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These are not necessarily the official descriptions of the courses. For the official descriptions, consult the catalog.
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Description: Students who have well defined mathematical problems worthy of investigation and advanced reading should submit to the department a semester work plan. Prerequisites: Instructor consent required. Credits: 1-6 |
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Description: Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stielties integral, functions of several variables. Offered: Fall. Offered Fall 2006 Credits: 3 |
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Description: Lebesgue measure and integration, differentiation,
Lp spaces. Banach spaces, general theory of measure and integration. Prerequisites: MATH 301 Offered: Spring Credits: 3 |
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Description: Development of mathematical models emphasizing linear algebra, differential equations, graph theory and probability. In-depth study of the model to derive information about phenomena in applied work. Prerequisites: Instructor consent required. Credits: 3 |
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Description: Development and computer-assisted analysis of mathematical models in chemistry, physics, and engineering. Topics include chemical equilibrium, reaction rates, particle scattering, vibrating systems, least squares analysis, quantum chemistry and physics. Prerequisites: Instructor consent required. Credits: 4 |
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Description: Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.
Offered: Fall. Offered Fall 2006 Credits: 3 |
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Description: Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces. Prerequisites: MATH 307 Offered: Spring Credits: 3 |
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Description: Theory of linear programming: convexity, bases, simplex method, dual and integer programming, assignment, transportation, and flow problems. Theory of nonlinear programming: unconstrained local optimization, Lagrange multipliers, Kuhn-Tucker conditions, computational algorithms. Credits: 3 |
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Description: Banach spaces, linear operator theory and application to differential equations, nonlinear operators, compact sets on Banach spaces, the adjoint operator on Hilbert space, linear compact operators, Fredholm alternative, fixed point theorems and application to differential equations, spectral theory, distributions. Offered: Spring Credits: 3 |
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Description: Calculus in Banach spaces, Leray-Schauder degree theory, variational methods, existence and multiplicity of nonlinear boundary value problems, variational methods. Offered: Fall. Credits: 3 |
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Description: The study of convergence, numerical stability, roundoff error, and discretization error arising from the approximation of differential and integral operators.
Prerequisites: MATH 301, which may be taken concurrently. Offered: Fall. Offered Fall 2006 Credits: 3 |
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Description: The study of convergence, numerical stability, roundoff error, and discretization error arising from the approximation of differential and integral operators. Prerequisites: MATH 313 Offered: Spring Credits: 3 |
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Description: Group theory, ring theory and modules, and universal mapping properties. Offered: Fall. Credits: 3 |
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Description: Linear and multilinear algebra, Galois theory, category theory and commutative algebra. Prerequisites: Math 315 Offered: Spring Credits: 3 |
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Description: The LU, QR, symmetric, polar, and singular value matrix decompositions. Schur and Jordan normal forms. Symmetric, positive-definite, normal and unitary matrices. Perron-Frobenius theory and graph criteria in the theory of non-negative matrices. Offered: Fall Credits: 3 |
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Description: Orthogonal polynomials. The theorems of Szego and
Krein. Classes of linear transformations. Canonical forms.
