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Linguistics |
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LING 506 - Syntax and Semantics
Analyzes and describes sentence structure and its relationship to meaning. (IR)
Prerequisites & Notes
Prerequisite: LNGS 325 and permission of the instructor.
Credits: 3
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LING 507 - Syntactic Theory
Studies the major schools of syntactic theory. (SI)
Prerequisites & Notes
Prerequisite: LNGS 325 and permission of the instructor.
Credits: 3
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LING 509 - Teaching English as a Second Language
Studies the theory, problems, and methods in teaching English as a second language, focusing on relevant areas of general linguistics and the structure of English. (Y)
Prerequisites & Notes
Prerequisite: LNGS 701 and instructor permission.
Credits: 3
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LING 510 - Teaching Practicum - ESL
Credits: 1 to 3
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LING 525 - Romance Linguistics
Studies the vulgar Latin origins and patterns of linguistic change in the principal Romance languages. (SI)
Credits: 3
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LING 526 - Romance Linguistics
Studies the vulgar Latin origins and patterns of linguistic change in the principal Romance languages. (SI)
Credits: 3
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LING 545 - Language Learning and Teaching
Credits: 3
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LING 591 - Grammatical Concepts in Foreign Language Learning
Explores tense, mode, voice, subject, object, and predicate, and their applications in various languages. (O)
Credits: 3
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LING 601 - Between Two Cultures, Between Two Languages
Virginia teachers examine the relationship of language to culture and the motivational differences between native and non-native speakers learning standard English. (SS)
Credits: 2
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LING 897 - Non-Topical Research
Non-Topical Research
Credits: 3
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LING 898 - Non-Topical Research
Non-Topical Research
Credits: 3
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LING 901 - Directed Research
Special Areas Students should choose electives in one or more of the following areas: anthropology, Asian and Middle Eastern languages and Cultures, comparative Latin and Greek, English language study, Germanic linguistics, Indic linguistics, philosophy, psychology, Romance linguistics, Slavic linguistics. (S)
Credits: 3
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LING 902 - Directed Research
Special Areas Students should choose electives in one or more of the following areas: anthropology, Asian and Middle Eastern languages and Cultures, comparative Latin and Greek, English language study, Germanic linguistics, Indic linguistics, philosophy, psychology, Romance linguistics, Slavic linguistics. (S)
Credits: 3
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Management of Information Technology |
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GCOM 779 - IT Architecture
The IT Architecture course provides broad foundations for understanding the core information technologies that support today’s businesses. The class provides long lasting knolwedge of enterprise architectures, databases, business processes, and networks, at level of detail that is appropriate for IT managers. Students in GCOMM 779 learn how to envision IT infrastructures and applications that meet the needs of the business enterprise and add economic value.
Prerequisites & Notes
Mod 1 - 2
Credits: 6
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GCOM 780 - Advanced IT Architecture
Building on the foundations provided in GCOMM 779, this class fosters insights in contemporary IT architectures trends. Sample topics include security, components architectures, and emerging technologies. Students envision a business-value-adding initiative based on the use of modern information technology, describe their initiative by creating several architectural artifacts (e.g., process models and information models), and present it to an audience of tech-savvy leaders.
Prerequisites & Notes
Mod 1 - 2
Credits: 3
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GCOM 781 - Innovation and Technology Management
GCOM 781 develops a deeper understanding of how to manage IT for the creation of business value through an intensive focus on strategic and financial issues. IT professionals can make better decisions when they understand the specific kinds of value created by IT for the end consumers of the products and services provided by the firm, and the ways in which that value produces financial returns for the firm. By analyzing a firm’s industry and its competitive position within that industry, students learn how to producing technologies that can have an important impact on the firm’s competitive position.
Prerequisites & Notes
Mod 4 - 6
Credits: 3
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GCOM 783 - IT Project Management
This course is designed to develop more effective project managers through its coverage of concepts, techniques, and technologies relevant to the manager of an IT project. To this end, the module is closely tied to the requisite body of knowledge espoused by the Project Management Institute (PMBOK) and consists of seminars on such topics as planning (including integration & scope management), estimation & scheduling, cost management, risk management, sourcing and vendor management, portfolio management, project recovery, change management, and measuring project value; workshops on managerial communication; and tutorials on project management tools. In addition, student teams conduct a project retrospective over the course of the module for class presentation.
