
Mathematics 


MA 41600  Probability Credit Hours: 3.00. (STAT 41600 ) An introduction to mathematical probability suitable as a preparation for actuarial science, statistical theory, and mathematical modeling. General probability rules, conditional probability and Bayes theorem, discrete and continuous random variables, moments and moment generating functions, joint and conditional distributions, standard discrete and continuous distributions and their properties, law of large numbers and central limit theorem. Typically offered Fall Spring. 


MA 42100  Linear Programming And Optimization Techniques Credit Hours: 3.00. Solution of linear programming problems by the simplex method, duality theory, transportation problems, assignment problems, network analysis, dynamic programming. Typically offered Fall Spring. 


MA 42500  Elements Of Complex Analysis Credit Hours: 3.00. Complex numbers and complexvalued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping. Typically offered Spring. 


MA 42800  Introduction To Fourier Analysis Credit Hours: 3.00. Topics include: Fourier series, convolutions, kernels, summation methods, Fourier transforms, applications to the wave, heat, and Laplace equations. Prerequisites: Vector calculus and linear algebra. Typically offered Fall Spring. 


MA 44000  Real Analysis Honors Credit Hours: 3.00. Basic real analysis, limits, continuity, differentiation, and integration. Typically offered Fall. 


MA 44200  Multivariate Analysis I Honors Credit Hours: 3.00. Topics covered may include a unified modern treatment of functions of several variables. Topics covered include the topology of Euclidean spaces, mappings of Euclidean spaces, exterior algebra, Lebesgue integration, and integration on manifolds. Typically offered Spring. 


MA 45000  Algebra Honors Credit Hours: 3.00. This course, which is essentially the first half of MA 55300 , is recommended for students wanting a more substantial background in algebra than is afforded by MA 45300 , in particular students intending to do graduate work in science or engineering. Topics include the elements of number theory and group theory; unique factorization in polynomial rings and in principal ideal domains. Typically offered Fall. 


MA 45300  Elements Of Algebra I Credit Hours: 3.00. Fundamental properties of integers, polynomials, groups, rings, and fields, with emphasis on problem solving and applications. Not open to students with credit in MA 45000 . Typically offered Fall Spring. 


MA 45400  Galois Theory Credit Hours: 3.00. An introduction to Galois theory, covering both its origins in the theory of roots of polynomial equations and its modern formulation in terms of abstract algebra. Topics include finite extension fields and their symmetries, ruler and compass constructions, complex roots of unity, solvable groups, and the solvability of polynomial equations by arithmetic and radical operations. Typically offered Spring. 


MA 46000  Geometry Credit Hours: 3.00. This is a course in Euclidean geometry. It begins at the highschool level and then moves quickly to intermediate and advanced topics. Emphasis on proofs. Typically offered Fall Spring. 


MA 46200  Elementary Differential Geometry Credit Hours: 3.00. The geometry of curves and surfaces based on familiar parts of calculus and linear algebra. An introduction to the study of differentiable manifolds and Riemannian geometry. Typically offered Fall Spring Summer. 


MA 47400  Methods Of Random Modeling Credit Hours: 3.00. (STAT 47400) Poisson and compound Poisson processes, plus topics in discrete and continuous time Markov chains, Brownian motion (including the BlackScholes formula) and simluation. Typically offered Spring. 


MA 48100  Advanced ProblemSolving Seminar Credit Hours: 1.00. Seminar intended to prepare students for the national Putnam examination in mathematics. Typically offered Fall. 


MA 48400  Seminar On Teaching College Algebra And Trigonometry Credit Hours: 3.00. This course is a seminar on the teaching of mathematics for our best undergraduate mathematics education students. It provides supervised teaching experience along with a chance for the students to perfect their knowledge of algebra before going on to be high school teachers. Students who take this class will also teach a section of MA 15300 . Permission of instructor required. Typically offered Fall. 


MA 48700  Professional Practicum V Credit Hours: 0.00. Professional Practicum. Permission of department required. Typically offered Fall Spring Summer. 


MA 49000  Topics In Mathematics For Undergraduates Credit Hours: 1.00 to 6.00. Supervised reading courses as well as special topics courses for undergraduates are given under this number. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 50300  Abstract Algebra Credit Hours: 3.00. Group theory: definitions, examples, subgroups, quotient groups, homomorphisms, and isomorphism theorems. Ring theory: definitions, examples, homomorphisms, ideals, quotient rings, fraction fields, polynomial rings, Euclidean domains, and unique factorization domains. Field theory: algebraic field extensions, straightedge and compass constructions. Typically offered Fall. 


