
Latin 


LATI 3080  Horace Selections from Horace’s Satires, Epodes, Odes, and Epistles. For more details on this class, please visit the department website at http://www.virginia.edu/classics/.
Credits: 3 


LATI 3090  Introduction to Mediaeval Latin Selections of Mediaeval Latin prose and verse. For more details on this class, please visit the department website at http://www.virginia.edu/classics/.
Credits: 3 


LATI 3100  Vergil Selections from Vergil’s Aeneid. For more details on this class, please visit the department website at http://www.virginia.edu/classics/.
Credits: 3 


LATI 3110  Ovid Selections from either the narrative poems (Metamorphoses, Fasti) or from the amatory poems. For more details on this class, please visit the department website at http://www.virginia.edu/classics/.
Credits: 3 


LATI 3120  Pliny’s Letters In this course we read the selection of letters of the younger Pliny that are found in the edition by SherwinWhite. Pliny is one of the clearest and most stylish writers of Latin prose. We concentrate on translating the letters and putting them into their social and literary context.
Credits: 3 


LATI 3130  Roman Satire This class will explore the Romans’ “own genre: satire. After an overview of the development of satire and its early practitioners, we will read and translate selected satires of Horace and Juvenal. While reading these often funny and at the same time biting poems, we will learn a great deal about society and manners, life and death, rich men and poor slobs, and high & low life characters in the Augustan & early imperial periods of Rome.
Credits: 3 


LATI 3150  Sallust This course will focus on one or more works by the Roman historian Sallust, read in the original Latin. Additional reading in English.
Credits: 3 


LATI 3160  Lucretius In this course, we’ll read a variety of selections from Lucretius poem about the nature of the universe, including topics as wideranging as the body, sex, death, atomic theory, the origins of language and civilization, and why we need philosophy.
Credits: 3 


LATI 3200  Latin Bible Readings from the Latin Bible, beginning with selections from narrative books (e.g., Genesis, Acts) and progressing to more elaborate and poetic portions (e.g. Psalms, Job, Song of Songs). Readings will be taken mainly from the Vulgate, but we will look briefly at the Old Latin versions and at modern English translations. We will also consider some medieval Bible manuscripts, including several in Special Collections at UVA.
Credits: 3 


LATI 4010  Catullus Translation and interpretation of the poems of Catullus.
Credits: 3 


LATI 4993  Independent Study Independent Study in Latin. For more details on this class, please visit the department website at http://www.virginia.edu/classics/.
Credits: 1 to 3 


LATI 4998  Latin Distinguished Majors Thesis Research Independent research under direction of a faculty member leading to writing of a Distinguished Majors thesis or comparable project
Credits: 3 


LATI 4999  Latin Distinguished Majors Thesis Writing Writing of Distinguished Majors thesis or comparable project.
Prerequisites: LATI 4998
Credits: 3 
Latin American Studies 


LAST 2050  Latin American Interdisciplinary Seminar An interdisciplinary seminar taught by the faculty of the Latin Americans Studies Program, containing twelve different subjects, from historical, anthropological, literary, political and media studies disciplines.
Credits: 4 


LAST 4655  Sustainability in Brazil’s Emerging Markets This class will discuss the economic and environmental impacts of Brazil’s past, present, and future growth. It will also survey Brazil’s attitudes and approach to balancing economic growth with environmental sustainability since the Industrial Revolution.
Credits: 3 


LAST 4993  Majors Thesis, Independent Studies Majors Thesis, Independent Studies
Credits: 3 


LAST 4999  Majors Thesis, Independent Studies Majors Thesis, Independent Studies
Credits: 3 
Liberal Arts Seminar 


LASE 1200  The Liberal Arts and the World of Work LASE 1200 connects the skills and competencies unique to a Liberal Arts education with the core proficiencies of prominent professions, and through the introduction of design thinking techniques, to design their future, both at UVA and beyond. Students will apply this understanding as they begin to discover the possibilities of life after college. Students will gain a thorough knowledge of the design thinking process and apply that processes.
Credits: 3 