Prerequisites & Notes
Mod 2 - 3
Credits: 6
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GCOM 784 - Strategic Management of IT
Through readings, classes, and projects, GCOM 784 will develop your skills in discovering, describing, and securing management support for new IT-based initiatives operating within an existing IT organization. While IT has the potential to enhance operational efficiency, in this course we focus instead on identifying opportunities that are more transformational in nature. Projects of this sort have the potential to impact how an organization pursues its strategic goals, and in some cases may also suggest shifts in strategy to pursue new opportunities that are compatible with the firm’s resources and capabilities. Students will become comfortable in the role of internal IT entrepreneur – someone who can see how developments in information technologies can open up new strategic possibilities for how their organizations choose to compete, and who can package those ideas in compelling ways.
Prerequisites & Notes
Mod 4 - 7
Credits: 6
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GCOM 785 - Enterprise IT Management
GCOM 785 teaches the body of knowledge associated with IT Enterprise Management, using enterprise decision making as the conceptual framework. Enterprise IT management represents a wide range of activities, and in this class students will learn how to develop and manage strategies for operations and business continuity, data management, data integration, process integration, and compliance. Lectures, case discussions, projects, and workshops provide the students with opportunities to hone their skills in this area.
Prerequisites & Notes
Mod 3 -4
Credits: 3
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GCOM 786 - Advanced Enterprise IT Management
GCOM 786 teaches IT Enterprise Management applications and special topics, with an emphasis on using the IT enterprise to deliver value to the organization. Students will experience lectures, case discussions, projects, and workshops to learn about enterprise decision making, knowledge management, business intelligence, and other enterprise management-related special topics.
Credits: 3
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Materials Science and Engineering |
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MSE 601 - Electronic and Crystal Structure of Materials
Provides a fundamental understanding of the structure of crystalline and non-crystalline engineering materials from electronic to macroscopic properties. Topics include symmetry and crystallography, the reciprocal lattice and diffraction, quantum physics, bonding and band theory. (Y)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 602 - Defects and Microstructure in Materials
Basic course designed to provide a foundation for correlating defect structure and microstructure with physical, mechanical and chemical properties of engineering materials. The fundamental properties of point, line and surface defects in ordered media will be formulated. The thermodynamics of point defects in various types of solids will be discussed as well as the geometry and mechanics of crystal dislocations and their role in crystal plasticity elucidated. The essential elements of microstructure will be characterized emphasizing the concepts of phase constitution, microconstituent, polycrystalline aggregate and multiphase materials. The concept of real materials embodying a hierarchy of structures is emphasized. The principles governing the genesis and stability of material structure at various levels will be discussed. (Y)
Prerequisites & Notes
Prerequisite: MSE 601 and MSE 623.
Credits: 3
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MSE 604 - Scanning Electron Microscopy and Related Techniques
Covers the physical principles of scanning electron microscopy and electron probe microanalysis. Laboratory demonstrations and experiments cover the operation of the SEM and EPMA. Applications of secondary and backscattered electron imaging, energy dispersive x-ray microanalysis, wave- analysis are applied to materials characterization. Laboratory experiments may include either materials science or biological applications, depending on the interests of the student. (SS)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 605 - Structure and Properties of Materials I
This is the first of a sequence of two basic courses for first-year graduate students or qualified undergraduate students. Topics include atomic bonding, crystal structure, and crystal defects in their relationship to properties and behavior of materials (polymers, metals, and ceramics); phase equilibria and non-equilibrium phase transformation; metastable structures; solidification; and recrystallization. (Y)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 606 - Structure and Properties of Materials II
This is the second of a two-course sequence for the first-year graduate and qualified undergraduate students. Topics include diffusion in solids; elastic, anelastic, and plastic deformation; and electronic and magnetic properties of materials. Emphasizes the relationships between microscopic mechanisms and macroscopic behavior of materials. (Y)
Prerequisites & Notes
Prerequisite: MSE 605 or instructor permission.
Credits: 3
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MSE 608 - Chemical and Electrochemical Properties
Introduces the concepts of electrode potential, double layer theory, surface charge, and electrode kinetics. These concepts are applied to subjects that include corrosion and embrittlement, energy conversion, batteries and fuel cells, electro-catalysis, electroanalysis, electrochemical industrial processes, bioelectrochemistry, and water treatment. (Y)
Prerequisites & Notes
Prerequisite: Physical chemistry course or instructor permission.