MA 50400  Real Analysis Credit Hours: 3.00. Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the RiemannStieltjes integral, sequences and series of functions, uniform convergence, the StoneWeierstrass theorem, equicontinuity, and the ArzelaAscoli theorem. Typically offered Fall. 


MA 51000  Vector Calculus Credit Hours: 3.00. Calculus of functions of several variables and of vector fields in orthogonal coordinate systems. Optimization problems, implicit function theorem, Green’s theorem, Stokes’ theorem, divergence theorems. Applications to engineering and the physical sciences. Not open to students with credit in MA 36200 or MA 41000. Typically offered Fall Spring Summer. 


MA 51100  Linear Algebra With Applications Credit Hours: 3.00. Real and complex vector spaces; linear transformations; GramSchmidt process and projections; least squares; QR and LU factorization; diagonalization, real and complex spectral theorem; Schur triangular form; Jordan canonical form; quadratic forms. Typically offered Summer. 


MA 51400  Numerical Analysis Credit Hours: 3.00. (CS 51400 ) Iterative methods for solving nonlinear; linear difference equations, applications to solution of polynomial equations; differentiation and integration formulas; numerical solution of ordinary differential equations; roundoff error bounds. Typically offered Fall Spring. 


MA 51500  Mathematics Of Finance Credit Hours: 3.00. An introduction to the mathematical tools and techniques of modern finance theory, in the context of BlackScholes option pricing. Brownian motion and its stochastic calculus, Ito’s formula, and FeynmanKac formula. Pricing and hedging of claims on BlackScholes assets. Incomplete markets. Pathdependent options. Stochastic portfolio optimization. Typically offered Spring. 


MA 51600  Advanced Probability And Options With Numerical Methods Credit Hours: 3.00. Stochastic interest rate models. American options from the probabilistic and PDE points of view. Numerical methods for European and American options, including binomial, trinomial, and MonteCarlo methods. Typically offered Fall. 


MA 51800  Advanced Discrete Mathematics Credit Hours: 3.00. The course covers mathematics useful in analyzing computer algorithms. Topics include recurrence relations, evaluation of sums, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods. Typically offered Spring. 


MA 51900  Introduction To Probability Credit Hours: 3.00. (STAT 51900 ) Algebra of sets, sample spaces, combinatorial problems, independence, random variables, distribution functions, moment generating functions, special continuous and discrete distributions, distribution of a function of a random variable, limit theorems. Typically offered Spring Fall. 


MA 52000  Boundary Value Problems Of Differential Equations Credit Hours: 3.00. Separation of variables; Fourier series; boundary value problems; Fourier transforms; Bessel functions; Legendre polynomials. Typically offered Fall Spring Summer. 


MA 52100  Introduction To Optimization Problems Credit Hours: 3.00. Necessary and sufficient conditions for local extrema in programming problems and in the calculus of variations. Control problems; statement of maximum principles and applications. Discrete control problems. Typically offered Fall. 


MA 52300  Introduction To Partial Differential Equations Credit Hours: 3.00. First order quasilinear equations and their applications to physical and social sciences; the CauchyKovalevsky theorem; characteristics, classification and canonical forms of linear equations; equations of mathematical physics; study of Laplace, wave and heat equations; methods of solution. Typically offered Fall Spring Summer. 


MA 52500  Introduction To Complex Analysis Credit Hours: 3.00. Complex numbers and complexvalued functions of one complex variable; differentiation and contour integration; Cauchy’s theorem; Taylor and Laurent series; residues; conformal mapping; applications. Not open to students with credit in MA 42500 . Typically offered Fall Spring Summer. 


MA 52700  Advanced Mathematics For Engineers And Physicists I Credit Hours: 3.00. Courses MA 52700 and MA 52800 constitute a twosemester sequence covering a broad range of subjects useful in early graduate engineering courses. Topics in MA 52700 include linear algebra, systems of ordinary differential equations, Laplace transforms, Fourier series and transforms, and partial differential equations. MA 51100 is recommended. Typically offered Fall. 


