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Law |
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LAW 9152 - African-American Lawyers from the Civil War to the Present
This seminar explores the history of the African-American lawyer from the nineteenth century to the present. Special attention is given to the place of the black lawyer in the African-American community, the relationship of black lawyers to the larger predominantly white legal community, and the role of black lawyers in the Civil Rights Movement.
Credits: 3
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LAW 9153 - Regulating Public Space
This seminar will explore how law creates public space and non-law actors police, regulate, and contest it. The course brings both historical and theoretical perspectives to bear on street-level crime control strategies, including the uses and abuses of vagrancy, stop-and-frisk,drug possession, and gang loitering laws.
Credits: 3
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LAW 9154 - Money and Rights
This seminar will explore the relationship between money and rights.
Credits: 3
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LAW 9155 - Sovreign Debt Crises
This seminar will examine the sovereign debt crises now unfolding across much of North America and Europe. Attention will be paid to three different groups of sovereign entities.
Credits: 3
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LAW 9156 - Advanced Campaign Finance
This seminar examines the variety of laws governing the ways money is raised and spent on political campaigns in America. Specific focus will be brought to the rules governing candidate committees, political party committees, independent expenditures and issue advocacy, as well as donor-focused restrictions such as ¿pay to play¿ limitations and particular limits on lobbyists and government contractors.
Credits: 3
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LAW 9157 - Citizenship and Group Identity
This seminar will explore the various forms of citizenship and membership reflected in law. We will consider theories of citizenship and nationalism, examine closely the history of citizenship law in the United States, and compare how citizenship is conceived of and debated with the U.S. with ideas of citizenship in other countries.
Credits: 3
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LAW 9158 - Literature, Law and the Environment
Taught joinly by professors of literature and environmental law, this seminar will explore the evolution of the environmental movement through literature and its fruition in U.S. law and policy.
Credits: 3
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LAW 9159 - Constitutional Theory
This course examines some of the main topics in constitutional theory, including the legitimacy of judicial review, theories of constitutional interpretation, the role of non-judicial actors in determining constitutional meaning, and the politics of constitutional change. Readings will include classics in constitutional theory, along with recent work in the field.
Credits: 3
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LAW 9160 - Evidence Law: Psychological Bases
Underlying the Rules of Evidence are many assumptions about how people behave and how people (in particular jurors) reason. We will think about the origins and necessity of the rules in general, and specifically look at things like the usefulness of the examination/cross-examination style, character evidence, and other variables.
Credits: 3
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LAW 9161 - International Law and Global Economy Colloquium (YR)
This is the first part of a year-long colloquium that will allow students to engage with cutting-edge scholarship on the role of international law in regulating the global economy.
Credits: 0
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LAW 9162 - International Law and Global Economy Colloquium (YR)
This is the second part of a year-long colloquium that will allow students to engage with cutting-edge scholarship on the role of international law in regulating the global economy.
Credits: 3
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LAW 9163 - Issues in Criminal Law Theory
This course explores some of the philosophical issues involved in the fundamental principles of criminal law.
Credits: 2
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LAW 9164 - Government Finance
This seminar will examine the financing of government operations at the federal, state and local levels. Topics include the federal budget deficit; state constitutional limits on the incurrence of debt; and the expenditure of public funds for economic development and to attract or retain professional sports franchises.
Credits: 3
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LAW 9165 - Privacy and Surveillance
This seminar will consider the history and current applications of technologies and cultures of surveillance.
Credits: 3
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LAW 9166 - Federal Civil Litigation
In this seminar we will be discussing the history, development, and reform of the Federal Rules of Civil Procedure and then focus on a survey of some of the more contentious issues within federal practice and procedure.
Credits: 3
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LAW 9167 - Lawyers in History and American Life
This seminar considers connections between the legal profession and main themes in the history of American public life.
Credits: 3
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LAW 9168 - Federal Navigation and Water Resources
Topics addressed in detail will include the evolution of federal authority over the navigable waters of the United States for navigation and flood control; legal and environmental issues involved in the planning, construction, and operation of multipurpose federal water resource development projects by federal and state agencies, and the role of the federal government in municipal and industrial water supply.
Credits: 3
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LAW 9169 - Social Work of Law
For many lawyers the line between their work and social work is not a clear one. The seminar will examine the social work that lawyers do with individuals, families, and communities, and it will aim to expose students to the diverse sorts of clients and groups whom they will encounter and join with in a variety of practice areas.
Credits: 3
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LAW 9170 - International Tax Policy
This seminar examines the fundamental structural issues that states confront as they attempt to impose income taxes on cross-border transactions involving the movement of goods, services, capital, and individuals.
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LAW 9171 - Law and Business Management in the Healthcare Sector
Health care currently represents 17% of the United States GDP and that share is growing. This course will analyze legal, economic, financial and ethical issues in the major sectors of the health care industry.