Credits: 3
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MSE 610 - Nanomaterials
Introduces relevant concepts governing the synthesis, science, and engineering of nanomaterials. Course modules cover the fundamental scientific principles controlling assembly of nanostructured materials; the types of nanomaterials that are extant; synthesis, measurement and computational tools; new properties at the nanoscale, and existing and emerging applications of nanomaterials. (IR)
Credits: 3
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MSE 614 - Magnetism and Magnetic Materials
Fundamental course on the principles governing the behavior of modern magnetic materials employed in technology from transformer materials to permanent magnets and magnetic recording media including such new areas as nanomagnetism. The approach integrates the basic physics of magnetism with the materials science paradigm of processing-structure-properties-performance. The subject matter is developed at a level to enable students to understand magnetism and magnetic materials at the forefront of the field and to readily read the current research and technological literature. (Y)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 623 - Thermodynamics and Phase Equilibria of Materials
Emphasizes the understanding of thermal properties such as heat capacity, thermal expansion, and transitions in terms of the entropy and the other thermodynamic functions. Develops the relationships of the Gibbs and Helmholtz functions to equilibrium systems, reactions, and phase diagrams. Atomistic and statistical mechanical interpretations of crystalline and non-crystalline solids are linked to the general thermodynamical laws by the partition function. Nonequilibrium and irreversible processes in solids are discussed. (Y)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 624 - Kinetics of Transport and Transformations in Materials
An introduction to basic kinetic processes in materials and develops basic mathematical skills necessary for materials research. Students learn to formulate the partial differential equations and boundary conditions used to describe basic materials phenomena in the solid state including mass and heat diffusion in single- and two-phase systems, the motion of planar phase boundaries, and interfacial reactions. Students develop analytical and numerical techniques for solving these equations and apply them to understanding microstructural evolution. (Y)
Prerequisites & Notes
Prerequisite: MSE 623.
Credits: 3
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MSE 627 - Introduction to Atomistic Simulations
Introduction to several classical atomic-level simulation techniques (molecular dynamics, Metropolis and kinetic Monte Carlo). The basic concepts, capabilities and limitations of the methods are discussed, an overview of the current state-of-the-art is provided, and examples of recent success stories are considered. The emphasis of the course is on getting practical experience in designing and performing computer simulations. Students use and modify pre-written codes and write their own simulation and data analysis codes. (Y)
Prerequisites & Notes
Prerequisite: Basic knowledge/experience in computer programming or instructor permission.
Credits: 3
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MSE 632 - Deformation and Fracture of Structural Materials
Deformation and fracture are considered through integration of materials science microstructure and solid mechanics principles over a range of length scales, emphasizing the mechanical behavior of metallic-structural alloys and electronic materials. Metal deformation is understood based on elasticity theory and dislocation concepts. Fracture is understood based on continuum fracture mechanics and microstructural damage mechanisms. Additional topics include fatigue, elevated temperature behavior, material embrittlement, time-dependency, experimental design, damage-tolerant life prognosis, small-volume behavior, and material property modeling. (Y)
Prerequisites & Notes
Prerequisite: MSE 432, or BS in MSE, or MSE 605, or permission of instructor for graduate students outside of MSE.
Credits: 3
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MSE 635 - Physical Metallurgy of Light Alloys
Develops the student’s literacy in aluminum and titanium alloys used in the aerospace and automotive industries. Considers performance criteria and property requirements from design perspectives. Emphasizes processing-microstructure development, and structure-property relationships. (E)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 647 - Physical Metallurgy of Transition-Element Alloys
Reinforces fundamental concepts, introduces advance topics, and develops literacy in the major alloy systems. Emphasizes microstructural evolution by composition and thermomechanical process control. Topics include phase diagrams, transformation kinetics, martensitic transformation, precipitation, diffusion, recrystallization, and solidification. Considers both experimental and model-simulation approaches. (O)
Prerequisites & Notes
Prerequisite: MSE 606 or instructor permission.