MA 52800  Advanced Mathematics For Engineers And Physicists II Credit Hours: 3.00. MA 52700 and 52800 constitute a twosemester sequence covering a broad range of subjects useful in early graduate engineering courses. Topics in MA 52800 include divergence theorem, Stokes theorem, complex variables, contour integration, calculus of residues and applications, conformal mapping, and potential theory. MA 51000 is recommended. Typically offered Spring. 


MA 53000  Functions Of A Complex Variable I Credit Hours: 3.00. Complex numbers and complexvalued functions of one complex variable; differentiation and contour integration; Cauchy’s theorem; Taylor and Laurent series; residues; conformal mapping; special topics. More mathematically rigorous than MA 52500 . Typically offered Fall Spring. 


MA 53100  Functions Of A Complex Variable II Credit Hours: 3.00. Advanced topics. Typically offered Fall Spring Summer. 


MA 53200  Elements Of Stochastic Processes Credit Hours: 3.00. (STAT 53200 ) A basic course in stochastic models, including discrete and continuous time Markov chains and Brownian motion, as well as an introduction to topics such as Gaussian processes, queues, epidemic models, branching processes, renewal processes, replacement, and reliability problems. Typically offered Spring. 


MA 53800  Probability Theory I Credit Hours: 3.00. (STAT 53800 ) Mathematically rigorous, measuretheoretic introduction to probability spaces, random variables, independence, weak and strong laws of large numbers, conditional expectations, and martingales. Typically offered Spring. 


MA 53900  Probability Theory II Credit Hours: 3.00. (STAT 53900 ) Convergence of probability laws; characteristic functions; convergence to the normal law; infinitely divisible and stable laws; Brownian motion and the invariance principle. Typically offered Fall. 


MA 54200  Theory Of Distributions And Applications Credit Hours: 3.00. Definition and basic properties of distributions; convolution and Fourier transforms; applications to partial differential equations; Sobolev spaces. Typically offered Fall. 


MA 54300  Ordinary Differential Equations And Dynamical Systems Credit Hours: 3.00. This course focuses on the theory of ordinary differential equations and methods of proof for developing this theory. Topics include basic results for linear systems, the local theory for nonlinear systems (existence and uniqueness, dependence on parameters, flows and linearization, stable manifold theorem) and the global theory for nonlinear systems (global existence, limit sets and periodic orbits, Poincare maps). Permission of instructor required. Typically offered Spring. 


MA 54400  Real Analysis And Measure Theory Credit Hours: 3.00. Metric space topology; continuity, convergence; equicontinuity; compactness; bounded variation, Helly selection theorem; RiemannStieltjes integral; Lebesgue measure; abstract measure spaces; LPspaces; Holder and Minkowski inequalities; RieszFischer theorem. Typically offered Fall Spring. 


MA 54500  Functions Of Several Variables And Related Topics Credit Hours: 3.00. Differentation of functions; Besicovitch covering theorem; differentation of one measure with respect to another; HardyLittlewood maximal function; functions of several variables; Sobolev spaces. Typically offered Spring. 


MA 54600  Introduction To Functional Analysis Credit Hours: 3.00. Fundamentals of functional analysis. Banach spaces, HahnBanach theorem. Principle of uniform boundedness. Closed graph and open mapping theorems. Applications. Hilbert spaces. Orthonormal sets. Spectral theorem for Hermitian operators and compact operators. Typically offered Fall. 


MA 55300  Introduction To Abstract Algebra Credit Hours: 3.00. Group theory: Sylow theorems, Jordan Hlder theorem, solvable groups. Ring theory: unique factorization in polynomial rings and principal ideal domains. Field theory: ruler and compass constructions, roots of unity, finite fields, Galois theory, solvability of equations by radicals. Typically offered Fall. 


MA 55400  Linear Algebra Credit Hours: 3.00. Review of basics: vector spaces, dimension, linear maps, matrices determinants, linear equations. Bilinear forms; inner product spaces; spectral theory; eigenvalues. Modules over a principal ideal domain; finitely generated abelian groups; Jordan and rational canonical forms for a linear transformation. Typically offered Fall Spring. 


MA 55600  Introduction To The Theory Of Numbers Credit Hours: 3.00. Divisibility, congruences, quadratic residues, Diophantine equations, the sequence of primes. Typically offered Fall Spring Summer. 