LASE 2110  Critical Reading, Writing, and Reasoning Critical Reading, Writing, and Reasoning is designed to strengthen your thinking, reading, and writing skills across genres and disciplines, with an emphasis on critical analysis. Through a series of increasingly complex assignments, we will demystify and engage interdisciplinary academic discourse. The aim of this class is to stir your intellectual inquiry and provide you with an interdisciplinary context for your academic exploration.
Credits: 3 


LASE 3110  Academic Analysis and Research: Power and Responsibility Academic Analysis and Research is a threecredit course providing firstyear college students with the experience of analyzing, researching, and developing ideas through close readings, class discussions, presentations, and academic writing.The goal of the class is to achieve improved fluency in critical thinking, reading, and writing, through close reading and annotation; intensive and recursive writing; and focused discussion. Prerequisites: LASE 2110.
Credits: 3 


LASE 3111  Skills of Scholarship Skills of Scholarship is a threecredit course designed to help you expand your critical thinking skills, including building your awareness of the process of observing, analyzing, and reasoning. This course will strengthen your ability to evaluate arguments, read critically, manage academic goals, and communicate effectively in written and spoken form. Prerequisites: LASE 2110 and LASE 3110.
Credits: 3 


LASE 3200  Liberal Arts and Professional Engagement The course aims to give students a greater awareness of the connection between a liberal arts education and professional opportunities. It will make opportunities available to students to learn about emerging and growing career fields and provide practical skills development to prepare students for entry into the world of professional life.
Credits: 3 


LASE 3500  Civic and Community Engagement A community engagement curriculum refers to teaching, scholarship & learning that connects faculty, students, & the community in mutually beneficial collaborations. Community engagement improves students’ content knowledge, critical thinking, career choice, cultural competency, leadership, & commitment to social change. These classes complement & build on existing course offerings and offer an opportunity to move beyond the classroom.
Credits: 3 
Linguistics 


LING 2500  English as a Global Language This course examines the rise of English, its progress towards filling the need for a global language and the reasons why English has been adopted in this role. We shall pay particular attention to the role English plays in the countries we visit on this voyage as well as its competition with prestigious national and local languages.
Credits: 3 


LING 3400  Structure of English Introduces students to the descriptive grammar of English and methods of reasoning about linguistic structure. Covers units of sound and phonemic transcriptions, word building and inflectional forms, lexical categories, basic sentence types, common phrase and clause patterns, and syntactic transformations.
Credits: 3 


LING 3500  Language Death Languages are living organisms in the sense that they are constantly being passed on to the succeeding generation. When this transmission from one generation to the next fails, it is only a matter of time before the last speaker of the language dies, which also spells the death of the language in question. This course sets to examine why and how languages die and what measures can or should be taken to reverse it.
Credits: 3 


LING 4993  Independent Study in Linguistics Conducted by students under the supervision of an instructor of their choice.
Credits: 3 


LING 4994  Linguistics Internship In this course students will work closely with a professor on an ongoing research project.
Credits: 1 to 3 


LING 4995  Supervised Research in Linguistics Conducted by students under the direction of an instructor of their choice.
Credits: 1 to 6 


LING 4998  Distinguished Major Thesis A twosemester course in which the student prepares a thesis under the supervision of a Linguistics faculty member. Prerequisite: Participants in the Distinguished Majors Program in Linguistics.
Credits: 0 


LING 4999  Distinguished Major Thesis A twosemester course in which the student prepares a thesis under the supervision of a Linguistics faculty member. Prerequisite: Participants in the Distinguished Majors Program in Linguistics.
Credits: 6 
Materials Science and Engineering 


MSE 2010  Materials That Shape Our Civilization A general review of structure, properties, methods of production, uses and world supply of the materials on which present and past civilizations have been based, including materials used in heavy industry, construction, communications, energy production, and medicine as well as textiles and naturallyoccurring organic materials. Crosslisted as EVSC 2010.
Credits: 3 


MSE 2090  Introduction to the Science and Engineering of Materials The collective properties of the materials in an engineering structure often dictate the feasibility of the design. Provides the scientific foundation for understanding the relations between the properties, microstructure, and behavior during use of metals, polymers, and ceramics. Develops a vocabulary for the description of the empirical facts and theoretical ideas about the various levels of structure from atoms, through defects in crystals, to larger scale morphology of practical engineering materials.
Credits: 3 