Credits: 3
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LAW 9172 - Rights and Revolution in North Africa and the Arab Middle East
This seminar will examine the human rights impetus and impact of the “Arab Spring” of 2011 and beyond, considering case studies of the revolutions in (for example): Tunisia, Egypt, Syria, Palestine, Yemen and Libya.
Credits: 3
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LAW 9173 - Presidentialism in Administrative Law
This seminar will explore the doctrine of “presidentialism” in administrative law.
Credits: 3
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LAW 9174 - Comparative Constitutional Design
In this seminar, we explore the considerations and challenges in designing a constitution. We will focus on the “hard-wired” aspects of a constitution – that is, its institutional or structural components – not its interpretation per se.
Credits: 3
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LAW 9176 - Topics in U.S. Foreign Policy
In this course we will examine a variety of historical topics in U.S. foreign policy that involved significant aspects of both domestic and international law, such as Jefferson’s war on the Barbary Pirates, Lincoln’s Emancipation Proclamation (and its impact on the prospects of foreign recognition of the Confederacy), and Truman’s conduct of the Korean War.
Credits: 3.0
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LAW 9995 - Visiting Scholar
Billing and enrollment course for visiting scholars at the Law School.
Credits: 0
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LAW 9999 - Dissertation Research
For doctoral research taken under the supervision of a dissertation director.
Credits: 1 to 12
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Linguistics |
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LING 5010 - Synchronic Linguistics
Studies the theoretical foundations of major linguistic models focusing on problem-solving and descriptive techniques. Emphasizes the American structuralist and transformational-generative models of language. Prerequisite: LNGS 701 and instructor permission.
Credits: 3
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LING 5020 - Introduction to Comparative and Historical Linguistics
Introduction to Comparative and Historical Linguistics
Credits: 3
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LING 5050 - Phonology and Morphology
Phonology and Morphology
Credits: 3
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LING 5060 - Syntax and Semantics
Analyzes and describes sentence structure and its relationship to meaning. Prerequisite: LNGS 325 and permission of the instructor.
Credits: 3
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LING 5070 - Syntactic Theory
Studies the major schools of syntactic theory. Prerequisite: LNGS 325 and permission of the instructor.
Credits: 3
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LING 5090 - Teaching English as a Second Language
Studies the theory, problems, and methods in teaching English as a second language, with attention to relevant areas of general linguistics and the structure of English. Prerequisite: LNGS 325 and instructor permission.
Credits: 3
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LING 5100 - Teaching Practicum - ESL
Teaching Practicum - ESL
Credits: 1
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LING 5250 - Romance Linguistics
Studies the vulgar Latin origins and patterns of linguistic change in the principal Romance languages.
Credits: 3
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LING 5260 - Romance Linguistics
Studies the vulgar Latin origins and patterns of linguistic change in the principal Romance languages.
Credits: 3
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LING 5450 - Language Learning and Teaching
Language Learning and Teaching
Credits: 3
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LING 5569 - New Course in Linguistics
New course in the subject of linguistics.
Credits: 1 to 4
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LING 5910 - Grammatical Concepts in Foreign Language Learning
Explores tense, mode, voice, subject, object, and predicate, and their applications in various languages.
Credits: 3
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LING 6010 - 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.
Credits: 2
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LING 6559 - New Course in Linguistics
New course in the subject of linguistics.
Credits: 1 to 4
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LING 8559 - New Course in Linguistics
New course in the subject of linguistics.
Credits: 1 to 4
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LING 8998 - Non-Topical Research
Preparation for Master’s Research, no thesis director.
Credits: 1 to 12
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LING 8999 - Non-Topical Research
For Master’s thesis, taken under the supervision of a thesis director.
Credits: 3
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LING 9010 - 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.
Credits: 3
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LING 9020 - 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.
Credits: 3
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LING 9559 - New Course in Linguistics
New course in the subject of linguistics.
Credits: 1 to 4
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Materials Science and Engineering |
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MSE 6010 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6020 - 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. Prerequisite: MSE 601 and MSE 623.
Credits: 3
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MSE 6050 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6060 - 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. Prerequisite: MSE 605 or instructor permission.
Credits: 3
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MSE 6080 - 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. Prerequisite: Physical chemistry course or instructor permission.
Credits: 3
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MSE 6120 - 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. MSE 367 or equivalent, or a solid state materials/physics course.
Credits: 3
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MSE 6130 - 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. Prerequisite: MSE 601 or instructor permission.
Credits: 3
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MSE 6140 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6160 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6167 - Electrical, 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. Cross-listed as ECE 6167. Prerequisite: Some background in solid state materials and elementary quantum principles.
Credits: 3
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MSE 6230 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6240 - 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. Prerequisite: MSE 623.
Credits: 3
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MSE 6270 - 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.
Credits: 3
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MSE 6310 - 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.
Credits: 3
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MSE 6320 - 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. 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 6340 - 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. Prerequisite: MSE 606 or instructor permission.