MA 55700  Abstract Algebra I Credit Hours: 3.00. Review of fundamental structures of algebra (groups, rings, fields, modules, algebras); JordanHolder and Sylow theorems; Galois theory; bilinear forms; modules over principal ideal domains; Artinian rings and semisimple modules. Polynomial and power series rings; Noetherian rings and modules; localization; integral dependence; rudiments of algebraic geometry and algebraic number theory; ramification theory. Typically offered Fall. 


MA 55800  Abstract Algebra II Credit Hours: 3.00. A continuation of MA 55700 . Typically offered Spring. 


MA 56000  Fundamental Concepts Of Geometry Credit Hours: 3.00. Foundations of Euclidean geometry, including a critique of Euclid’s “Elements” and a detailed study of an axiom system such as that of Hilbert. Independence of the parallel axiom and introduction to nonEuclidean geometry. Typically offered Fall Spring Summer. 


MA 56200  Introduction To Differential Geometry And Topology Credit Hours: 3.00. Smooth manifolds; tangent vectors; inverse and implicit function theorems; submanifolds; vector fields; integral curves; differential forms; the exterior derivative; DeRham cohomology groups; surfaces in E3., Gaussian curvature; two dimensional Riemannian geometry; GaussBonnet and Poincare theorems on vector fields. Typically offered Fall. 


MA 57100  Elementary Topology Credit Hours: 3.00. Fundamentals of point set topology with a brief introduction to the fundamental group and related topics, topological and metric spaces, compactness, connectedness, separation properties, local compactness, introduction to function spaces, basic notions involving deformations of continuous paths. Typically offered Fall. 


MA 57200  Introduction In Algebraic Topology Credit Hours: 3.00. Singular homology theory; EilenbergSteenrod asioms; simplicial and cell complexes; elementary homotopy theory; Lefschetz fixed point theorem. Typically offered Spring. 


MA 57500  Graph Theory Credit Hours: 3.00. Introduction to graph theory with applications. Typically offered Summer Fall Spring. 


MA 58400  Algebraic Number Theory Credit Hours: 3.00. Dedekind domains, norm, discriminant, different, finiteness of class number, Dirichlet unit theorem, quadratic and cyclotomic extensions, quadratic reciprocity, decomposition and inertia groups, completions and local fields. Typically offered Fall Spring. 


MA 58500  Mathematical Logic I Credit Hours: 3.00. Propositional and predicate calculus; the Gdel completeness and compactness theorem, primitive recursive and recursive functions; the Gdel incompleteness theorem; Tarski’s theorem; Church’s theorem; recursive undecidability; special topics such as nonstandard analysis. Typically offered Fall. 


MA 59800  Topics In Mathematics Credit Hours: 1.00 to 5.00. Supervised reading courses as well as duallevel special topics courses are given under this number. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 61100  Methods Of Applied Mathematics I Credit Hours: 3.00. Banach and Hilbert spaces; linear operators; spectral theory of compact linear operators; applications to linear integral equations and to regular SturmLiouville problems for ordinary differential equations. Prerequisite: MA 51100 , MA 54400 . Typically offered Spring. 


MA 61500  Numerical Methods For Partial Differential Equations I Credit Hours: 3.00. (CS 61500 ) Finite element method for elliptic partial differential equations; weak formulation; finitedimensional approximations; error bounds; algorithmic issues; solving sparse linear systems; finite element method for parabolic partial differential equations; backward difference and CrankNicholson timestepping; introduction to finite difference methods for elliptic, parabolic, and hyperbolic equations; stability, consistency, and convergence; discrete maximum principles. Prerequisite: MA 51400 , MA 52300 . Typically offered Spring. 


MA 62000  Mathematical Theory Of Optimal Control Credit Hours: 3.00. Existence theorems; the maximum principle; relationship to the calculus of variations; linear systems with quadratic criteria; applications. Offered in alternate years. Prerequisite: MA 54400 . Typically offered Spring. 


MA 63100  Several Complex Variables Credit Hours: 3.00. Power series, holomorphic functions, representation by integrals, extension of functions, holomorphically convex domains. Local theory of analytic sets (Weierstrass preparation theorem and consequences). Functions and sets in the projective space Pn (theorems of Weierstrass and Chow and their extensions). Prerequisite: MA 53000 . Typically offered Fall Spring Summer. 


MA 63800  Stochastic Processes I Credit Hours: 3.00. (STAT 63800 ) Advanced topics in probability theory which may include stationary processes, independent increment processes, Gaussian processes; martingales, Markov processes, ergodic theory. Prerequisite: MA 53900 . Typically offered Spring. 