MSE 2500  Special Topics in Materials Science and Engineering Special topic courses in Materials Science and Engineering
Credits: 1 to 3 


MSE 3050  Thermodynamics and Kinetics of Materials Demonstrates how the interplay of thermodynamic driving forces and kinetics of mass transfer defines the formation of complex microstructures in real materials. The course begins with an overview of classical thermodynamics and applies the thermodynamic concepts to the analysis of phase equilibrium and phase transformations in onecomponent systems and binary solutions. Students learn how to read, analyze and even construct phase diagrams from thermodynamic data. The second part of the course provides an introduction to the basic concepts of kinetic phenomena in materials, with the focus on diffusion and phase transformations. Prerequisite: MSE 2090 or instructor permission.
Credits: 3 


MSE 3060  Structures and Defects of Materials Basic materials structure concepts are developed, include bonding and crystallography. The structureproperty paradigm is illustrated through discussion of the frequently anisotropic properties of crystalline solids, such as elastic moduli, thermal expansion, magnetic properties, and the piezoelectric effect. Descriptions of important defects in crystalline solids, from point defects, to dislocations, to interfaces are introduced along with the thermodynamic and kinetic principles that govern their interactions and roles during materials processing, such as annealing, aging, and sintering. Applications are made to a broad range of materials, from structural alloys to socalled “smart materials” used in sensors and actuators. Prerequisite: MSE 2090 and APMA 2120 or instructor permission.
Credits: 3 


MSE 3080  Corrosion, Batteries and Fuel Cells Includes basic electrochemical principles, terminology, definitions and examples of corrosion, batteries and fuel cells, as well as the thermodynamics and kinetic principles of electrochemistry applied to corrosion, batteries and fuel cells. Discusses the eight forms of corrosion and various battery and fuel cell systems. Provides instruction on the various corrosion mitigation methods such as cathodic protection, inhibitors, and coatings as well as design issues in corrosion, batteries and fuel cells at the materials science and engineering level.
Credits: 3 


MSE 3081  Corrosion, Batteries, and Fuel Cells Laboratory Provides instruction in standard corrosion, battery and fuel cell experimental methods that demonstrate the instrumentation of corrosion, battery and fuel cell testing and some of the ways to evaluate these electrochemical systems. Standard experiments involving cathodic protection, anodic protection, inhibitors, and simple examples of batteries and fuel cells. MSE 3080 may be taken without the lab, but MSE 3081 may not be taken without the lecture.
Credits: 1 


MSE 3101  Materials Science Investigations The course amplifies topics covered in introductory materials science through laboratory demonstration and experimentation. An understanding of modern instruments and experimental techniques including xray diffraction, optical and electron microscopy is gained through lecture and laboratory experience. Experimental determination of the processing, structure, property relationship is emphasized. Laboratory report writing skills are developed.
Prerequisite: MSE 2090
Credits: 3 


MSE 3610  Aerospace Materials Introduces physicalchemicalmicrostructuralmechanical property relations for aerospace materials. Metal, polymer, ceramic, and composite material systems are covered. Topics include strength, fracture, corrosion, oxidation/corrosion, materials selection, phase diagrams, kinetics of phase change, and materials processing. Case studies include materials for aero turbine engines and ultralight structures.
Credits: 3 


MSE 3670  Materials for Electronic, Magnetic and Optical Applications The course introduces the basics of materials interactions with electrons and electromagnetic radiation and describes the classes of materials that exhibit useful electronic, optical, magnetic, and superconductive properties. Particular attention will be devoted to the intrinsic (structure, chemistry) and extrinsic (processing, microstructure) material features that determine these properties. Examples of application of such materials in commercial electronic systems in common use are discussed. Prerequisite: MSE 2090 recommended.
Credits: 3 