Credits: 3
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MSE 665 - Electronic, Magnetic and Optical Properties of Materials
Explore the fundamental physical laws governing electrons in solids, and show how that knowledge can be applied to understanding electronic, optical and magnetic properties. Students will gain an understanding of how these properties vary between different types of materials, and thus why specific materials are optimal for important technological applications. (Y)
Credits: 3
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MSE 667 - Semiconductor Materials and Devices
Provides an understanding of the fundamentals, materials, and engineering properties of semiconductors; and the integration of semiconductors with other materials to make optoelectronic and microelectronic devices. Topics include basic properties of electrons in solids; electronic, optical, thermal and mechanical properties of semiconductors; survey of available semiconductors and materials choice for device design; fundamental principles of important semiconductor devices; sub-micron engineering of semiconductors, metals, insulators and polymers for integrated circuit manufacturing; materials characterization techniques; and other electronic materials. Cross-listed as ECE 667. (Y)
Prerequisites & Notes
Prerequisite: Some background in solid state materials and elementary quantum principles.
Credits: 3
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MSE 692 - Topics in Material Science
A study of special subjects related to developments in materials science under the direction of members of the staff. Offered as required under the guidance of a faculty member. (SI)
Credits: 3
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MSE 694 - Characterization of Materials
Provides a fundamental understanding of a broad spectrum of techniques utilized to characterize properties of solids. The methods used to assess properties are described through integration of the basic principles and application. Methods more amenable to analysis of bulk properties are differentiated from those aimed at measurements of local/surface properties. (SI)
Prerequisites & Notes
MSE 367 or equivalent, or a solid state materials/physics course.
Credits: 3
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MSE 695 - Supervised Project Research
Formal record of student commitment to project research for Master of Science or Master of Materials Science degree under the guidance of a faculty advisor. May be repeated as necessary. (S)
Credits: 1-12
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MSE 702 - Materials Science Seminar
Broad topics and in-depth subject treatments are presented. The course is related to research areas in materials science and involves active student participation. (S)
Credits: 1
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MSE 703 - Transmission Electron Microscopy
Emphasizes the fundamental principles of transmission electron microscopy and illustrates its capabilities for characterizing the internal structures of materials by diffraction, imaging and spectroscopic techniques; includes weekly laboratory exercises. (Y)
Prerequisites & Notes
Prerequisite: MSE 601 or instructor permission.
Credits: 3
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MSE 706 - Advanced Electron Microscopy
Emphasis placed on the applications of advanced techniques of transmission and scanning electron microscopy to modern research problems in materials science and engineering. Microdiffraction and microanalysis, lattice imaging, and convergent beam diffraction in TEM and STEM are treated. In SEM, quantitative probe analysis techniques and back scattered electron imaging and channeling are covered. (SI)
Prerequisites & Notes
Prerequisite: MSE 703 or instructor permission.
Credits: 3
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MSE 712 - Diffusional Processes in Materials
An introduction to elasticity theory, the thermodynamics of stressed crystals, and diffuse interface theory with application to understanding microstructural evolution in bulk materials and thin films. (SI)
Prerequisites & Notes
Prerequisite: MSE 623, 624.
Credits: 3
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MSE 714 - Physics of Materials
Basic course dealing with the physical principles governing the thermal, electronic, optical and magnetic properties of engineering materials. The approach integrates the fundamentals of materials science with essential concepts in solid state and condensed matter physics. Special attention is given to understanding the nature of the crystalline state and wave-particle diffraction with a strong emphasis on the reciprocal lattice concept. Thermal properties are approached by discussing the Einstein and Debye solids and the concept of lattice waves and phonons. The elements of Boltzmann, Bose-Einstein and Fermi-Dirac statistics are reviewed leading to the development of an electron theory of solids. The concepts of Fermi surface and Fermi energy, Brillouin zones, valence and conduction bands are discussed extensively. The atomic origin of magnetism and magnetic effects in solids are analyzed as well as magnetic hysteresis and technical magnetic properties. The fundamental electrical and magnetic properties of superconductors are discussed including the new high Tc ceramic materials. (SI)
Prerequisites & Notes
Prerequisite: MSE 665 or equivalent or instructor permission.
Credits: 3
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MSE 722 - Surface Science
Analyzes the structure and thermodynamics of surfaces, with particular emphasis on the factors controlling chemical reactivity of surfaces; adsorption, catalysis, oxidation, and corrosion are considered from both theoretical and experimental viewpoints. Modern surface analytical techniques, such as Auger, ESCA, and SIMS are considered. (SI)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 732 - Deformation and Fracture of Materials
Emphasizes the roles of defects, state of stress, temperature, strain rate, and environment on macroscopic mechanical behavior of materials, as well as nano-to-micro scale modeling of such responses. The first half of the course considers dislocation theory with application to understanding materials plasticity, strengthening mechanisms and creep. The second half develops tools necessary for advanced fatigue and fracture control in structural materials. Linear and nonlinear continuum fracture mechanics principles are developed and integrated with microscopic plastic deformation and fracture mechanisms. Topics include cleavage, ductile fracture, fatigue, environmental cracking and micromechanical modeling of governing properties. (SI)
Prerequisites & Notes
Prerequisite: MSE 632 or AM/MAE/CE/APMA 602 or instructor permission.