MA 63900  Stochastic Process II Credit Hours: 3.00. (STAT 63900 ) Continuation of MA 63800 . Typically offered Fall. 


MA 64200  Methods Of Linear And Nonlinear Partial Differential Equations I Credit Hours: 3.00. Second order elliptic equations including maximum principles, Harnack inequality, Schauder estimates, and Sobolev estimates. Applications of linear theory to nonlinear equations. Prerequisite: MA 52300 . Typically offered Fall Spring Summer. 


MA 64300  Methods Of Partial Differerntial Equations II Credit Hours: 3.00. Continuation of MA 64200 . Topics to be covered are Lp theory for solutions of elliptic equations, including Moser’s estimates, Aleksandrov maximum principle, and the CalderonZygmund theory. Introduction to evolution problems for parabolic and hyperbolic equations, including Galerkin approximation and semigroup methods. Applications to nonlinear problems. Prerequisite: MA 64200 . Typically offered Spring. 


MA 64400  Calculus Of Variations Credit Hours: 3.00. Direct methods; necessary and sufficient conditions for lower semicontinuity of multiple integrals; existence theorems and connections with optimal control theory. Prerequisite: MA 54400 . Typically offered Fall Spring Summer. 


MA 65000  Commutative Algebra Credit Hours: 3.00. The study of those rings of importance in algebraic and analytic geometry and algebraic number theory. Prerequisite: MA 55800 . Typically offered Fall Spring Summer. 


MA 66100  Modern Differential Geometry Credit Hours: 3.00. Topics chosen by the instructor. Prerequisite: MA 54400 , MA 55400 . Typically offered Fall Spring Summer. 


MA 66300  Algebraic Curves And Functions I Credit Hours: 3.00. Algebraic functions of one variable from the geometric, algebraic, or functiontheoretic points of view. RiemannRoch theorem, differentials. Prerequisite: MA 55800 . Typically offered Fall Spring Summer. 


MA 66400  Algebraic Curves And Functions II Credit Hours: 3.00. Continuation of MA 66300 . Topics chosen by the instructor. Prerequisite: MA 66300 . Typically offered Fall Spring Summer. 


MA 66500  Algebraic Geometry Credit Hours: 3.00. Topics of current interest will be chosen by the instructor. Prerequisite: MA 65000 or MA 66300 . Typically offered Fall Spring Summer. 


MA 68400  Class Field Theory Credit Hours: 3.00. Ideles, adeles, Lfunctions, Artin symbol, reciprocity, local and global class fields, KroneckerWeber Theorem. Prerequisite: MA 58400 . Typically offered Fall Spring. 


MA 69000  Topics In Algebra Credit Hours: 1.00 to 3.00. Topics vary. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69200  Topics Applied Math Credit Hours: 1.00 to 3.00. Topics in applied math. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69300  Topics In Analysis Credit Hours: 1.00 to 3.00. Topics in analysis. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69400  Topics In Differntial Equations Credit Hours: 1.00 to 3.00. Topics In Differntial Equations. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69600  Topics In Geometry Credit Hours: 1.00 to 3.00. Topics in geometry. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69700  Topics In Topology Credit Hours: 1.00 to 3.00. Topics in topology. Permission of instructor required. Typically offered Fall Spring Summer. 


MA 69900  Research PhD Thesis Credit Hours: 1.00 to 18.00. Research PhD Thesis. Permission of instructor required. Typically offered Fall Spring Summer. 
Materials Engineering 


MSE 19000  Introduction To Materials Engineering Credit Hours: 1.00. An introduction to materials science and engineering. Emphasis on the “processing, structure, properties, performance” relationships that lead to the development of materials for society’s needs. Examples drawn from the major materials classes. Typically offered Fall Spring. 


MSE 23000  Structure And Properties Of Materials Credit Hours: 3.00. The relationship between the structure of materials and the resulting mechanical, thermal, electrical, and optical properties. Atomic structure, bonding, atomic arrangement; crystal symmetry, crystal structure, habit, lattices, defects, and the use of Xray diffraction. Phase equilibria and microstructural development. Applications to design. Typically offered Fall Spring. 


MSE 23500  Materials Properties Laboratory Credit Hours: 3.00. Laboratory experiments involving usage of standard equipment in the measurement of mechanical, microstructural, thermal, electrical, and optical properties. Introduction to computer aided data analysis. Experiments are carried out with metal, ceramic, and polymeric materials to illustrate propertystructureprocessing relationships. Typically offered Fall. 