MSE 4055  Nanoscale Science & Technology Covers the basic phenomena exhibited by material structures at the scale of one hundred nanometers of less, and the applications to technology. The goal of the course is to provide students with fundamental physical principles which can be used to analyze nanoscale phenomena, the assembly of nanostructures, and their characterization. Different properties: electrical, mechanical, optical, etc. will be discussed in detail on the basis of quantum mechanics and the atomistic description of solids. The description will include the behavior of clusters, nanoparticles, graphene, carbon nanotubes, nanoporous material, and examples from the natural world (DNA, membranes, cells, mineral nanostructures). Different methods of fabrication of nanostructures will be covered, from selfassembly to direct writing with electron beams. The characterization of the microstructures by different methods will be described and compared. The course will give a broad view of current and potential applications, with consideration of economic an societal aspects of the technology. Prerequisite: Exposure to Quantum Mechanics (MSE 3670, PHYS 2320, PHYS 2620, or CHEM 3610) or instructor permission.
Credits: 3 


MSE 4210  Materials Processing This course examines the fundamental principles of physics, chemistry, materials science, and manufacturing which underlie the making, shaping, and fabrication of engineering components from casting and deformation processing (e.g. rolling, extrusion, forging) of metals, to powder processing of metals and ceramics, to polymer injection molding, to thinfilm processing and lithography relevant to microelectronic circuit fabrication. Corequisite MSE 3050
Credits: 3 


MSE 4270  Introduction to Atomistic Simulations Introduction to several classical atomiclevel 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 stateoftheart 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 


MSE 4320  Origins of Mechanical Behavior Develops understanding of material deformation and fracture in response to mechanical loading. Engineering and scientific principles are integrated in an approach that includes: (a) material property phenomenology,(b) test methods, (c) causal mechanisms at the atomic defect to microstructure scale, (d) governing continuum mechanics equations, and (e) problem solving. Plastic deformation and creep are understood based on elasticity theory and dislocation concepts. Fatigue and fracture are understood based on continuum fracture mechanics and microstructural damage mechanisms. Special Topics provide capstone descriptions of content, and engage the student with future challenges and opportunities.
Prerequisite: MSE 3060 or MSE 2090 plus instructor permission.
Credits: 3 


MSE 4592  Special Topics in Materials Science Advanced undergraduate course on topics not normally covered in other course offerings. The topic usually reflects new developments in the materials science and engineering field. Offerings are based on student and faculty interests.
Credits: 3 


MSE 4960  Special Project in Materials Science and Engineering A fourth year project in MSE, under the supervision of a faculty member, is designed to give undergraduate students an application of principles learned in the classroom. The work may be experimental or computational, and the student is expected to become proficient in techniques used to process, characterize, or model materials. The project should make use of design principles in the solution of a problem. Six hours in lab per week, notebook.
Prerequisite: 4th year standing and prior approval by a faculty member who is project supervisor.
Credits: 1 to 6 
Mathematics 


MATH 1110  Probability/Finite Mathematics Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes’ theorem, expectation and variance, and Markov chains.
Credits: 3 


MATH 1140  Financial Mathematics The study of the mathematics needed to understand and answer a variety of questions that arise in everyday financial dealings. The emphasis is on applications, including simple and compound interest, valuation of bonds, amortization, sinking funds, and rates of return on investments. A solid understanding of algebra is assumed.
Credits: 3 


MATH 1150  The Shape of Space Provides an activity and projectbased exploration of informal geometry in two and three dimensions. Emphasizes visualization skill, fundamental geometric concepts, and the analysis of shapes and patterns. Topics include concepts of measurement, geometric analysis, transformations, similarity, tessellations, flat and curved spaces, and topology.
Credits: 3 


MATH 1160  Algebra, Number Systems, and Number Theory Studies basic concepts, operations, and structures occurring in number systems, number theory, and algebra. Inquirybased student investigations explore historical developments and conceptual transitions in the development of number and algebraic systems.
Credits: 3 


MATH 1190  A Survey of Calculus I with Algebra A first calculus course for business/biology/socialscience students. Topics include college algebra/limits and continuity/differentiation and integration of algebraic and elementary transcendental functions/applications to relatedrates & optimization problems as well as to curve sketching & exponential growth. At most one of MATH 1190, MATH 1210, and 1310 may be taken for credit. Prerequisite: No previous exposure to Calculus.
Credits: 4 