Credits: 3
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MSE 734 - Phase Transformations
Includes the fundamental theory of diffusional phase transformations in solid metals and alloys; applications of thermodynamics to calculation of phase boundaries and driving forces for transformations; theory of solid-solid nucleation, theory of diffusional growth, comparison of both theories with experiment; applications of thermodynamics and of nucleation and growth theory to the principal experimental systematics of precipitation from solid solution, the massive transformations, the cellular and the pearlite reactions, martensitic transformations, and the questions of the role of shear in diffusional phase transformations. (SI)
Prerequisites & Notes
Prerequisite: MSE 623 or comparable thermodynamics.
Credits: 3
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MSE 741 - Crystal Defect Theory
Studies the nature and major effects of crystal defects on the properties of materials, emphasizing metals. The elasticity theory of dislocations is treated in depth. (SI)
Prerequisites & Notes
Prerequisite: MSE 601 and 602 or instructor permission.
Credits: 3
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MSE 757 - Materials Processing
Discusses scientific and technological bases of material processing. Examines solidification, deformation, particulate and thermomechanical processing from a fundamental point of view and discusses their current technological applications. (SI)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 771 - Advanced Electrochemistry
A highly-specialized course detailing specific subject matter in the areas of corrosion of stainless steel, cyclic voltammetry, and the adsorption of hydrogen on and diffusion of hydrogen through Palladium. Associated experimental methods are discussed. (SI)
Credits: 3
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MSE 792 - Advanced Topics in Materials Science
An advanced level study of special topics related to developments in materials science. (SI)
Prerequisites & Notes
Prerequisite: Instructor permission.
Credits: 3
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MSE 793 - Independent Study
Detailed study of graduate course material on an independent basis under the guidance of a faculty member. (S)
Credits: 1-12
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MSE 795 - Supervised Project Research
Formal record of student commitment to project research for Doctor of Philosophy degree under the guidance of a faculty advisor. May be repeated as necessary. (S)
Credits: 1-12
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MSE 897 - Graduate Teaching Instruction-M.S.
For master’s students. (S)
Credits: 1-12
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MSE 898 - Masters Degree Research
Formal record of student commitment to master’s thesis research under the guidance of a faculty advisor. May be repeated as necessary. (S)
Credits: 1-12
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MSE 997 - Graduate Teaching Instruction-Ph.D.
For doctoral students. (S)
Credits: 1-12
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MSE 999 - PHD Dissertation Research
Formal record of student commitment to doctoral research under the guidance of a faculty advisor. May be repeated as necessary. (S)
Credits: 1-12
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Mathematics |
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MATH 501 - The History of the Calculus
Studies the evolution of the various mathematical ideas leading up to the development of calculus in the 17th century, and how those ideas were perfected and extended by succeeding generations of mathematicians. Emphasizes primary source materials. (E)
Prerequisites & Notes
Prerequisite: MATH 231 and 351, or instructor permission.
Credits: 3
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MATH 503 - The History of Mathematics
Studies the development of mathematics from classical antiquity to the end of the 19th century, focusing on critical periods in the evolution of geometry, number theory, algebra, probability, and set theory. Emphasizes primary source materials. (O)
Prerequisites & Notes
Prerequisite: MATH 231 and 351, or instructor permission.
Credits: 3
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MATH 510 - Probability
Studies the development and analysis of probability models through the basic concepts of sample spaces, random variables, probability distributions, expectations, and conditional probability. Additional topics include distributions of transformed variables, moment generating functions, and the central limit theorem. (Y)
Prerequisites & Notes
Prerequisite: MATH 132 or equivalent, and graduate standing. Credit cannot be received for both MATH 310 and 510.
Credits: 3
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MATH 511 - Introduction to Stochastic Processes
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. (Y)
Prerequisites & Notes
Prerequisite: MATH 310 and a knowledge of matrix algebra, or instructor permission.