H-selfadjoint matrices. Sign characteristic. Definite invariant
subspaces. Matrix polynomials. Algebraic Riccati equations. Offered: Fall Credits: 3 |
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Description: Homological Algebra is a powerful tool used in a number of areas of mathematics to deepen the understanding of the structure of its objects of investigation. In this course we will develop ?the fundamental notions of Homological Algebra and their uses in Commutative Algebra, with short detours into other applications. Topics will include: Hom and Tensor Products, and their ?relation to Projectivity, Flatness, and Injectivity of modules; the introduction of the Ext and Tor functors, and ways of computing them in some settings; the development of the ring invariants: ?global dimension, weak global dimension, and several other homological dimensions, and their uses in describing properties of rings. Other topics may be introduced as time allows. Prerequisites: MATH 316 Offered: Fall 2007 Credits: 3 |
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Description: Geometric constructions of Sn-modules and sln-modules Prerequisites: MATH 316 Offered: Fall 2007 Credits: 3 |
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Description: Convergence of random variables and their probability laws, maximal inequalities, series of independent random variables and laws of large numbers, central limit theorems, martingales, Brownian motion. Contemporary theory of stochastic processes, including stopping times, stochastic integration, stochastic differential equations and Markov processes, Gaussian processes, and empirical and related processes with applications in asymptotic statistics. Prerequisites: MATH 303 Offered: Offered Fall 2006 Credits: 3 |
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Description: Convergence of random variables and their probability laws, maximal inequalities, series of independent random variables and laws of large numbers, central limit theorems, martingales, Brownian motion. Contemporary theory of stochastic processes, including stopping times, stochastic integration, stochastic differential equations and Markov processes, Gaussian processes, and empirical and related processes with applications in asymptotic statistics. Prerequisites: MATH 322 Credits: 3 |
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Description: An introduction to the standard models of modern financial mathematics including martingales, the binomial asset pricing model, Brownian motion, stochastic integrals, stochastic differential equations, continuous time financial models,
completeness of the financial market, the Black-Scholes formula, the fundamental theorem of finance, American options, and term structure models. Offered: Spring Credits: 3 |
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Description: Existence and uniqueness of solutions, stability and asymptotic behavior. If time permits: eigenvalue problems, dynamical systems, existence and stability of periodic solutions. Prerequisites: MATH 303 Credits: 3 |
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Description: Cauchy Kowalewsky Theorem, classification of second order equations, systems of hyperbolic equations, the wave equation, the potential equation, the heat equation in Rn. Prerequisites: MATH 340 Credits: 3 |
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Description: In this course, new mathematical methods will be introduced and applied
to image processing. Tasks such as image segmentation, image deblurring,
image denoising, image registration, etc will be considered.
Both analytic and numerical aspects will be discussed. Students need to
do projects in Matlab. (This section is taught by Chanfeng Gui) Offered: Fall 2006 Credits: 3 |
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Description: Advanced topics from the theory of ordinary or partial differential equations. Other possible topics: integral equations, optimization theory, the calculus of variations, advanced approximation theory. Prerequisites: Instructor consent required. Credits: 3 |
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Description: Introduction to the representation theory of finite groups and Lie
algebras. Characters, induced representations, representations of the
symmetric and general linear groups, symmetric functions, Schur-Weyl
duality, representations of complex semi-simple Lie algebras, and the
Weyl character formulae. Prerequisites: Familiarity with abstract groups, rings and vector spaces at the level of Math 315. Offered: Spring 2007 Credits: 3 |
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Description: Algebraic integers, ideal class group, Dirichlet unit theorem, applications to diophantine equations. Further topics (localization, Frobenius elements in Galois groups, zeta-functions) as time permits.
Prerequisites: MATH 316 Offered: Offered Fall 2006 Credits: 3 |
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Description: The course will follow the celebrated book by Kenneth Falconer with the same title, which recently had its second paperback edition.
If time permits, the material can be supplemented by other topics, such as differential equations and/or probability on fractals. No background is required beyond a basic Real Analysis course such as Math 301. Prerequisites: MATH 301 Credits: 3 |
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Description: This is an introduction to the theory of Lie groups, Lie algebras, and their representations. The course is intended for graduate students in mathematics and physics with little or no prior exposure to the Lie theory. We will focus on matrix Lie groups and Lie algebras to keep the exposition concrete. First we will look at the relationship between Lie groups and Lie algebras, along with basic representation theory. One of the main objects is the exponential map, and we will study its properties including the Baker-Campbell-Dynkin-Hausdorff formula. Then we will study root systems, and classification of semisimple Lie algebras. One of the goals of the course will be to show how the Lie theory is used in applications such as differential geometry (symmetric spaces) and physics. The only prerquisite for taking the course is a background in linear algebra. Prerequisites: Instructor consent required. Offered: Spring Credits: 3 |