MATH 1210  A survey of Calculus I A first calculus course for business/biology/socialscience students. Topics include limits and continuity/differentiation & integration of algebraic & elementary transcendental functions/applications to relatedrates & optimization problems as well as to curve sketching & exponential growth. At most one of Math 1190, MATH 1210, and 1310 ma1y be taken for credit.
Credits: 3 


MATH 1220  A Survey of Calculus II A second calculus course for business/biology/and socialscience students. Topics include differential equations/infinite series/analysis of functions of several variables/analysis of probability density functions of continuous random variables. The course begins with a review of basic singlevariable calculus. Prerequisite: MATH 1210 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.
Credits: 3 


MATH 1310  Calculus I A first calculus course for naturalscience majors/students planning further work in mathematics/students intending to pursue graduate work in applied social sciences. Introduces differential & integral calculus for singlevariable functions, emphasizing techniques/applications & major theorems, like the fundamental theorem of calculus. Prerequisite: Background in algebra/trigonometry/exponentials/logarithms/analytic geometry.
Credits: 4 


MATH 1320  Calculus II A second calculus course for naturalscience majors, students planning additional work in mathematics, and students intending to pursue graduate work in the applied social sciences. Topics include applications of the integral, techniques of integration, differential equations, infinite series, parametric equations, and polar coordinates.
Prerequisite: MATH 1310 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.
Credits: 4 


MATH 1330  Calculus Workshop I Intensive calculus problemsolving workshop with topics drawn from MATH 1310. Prerequisite: Instructor permission; corequisite: MATH 1310.
Credits: 2 


MATH 1340  Calculus Workshop II Intensive calculus problemsolving workshop with topics drawn from MATH 1320. Prerequisite: Instructor permission; corequisite: MATH 1320.
Credits: 2 


MATH 2310  Calculus III A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in threedimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real world applications. Prerequisite: MATH 1320 or the equivalent.
Credits: 4 


MATH 2315  Advanced Calculus and Linear Algebra I Covers the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory and linear algebra. Prepares students for taking advanced mathematics classes at an early stage.
Credits: 4 


MATH 2700  Euclidean and NonEuclidean Geometry Examines assumptions and methods in the original text of Euclid’s Elements. Covers selected geometric topics such as symmetries, spherical geometry, curvature, the dissection theory of area, constructible numbers, and the discovery of nonEuclidean geometry. Prerequisite: Some familiarity with calculus.
Credits: 3 


MATH 3000  Transition to Higher Mathematics Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality.
Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000level Math course are not eligible to enroll in Math 3000.
Credits: 4 


MATH 3100  Introduction to Probability Introduces fundamental concepts/techniques of probability/the theory of randomness. Focuses on problem solving/understanding key theoretical ideas. Topics include sample spaces combinatorial analysis/discrete and continuous random variables/classical distributions/expectation/Chebyshev’s inequality/independence/central limit theorem/conditional probability/generating functions. Prerequisite: MATH 1320. Recommended: knowledge of double integrals.
Credits: 3 


MATH 3250  Ordinary Differential Equations Introduces the methods, theory, and applications of differential equations. Includes firstorder, second and higherorder linear equations, series solutions, linear systems of firstorder differential equations, and the associated matrix theory. May include numerical methods, nonlinear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.
Credits: 4 


MATH 3310  Basic Real Analysis A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits/ continuity/differentiability/convergence of infinite series/the construction of the Riemann integral. The focus of students’ work will be on getting experience in constructing proofs and developing examples. Prerequisite: MATH 1320.
Credits: 3 


MATH 3315  Advanced Calculus and Linear Algebra II This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315.
Credits: 4 


MATH 3340  Complex Variables with Applications Covers functions of a complex variable that are complex differentiable and the unusual and useful properties of such functions. Some topics: Cauchy’s integral formula/power series/the residue theorem/Rouché’s theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310.
Credits: 3 


MATH 3350  Applied Linear Algebra Topics will include systems of linear equations, matrix operations and inverses, vector spaces and subspaces, determinants, eigenvalues and eigenvectors, matrix factorizations, inner products and orthogonality, and linear transformations. Emphasis will be on applications, with computer software integrated throughout the course. The target audience for MATH 3350 is nonmath majors from disciplines that apply tools from linear algebra. Credit is not given for both MATH 3350 and 3351.
Credits: 3 