Credits: 3
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MATH 514 - Mathematics of Derivative Securities
Topics include arbitrage arguments, valuation of futures, forwards and swaps, hedging, option-pricing theory, and sensitivity analysis. (Y)
Prerequisites & Notes
Prerequisite: MATH 231 or 122 or its equivalent, and a knowledge of probability and statistics; MATH 310 or its equivalent is recommended.
Credits: 3
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MATH 521 - Advanced Calculus with Applied Mathematics
Includes vector analysis, Green’s, Stokes’, divergence theorems, conservation of energy, and potential energy functions. Emphasizes physical interpretation, Sturm-Liouville problems and Fourier series, special functions, orthogonal polynomials, and Green’s functions. (Y)
Prerequisites & Notes
Prerequisite: MATH 231, 325; 351 recommended.
Credits: 3
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MATH 522 - Partial Differential Equations and Applied Mathematics
Introduces partial differential equations, Fourier transforms. Includes separation of variables, boundary value problems, classification of partial differential equations in two variables, Laplace and Poisson equations, and heat and wave equations. (Y)
Prerequisites & Notes
Prerequisite: MATH 521; 351 recommended.
Credits: 3
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MATH 525 - Advanced Ordinary Differential Equations
Studies the qualitative geometrical theory of ordinary differential equations. Includes basic well posedness; linear systems and periodic systems; stability theory; perturbation of linear systems; center manifold theorem; periodic solutions and Poincaré-Bendixson theory; Hopf bifurcation; introduction to chaotic dynamics; control theoretic questions; differential geometric methods. (IR)
Prerequisites & Notes
Prerequisite: MATH 231, 325, 351 or instructor permission.
Credits: 3
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MATH 531 - Introduction to Real Analysis
The basic topology of Euclidean spaces; continuity, and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series. (Y)
Prerequisites & Notes
Prerequisite: MATH 231, 351.
Credits: 3
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MATH 533 - Real Analysis in Several Variables
Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes’ Theorem. (Y)
Prerequisites & Notes
Prerequisite: MATH 531.
Credits: 3
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MATH 534 - Complex Variables with Applications
Analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. (Y)
Prerequisites & Notes
Prerequisite: MATH 231 and graduate standing.
Credits: 3
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MATH 551 - Advanced Linear Algebra
Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory. (Y)
Prerequisites & Notes
Prerequisite: MATH 351 or instructor permission.
Credits: 3
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MATH 552 - Introduction to Abstract Algebra
Structural properties of basic algebraic systems such as groups, rings and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization and symmetric polynomials. Time permitting, such topics as group representations or algebras over a field may be included. (Y)
Prerequisites & Notes
Prerequisite: MATH 351 or551, or instructor permission.
Credits: 3
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MATH 553 - Number Theory
Includes congruences, quadratic reciprocity, Diophantine equations, and number-theoretic functions, among others. (O)
Prerequisites & Notes
Prerequisite: MATH 354 or instructor permission.
Credits: 3
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MATH 554 - Survey of Algebra
Surveys groups, rings, and fields, and presents applications to other areas of mathematics, such as geometry and number theory. Explores the rational, real, and complex number systems, and the algebra of polynomials. (Y)
Prerequisites & Notes
Prerequisite: MATH 132 or equivalent and graduate standing.
Credits: 3
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MATH 570 - Introduction to Geometry
Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. (O)
Prerequisites & Notes
Prerequisite: MATH 231, 351, or instructor permission.
Credits: 3
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MATH 572 - Introduction to Differential Geometry
Topics selected from the theory of curves and surfaces in Euclidean space and the theory of manifolds. (E)
Prerequisites & Notes
Prerequisite: MATH 231 and 351, or instructor permission.
Credits: 3
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MATH 577 - General Topology
Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projectives spaces, as well as an introduction to the fundamental group will be covered. (Y)
Prerequisites & Notes
Prerequisite: MATH 231 and 351, with 331 recommended.
Credits: 3
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MATH 583 - Seminar
Presentation of selected topics in mathematics. (SI)
Prerequisites & Notes
Prerequisite: MATH 531; corequisite: MATH 552 or instructor permission.
Credits: 3
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MATH 596 - Supervised Study in Mathematics
A rigorous program of supervised study designed to expose the student to a particular area of mathematics. (S)
Prerequisites & Notes
Prerequisite: Instructor permission and graduate standing.