Credits: 3
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MSE 6350 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 6555 - Special Topics in Distance Learning
Special Topics in Distance Learning
Credits: 3
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MSE 6592 - 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.
Credits: 3
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MSE 6640 - Thin Film Growth
Students are exposed to materials issues concerning the relevant growth models, techniques, and characterization of thin films pertaining to metals, oxides, and semiconductor materials. Growth techniques including sputtering, chemical vapor deposition, thermal evaporation, pulsed laser deposition, and molecular beam epitaxy will be discussed in detail.
Credits: 3
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MSE 6993 - Independent Study
Detailed study of graduate course material on an independent basis under the guidance of a faculty member.
Credits: 1-12
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MSE 6995 - 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.
Credits: 1 to 12
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MSE 7020 - 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. Prerequisite: MSE 601 and 602 or instructor permission.
Credits: 3
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MSE 7080 - 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.
Credits: 3
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MSE 7130 - 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. Prerequisite: MSE 703 or instructor permission.
Credits: 3
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MSE 7140 - 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. Prerequisite: MSE 665 or equivalent or instructor permission.
Credits: 3
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MSE 7220 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 7240 - 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. Prerequisite: MSE 623, 624.
Credits: 3
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MSE 7310 - Mechanical Behavior of Materials
Studies the deformation of solids under stress; emphasizing the role of imperfections, state of stress, temperature and strain rate. Description of stress, strain, strain rate and elastic properties of materials comprise the opening topic. Then considers fundamental aspects of crystal plasticity, along with the methods for strengthening crystals at low temperatures. Covers deformation at elevated temperatures and deformation maps. Emphasizes the relationships between microscopic mechanisms and macroscopic behavior of materials. Prerequisite: MSE 532 or instructor permission.
Credits: 3
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MSE 7320 - 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. Prerequisite: MSE 632 or AM/MAE/CE/APMA 602 or instructor permission.
Credits: 3
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MSE 7340 - 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. Prerequisite: MSE 623 or comparable thermodynamics.
Credits: 3
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MSE 7555 - Advanced Topics in Distance Learning
Advanced Topics in Distance Learning
Credits: 3
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MSE 7570 - 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. Prerequisite: Instructor permission.
Credits: 3
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MSE 7592 - Advanced Topics in Materials Science
An advanced level study of special topics related to developments in materials science. Prerequisite: Instructor permission.
Credits: 3
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MSE 7820 - 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.
Credits: 1
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MSE 7993 - Independent Study
Detailed study of graduate course material on an independent basis under the guidance of a faculty member.
Credits: 1 to 12
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MSE 7995 - 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.
Credits: 1 to 12
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MSE 8970 - Graduate Teaching Instruction-M.S.
For master’s students.
Credits: 1 to 12
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MSE 8999 - 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.
Credits: 1 to 12
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MSE 9970 - Graduate Teaching Instruction-Ph.D.
For doctoral students.
Credits: 1 to 12
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MSE 9999 - PHD Dissertation Research
Formal record of student commitment to doctoral research under the guidance of a faculty advisor. May be repeated as necessary.
Credits: 1 to 12
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Mathematics |
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MATH 5010 - 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. Prerequisite: MATH 2310 and 3351, or instructor permission.
Credits: 3
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MATH 5030 - 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. Prerequisite: MATH 2310 and 3351, or instructor permission.
Credits: 3
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MATH 5090 - Mathematical Probability
Mathematical Probability
Credits: 3
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MATH 5100 - 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. Prerequisite: MATH 1320 or equivalent, and graduate standing. Credit cannot be received for both MATH 3100 and 5100.
Credits: 3
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MATH 5110 - 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. Prerequisite: MATH 3100 and a knowledge of matrix algebra, or instructor permission.
Credits: 3
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MATH 5140 - Mathematics of Derivative Securities
Topics include arbitrage arguments, valuation of futures, forwards and swaps, hedging, option-pricing theory, and sensitivity analysis. Prerequisite: MATH 2310 or 1220 or its equivalent, and a knowledge of probability and statistics; MATH 3100 or its equivalent is recommended.
Credits: 3
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MATH 5210 - 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. Prerequisite: MATH 2310, 3250; 3351 recommended.
Credits: 3
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MATH 5220 - 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. Prerequisite: MATH 5210; 3351 recommended.
Credits: 3
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MATH 5250 - 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. Prerequisite: MATH 2310, 3250, 3351 or instructor permission.
Credits: 3
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MATH 5305 - Proofs in Analysis
This course reviews the proofs of the main theorems in analysis in preparation for the advanced graduate analysis courses. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
Credits: 3
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MATH 5310 - 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. Prerequisite: MATH 3310 or permission of instructor.
Credits: 3
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MATH 5330 - Advanced Multivariate Calculus
Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes’ Theorem. Prerequisite: MATH 5310.
Credits: 3
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MATH 5340 - Complex Variables with Applications
Analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: graduate standing.
Credits: 3
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