MATH 3351  Elementary Linear Algebra Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and GramSchmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Credit is not given for both MATH 3350 and 3351. Prerequisite: MATH 1320.
Credits: 3 


MATH 3354  Survey of Algebra Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 1320 or equivalent.
Credits: 3 


MATH 4040  Discrete Mathematics Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya’s enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 3354 or instructor permission.
Credits: 3 


MATH 4080  Operations Research Development of mathematical models and their solutions, including linear programming, the simplex algorithm, dual programming, parametric programming, integer programming, transportation models, assignment models, and network analysis. Prerequisite: MATH 1320 and 3351.
Credits: 3 


MATH 4110  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 or APMA 3100; and a knowledge of matrix algebra
Credits: 3 


MATH 4140  Mathematics of Derivative Securities This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets and derivatives/pricing contingent claims in the binomial & the finite market model/(time permitting) the BlackScholes model. Prerequisites: MATH 3100 or APMA 3100. Students should have a knowledge of matrix algebra.
Credits: 3 


MATH 4210  Mathematics for Physics This course covers linear algebra/complex analysis/vector differential & integral calculus. Thus it is a compressed version of MATH 3351 & MATH 3340 and a review of some of the material in MATH 2310. Emphasis is on the physical interpretation. [This course does not count as a Mathematics elective for Mathematics majors if both MATH 3351 and MATH 3340 are to be counted.] Prerequisite: MATH 2310 or MATH 2315 or APMA 2120
Credits: 3 


MATH 4220  Partial Differential Equations and Applied Mathematics This course is a beginning course in partial differential equations/Fourier analysis/special functions (such as spherical harmonics and Bessel functions). The discussion of partial differential equations will include the Laplace and Poisson equations and the heat and wave equations. Prerequisites: MATH 3250 and either MATH 3351 or MATH 4210.
Credits: 3 


MATH 4250  Differential Equations and Dynamical Systems A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering.
Prerequisites: MATH 3351 or APMA 3080 and MATH 3310 or MATH 4310.
Credits: 3 


MATH 4300  Elementary Numerical Analysis Includes Taylor’s theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or leastsquare approximation. Prerequisite: MATH 3250 and computer proficiency.
Credits: 3 


MATH 4310  Introduction to Real Analysis This course covers the basic topology of metric spaces/continuity and differentiation of functions of a single variable/RiemannStieltjes integration/convergence of sequences and series. Prerequisite: MATH 3310 or permission of instructor.
Credits: 3 


MATH 4330  Advanced Multivariate Calculus Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes’ theorem.
Prerequisites: MATH 2310 or MATH 2315; MATH 3351 or MATH 4651 or APMA 3080; and MATH 3310 or MATH 4310
Credits: 3 


MATH 4452  Algebraic Coding Theory Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, ReedMuller codes, algebraic geometry codes, and connections with groups, designs, and lattices. Prerequisite: MATH 3351 and 3354, or instructor permission.
Credits: 3 


MATH 4595  Undergraduate Research Seminar Emphasizes direct contact with advanced mathematical ideas, communication of these ideas, the discovery of new results and connections among them, and the experience of mathematics as a collaborative venture among researchers at all levels. Students work collaboratively and individually on research projects, and present their results to the class. Prerequisite: Instructor permission.
Credits: 3 


MATH 4651  Advanced Linear Algebra Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included.
Prerequisite: MATH 3351
Credits: 3 


MATH 4652  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. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor.
Credits: 3 


MATH 4653  Number Theory The study of the integers and related number systems. Includes polynomial congruences, rings of congruence classes and their groups of units, quadratic reciprocity, diophantine equations, and numbertheoretic functions. Additional topics such as the distribution of prime numbers may be included. Prerequisite: MATH 3354.
Credits: 3 