Credits: 3
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MATH 700 - Seminar on College Teaching
Discussion of issues related to the practice of teaching, pedagogical concerns in college level mathematics, and aspects of the responsibilities of a professional mathematician. Credits may not be used towards a Master’s degree. (Y)
Prerequisites & Notes
Prerequisite: Graduate standing in mathematics.
Credits: 1 to 3
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MATH 701 - Seminar on Research in Mathematics
This seminar discusses the issues related to research in Mathematics. There are speakers from the different areas of mathematics represented at the University of Virginia. Credit may not be used towards a Master’s degree. (Y)
Prerequisites & Notes
Prerequisite: Graduate standing in mathematics.
Credits: 1 to 3
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MATH 725 - Ordinary Differential Equations and Dynamical Systems
Topics include well-posedness and stability of dynamical flows, attractors, invariant manifolds and their properties, and dissipative and Hamiltonian systems. (Y)
Prerequisites & Notes
Prerequisite: MATH 531 and linear algebra, or the equivalent.
Credits: 3
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MATH 731 - Real Analysis and Linear Spaces I
Introduces measure and integration theory. (Y)
Prerequisites & Notes
Prerequisite: MATH 531 or equivalent.
Credits: 4
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MATH 732 - Real Analysis and Linear Spaces II
Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. (O)
Prerequisites & Notes
Prerequisite: MATH 731, 734, or equivalent.
Credits: 3
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MATH 734 - Complex Analysis I
Studies the fundamental theorems of analytic function theory. (Y)
Credits: 4
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MATH 735 - Complex Analysis II
Studies the Riemann mapping theorem, meromorphic and entire functions, topics in analytic function theory. (O)
Prerequisites & Notes
Prerequisite: MATH 734 or equivalent.
Credits: 3
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MATH 736 - Probability Theory I
Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. (Y)
Prerequisites & Notes
Prerequisite: MATH 731 or equivalent.
Credits: 3
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MATH 741 - Functional Analysis I
Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. (Y)
Prerequisites & Notes
Prerequisite: MATH 734 and 731, or equivalent.
Credits: 3
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MATH 742 - Functional Analysis II
Studies the spectral theory of unbounded operators, semigroups, and distribution theory. (E)
Prerequisites & Notes
Prerequisite: MATH 741 or equivalent.
Credits: 3
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MATH 745 - Introduction to Mathematical Physics
An introduction to classical mechanics, with topics in statistical and quantum mechanics, as time permits. (IR)
Prerequisites & Notes
Prerequisite: MATH 531.
Credits: 3
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MATH 751 - Algebra I, II
Studies groups, rings, fields, modules, tensor products, and multilinear functions. (Y)
Prerequisites & Notes
Prerequisite: MATH 551, 552, or equivalent.
Credits: 4
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MATH 752 - Algebra I, II
Studies groups, rings, fields, modules, tensor products, and multilinear functions. (Y)
Prerequisites & Notes
Prerequisite: MATH 551, 552, or equivalent.
Credits: 4
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MATH 753 - Algebra III
Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. (Y)
Prerequisites & Notes
Prerequisite: MATH 751, 752, or equivalent.
Credits: 3
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MATH 754 - Algebra IV
Further topics in algebra. (Y)
Credits: 3
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MATH 760 - Homological Algebra
Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. (SI)
Prerequisites & Notes
Prerequisite: MATH 577.
Credits: 3
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MATH 780 - Algebraic Topology I
Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. (Y)
Prerequisites & Notes
Prerequisite: MATH 552, 577, or equivalent.
Credits: 3
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MATH 781 - Algebraic Topology II
Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. (Y)
Prerequisites & Notes
Prerequisite: MATH 780.
Credits: 3
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MATH 782 - Differential Topology
Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. (Y)
Prerequisites & Notes
Prerequisite: MATH 531, 577, or equivalent.
Credits: 3
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MATH 783 - Fiber Bundles
Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. (Y)
Prerequisites & Notes
Prerequisite: MATH 780.
Credits: 3
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MATH 784 - Homotopy Theory
Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead’s theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. (Y)
Prerequisites & Notes
Prerequisite: MATH 780.
Credits: 3
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MATH 825 - Partial Differential Equations
Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. (O)
Prerequisites & Notes
Prerequisites: MATH 741 and 725.
Credits: 3
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MATH 830 - Topics in Function Theory
Topics in real and complex function theory. (SI)
Credits: 3
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