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Description: Predicate calculus, completeness, compactness, Lowenheim-Skolem theorems, formal theories with applications to algebra, Godel's incompleteness theorem. Further topics chosen from: axiomatic set theory, model theory, recursion theory, computational complexity, automata theory and formal languages. Prerequisites: Math 335 Offered: Offered Fall 2006 Credits: 3 |
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Description: Advanced topics from uniform spaces, topological groups, Lie groups, fiber spaces, theory of submanifolds, PL topology, differential topology, cohomology operations, complex manifolds, Riemannian manifolds, transformation groups, fixed point theory. Prerequisites: Instructor consent required. Offered: Offered Fall 2006 Credits: 3 |
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Description: Advanced topics from uniform spaces, topological groups, Lie groups, fiber spaces, theory of submanifolds, PL topology, differential topology, cohomology operations, complex manifolds, Riemannian manifolds, transformation groups, fixed point theory. Prerequisites: MATH 337 Credits: 3 |
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Description: This class is an introduction to complex analysis at the graduate level. A practical purpose of the class is to prepare students to take the qualifying exams. Highlights of the course will be (not an exclusive list) analytic functions, meromorphic functions, the Cauchy Integral Formula, residues, maximum principle and the Schwartz Lemma. Prerequisites: MATH 301 Offered: Spring Credits: 3 |
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Description: Further investigation into selected topics such as the theory of entire functions, conformal mapping, automorphic functions or potential theory. Prerequisites: MATH 340 Offered: Offered Fall 2006 Credits: 3 |
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Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications. Credits: 3 |
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Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications. Prerequisites: MATH 342 Credits: 3 |
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Description: An introduction to tensor algebra and tensor calculus with applications chosen from the fields of the physical sciences and mathematics. Prerequisites: Instructor consent required. Offered: Offered Fall 2006 Credits: 3 |
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Description: An introduction to tensor algebra and tensor calculus with applications chosen from the fields of the physical sciences and mathematics. Prerequisites: Instructor consent required. MATH 347 Credits: 3 |
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Description: Functions of a complex variable, integration in the complex plane, conformal mapping. Prerequisites: Not open to students who have passed MATH 252. Not open for graduate credit toward degrees in Mathematics. Offered: Offered Fall 2006 Credits: 3 |
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Description: Normed linear spaces and algebras, the theory of linear operators, spectral analysis. Prerequisites: MATH 303 and MATH 316. Credits: 3 |
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Description: Normed linear spaces and algebras, the theory of linear operators, spectral analysis. Prerequisites: MATH 354 Credits: 3 |
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Description: An introduction to the study of differentiable manifolds on which various differential and integral calculi are developed. A special emphasis is placed on the global aspects of modern differential geometry. Offered: Offered Fall 2006 Credits: 3 |
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Description: The theory and practice of teaching mathematics at the college level.
Basic skills, grading methods, cooperative learning, active learning, use
of technology, classroom problems, history of learning theory, reflective
practice. Prerequisites: Open to graduate students in Mathematics, others with consent of instructor. May not be used to satisfy degree requirements Offered: Offered Fall 2006 Credits: 1 |
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Description: The mathematics of measurement of interest, accumulation and discount, present value, annuities, loans, bonds, and other securities. Prerequisites: Not open to students who have passed MATH 285Q Offered: Offered Fall 2006 Credits: 3 |
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Description: Introduction to the use of mathematical and statistical techniques to solve a wide variety of organizational problems. Topics include linear programming, project scheduling, queuing theory, decision analysis, dynamic and integer programming and computer simulation. Prerequisites: Not open to students who have passed MATH 286, STAT 286, or STAT 356. Credits: 3 |
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Description: The continuation of Math 365, focusing on the mathematics of finance: measurement of financial risk and the opportunity cost of capital, the mathematics of capital budgeting and securities valuation, mathematical analysis of financial decisions and capital structure, and option pricing theory. Provides VEE credit in the Corporate Finance subject area for Society of Actuaries and Casualty Actuarial Society requirements. Offered: Offered Spring And Fall Credits: 3 |
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Description:
Prerequisites: Math 322 Offered: Offered Fall 2006. Credits: 3 |
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Description: Complexes, homology and cohomology groups, homotopy theory. Prerequisites: MATH 316 and MATH 307, which may be taken concurrently. Credits: 3 |
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Description: Complexes, homology and cohomology groups, homotopy theory. Prerequisites: MATH 373 Credits: 3 |
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Description: Introduction to the theory of functions of a real variable. Not open for graduate crtedit toward degrees in Mathematics. Prerequisites: Not open for students who have passed MATH 273. Credits: 3 |
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Description: For Fall 2007 the main subject of this course will be wavelets
and related material.
The term wavelets is commonly used in several different contexts.
Here it refers to a complete orthonomal system consisting of dilates
and translates of one function.