MATH 4657  Bilinear Forms and Group Representations Covers the representation theory of finite groups/other interactions between linear & abstract algebra. Topics include: bilinear & sesquilinear forms & inner product spaces/important classes of linear operators on inner product spaces/the notion of group representation/complete reducibility of complex representations of finite groups/character theory/some applications of representation theory. Prerequisite: MATH 3351 (or 4651)/MATH 3354 (or 4652)
Credits: 3 


MATH 4658  Galois Theory This course studies the symmetries of solutions of polynomials. Topics include algebraic field extensions/field automorphisms/the fundamental theorem of Galois theory. Applications include the unsolvability of the quintic, as well as ruler & compass constructions. Prerequisites: MATH 3351 (or 4651) and MATH 4652.
Credits: 3 


MATH 4660  Algebraic Combinatorics Combinatorics of counting using basic tools from calculus, linear algebra, and occasionally group theory. Topics include: tableaux, symmetric polynomials, Catalan numbers, quantum binomial theorem, qexponentials, partition and qseries identities. Bijective proofs will be emphasized when appropriate.
Credits: 3 


MATH 4720  Introduction to Differential Geometry Geometric study of curves/surfaces/their higherdimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3space/geodesics/the GaussBonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission.
Credits: 3 


MATH 4750  Introduction to Knot Theory Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also considers knots as boundaries of surfaces and via algebraic structures arising from knots. Prerequisites: MATH 2310 and MATH 3351 and MATH 3354 or instructor permission.
Credits: 3 


MATH 4770  General Topology Topics include abstract topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., the fundamental group. Prerequisites: MATH 2310, MATH 3351, MATH 3310, or higher level versions of these courses.
Credits: 3 


MATH 4840  Introduction to Mathematical Research This course will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their findings in various formats (presentation, paper etc.).
Credits: 3 


MATH 4900  Distinguished Major Thesis This course provides a framework for the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides a student through the beginning phases of the process of research and writing. Prerequisite: Acceptance into the Distinguished Major Program.
Credits: 3 


MATH 4901  Distinguished Major Thesis This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee.
Prerequisite: MATH 4900.
Credits: 3 


MATH 4993  Independent Study Reading and study programs in areas of interest to individual students. For third and fourthyears interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.
Credits: 1 to 3 
Maya K’iche’ 


KICH 1010  Introduction to Maya K’iche’ I This class is an introduction to K’iche’, a Maya language spoken by about a million people in the western Highlands of Guatemala; it is one of the major indigenous languages in the Americas. This class aims to make students competent in basic conversation and to introduce students to Maya culture. It is offered as part of the UVaDukeVanderbilt consortium for distance learning in less commonly taught languages.
Credits: 3 


KICH 1020  Introduction to Maya K’iche’ II This class is the second part of a yearlong introductory sequence to K’iche’, a Maya language spoken by about a million people in the western Highlands of Guatemala, and one of the major indigenous languages in the Americas. Students will enrich and expand their conversational skills and cultural knowledge from K’iche’ 1010. It is offered as part of the UVaDukeVanderbilt consortium for distance learning in less commonly taught languages. The completion of KICH 1010 with a grade of C or higher.
Credits: 3 


KICH 2010  Intermediate Maya K’iche’ I This class is the 3rd level of a 4part sequence in K’iche’, a Maya language spoken by a million people in western Guatemala. Here students will cover more advanced grammar (verb modalities), a broader range of scripts (colonial vs. modern orthography), and conduct research based on the K’iche’ Oral History project at UNM. The class is offered as part of the UVaDukeVanderbilt consortium for distance learning in LCTLs. The completion of KICH 1010 and 1020 with a grade of C or higher.
Credits: 3 


KICH 2020  Intermediate Maya K’iche’ II KICH 2020 is the capstone course in a fourpart sequence in K’iche’, a Maya language spoken by a million people in western Guatemala. Students will build from earlier coursework to write an original essay in the target language, integrating primary and secondary sources like published works and interviews that they conduct. The class is offered as part of the UVaDukeVanderbilt consortium for distance learning in LCTLs. The completion of KICH 1010, 1020 and 2010 with a grade of C or higher.
Credits: 3 
Mechanical & Aerospace Engineering 


MAE 1501  Special Topics in Mechanical & Aerospace Engineering Studentled special topic courses which vary by semester.
Credits: 1 

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