communication, ethics, values and self-awareness, leadership and followership.
When Offered: Fall and spring sequences annually.
Credit Hours: 2
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MGMT 1260 - Business Law and Ethics
This course focuses on legal and ethical considerations in management. Topics include torts, contracts, criminal and property law, constitutional and administrative law, dispute resolution, business formation, and equal opportunity. Students will also develop an awareness of ethics in managerial decision making, including recognizing and analyzing ethical issues in the workplace, promoting ethical behavior in corporations and recognizing social responsibilities of business.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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