The course will begin by studying examples of such systems and
a standard paradigm, known as multiresolution analysis,
for generating such systems.
Properties that make such systems useful in various applications
will be highighted.
There will be no official textbook.
The books "Ten Lectures on Wavelets" by I. Daubechies,
"A First Course on Wavelets" by E. Hernandez and G. Weiss,
and related works will be used as references.
Prerequisites: Math 303 and 381 helpful but not required. Credits: 3 |
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Description: Solution of first and second order partial differential equations with applications to engineering and science. Credits: 3 |
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Description: Foundations of harmonic analysis developed through the study of Fourier series and Fourier transforms. Prerequisites: MATH 303 and MATH 341 Offered: Offered Fall 2006 Credits: 3 |
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Description: This is a continuation of Math 381 which will cover more of the fundamentals of Fourier Analysis along with current techniques used in the field. We will discuss Littlewood-Paley Theory, special function spaces including BMO, Carleson measures and singular integrals of nonconvolution type. Prerequisites: MATH 303 and MATH 341 Credits: 3 |
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Description: Vector algebra and vector calculus with particular emphasis on invariance. Classification of vector fields. Solution of the partial differential equations of field theory. Prerequisites: Instructor consent required. Offered: Offered Fall 2006 Credits: 3 |
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Description: Vector algebra and vector calculus with particular emphasis on invariance. Classification of vector fields. Solution of the partial differential equations of field theory. Prerequisites: Instructor consent required and MATH385. Credits: 3 |
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Description: Survival distributions, claim frequency and severity distributions, life tables, life insurance, life annuities, net premiums, net premium reserves, multiple life functions, and multiple decrement models. Prerequisites: MATH 285 or MATH 365, which may be taken concurrently. Not open to students who have passed MATH 287. Offered: Offered Fall 2006 Credits: 3 |
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Description: Lecture. Survival distributions, claim frequency and severity distributions, life tables, life insurance, life annuities, net premiums, net premium reserves, multiple life functions, and multiple decrement models. Prerequisites: MATH 387. Not open to students who have passed MATH 288. Credits: 3 |
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Description: Participation in internship and paper describing experiences. Offered: Spring And Fall Credits: 1 to 3 |
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Description: . Lecture. Survival models, mathematical graduation, or demography. Offered: Offered Fall 2006 Credits: 3 |
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Description: Lecture. Credibility theory or advanced theory of interest. Offered: Spring And Fall Credits: 3 |
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Description: Analysis, estimation, and validation of lifetime tables Prerequisites: MATH 387. Credits: 3 |
| GRAD 395: Masters Thesis Research |
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Credits: 1 |
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Credits: 3 |
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Credits: 3 |
| GRAD 398: Special Readings (Master's) |
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Credits: non-credit |
| GRAD 399: Thesis Preparation |
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Credits: non-credit |
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Description: Seminar. Participation and presentation of mathematical papers in joint student faculty seminars. Variable topics Offered: Offered Fall 2006 Credits: 1 |
| GRAD 410: Seminar in Algebra |
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Prerequisites: MATH 316 Credits: 1 |
| GRAD 430: Seminar in Geometry |
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Prerequisites: MATH 357 Credits: 1 |
| GRAD 435: Seminar in Mathematical Logic |
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Description: Seminar. Prerequisites: MATH 335. Credits: 1 |
| GRAD 450: Seminar in Analysis |
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Description: Seminar. Credits: 1 |
| GRAD 460: Computers in Mathematical Research |
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Credits: 1 |
| GRAD 470: Seminar in Topology |
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Description: Seminar. Prerequisites: MATH 374 Credits: 1 |
| GRAD 471: Seminar in Set Theory |
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Description: Seminar. Prerequisites: MATH 307 Credits: 1 |
| GRAD 480: Seminar in Applied Mathematics |
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Credits: 1 |
| GRAD 495: Doctoral Dissertation Research |
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Credits: 1 |
| GRAD 496: Full-Time Doctoral Research |
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Credits: 3 |
| GRAD 497: Full-Time Directed Studies |
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Description: (Doctoral Level). Credits: 3 |
| GRAD 498: Special Readings (Doctoral) |
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Credits: non-credit |
| GRAD 499: Dissertation Preparation |
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Credits: non-credit |
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