MSE 25000  Physical Properties In Engineering Systems Credit Hours: 3.00. Class connects math, science and engineering practice and applications. Presents foundational aspects of engineering problem solving, use of computer math tools for engineering problem solving, basic engineering statics, dynamics and mechanics, group problem solving approaches, and introductory aspects of design and materials selection. Typically offered Spring. 


MSE 26000  Thermodynamics Of Materials Credit Hours: 3.00. Fundamental laws of thermodynamics and their applications to material systems; criteria for equilibrium; reaction and phase equilibria; properties of solutions; thermodynamic origins of phase diagrams. Typically offered Spring. 


MSE 27000  Atomistic Materials Science Credit Hours: 3.00. Introductory course with an atomistic view point on material properties. Three primary class sections: bonding crystallography and statistical mechanics. Bonding topics include introduction to quantum mechanics, emphasis on understanding of metallic, ionic and covalent bonding. Crystallography topics include crystal descriptions and symmetry principles. Statistical mechanics development with application to electronic and thermodynamic properties. Typically offered Spring. 


MSE 29100  Industrial Practice I Credit Hours: 0.00. Practice in industry and comprehensive written reports of this practice. For cooperative program students only. Typically offered Fall Spring Summer. 


MSE 29199  Professional Practice Extensive CoOp I Credit Hours: 0.00. Professional experience in Materials Engineering. Program coordinated by school with cooperation of participating employers. Students submit summary report and company evaluation. Professional Practice students only. Permission of department required. Typically offered Fall Spring Summer. 


MSE 29200  Industrial Practice II Credit Hours: 0.00. Practice in industry and comprehensive written reports of this practice. For cooperative program students only. Typically offered Fall Spring Summer. 


MSE 29299  Professional Practice Extensive II Credit Hours: 0.00. Professional experience in Materials Engineering. Program coordinated by school with cooperation of participating employers. Students submit summary report and company evaluation. Professional Practice students only. Permission of department required. Typically offered Fall Spring Summer. 


MSE 33000  Processing And Properties Of Materials Credit Hours: 3.00. An introduction to the relationships between the processing of materials and their properties. Heat treating, forming, casting, consolidation, and other more materialspecific manufacturing processes. Elucidation of the role of phenomena such as heat flow, mass diffusion, nucleation, interfacial tension, elastic and plastic deformation, precipitation, grain growth. Typically offered Spring. 


MSE 33500  Materials Characterization Laboratory Credit Hours: 3.00. The principles of analytical methods for characterization of materials for structure and composition; optical microscopy, scanning electron microscopy, Xray spectroscopy and diffraction, atomic absorption, emission spectroscopy, and mass spectrometry. Laboratory experiments in Xray spectroscopy, Xray diffraction, optical microscopy, and scanning electron microscopy. Typically offered Fall. 


MSE 34000  Transport Phenomena Credit Hours: 3.00. Mechanism and rates of heat, mass, and momentum transfer. Macroscopic and differential energy, mass, and momentum balances. Application to systems with phase transformations and chemical reaction. Typically offered Fall. 


MSE 36700  Materials Processing Laboratory Credit Hours: 3.00. This laboratory is intended as an intensive experience in processing techniques used for ceramics, metals, and polymers. Sintering of a ceramic, casting and postprocessing (work hardening, heat treatment, etc.) of a metal, and preparation and extrusion of a polymer are the suggested processes. The measurements (e.g., powder size, compaction force, temperature, grain size, molecular weight) applicable to the successful processing of the material and the final properties (e.g., hardness, ductility, strength, stiffness) will be emphasized. Typically offered Spring. 


MSE 37000  Electrical, Optical, And Magnetic Properties Of Materials Credit Hours: 3.00. An introductory course to provide basic background on the behavior of materials; electronic band structure, electronic and ionic conduction, electronic processes in semiconductors, dielectric, optical, and magnetic properties, and superconductivity; emphasis is on the relation between the properties and the structural aspects of materials. Typically offered Fall. 


MSE 38199  Professional Practice CoOp I Credit Hours: 0.00. To obtain practice with qualified employers within industry, government, or small business. Permission of Department required. Typically offered Fall Spring Summer. 


MSE 38200  Mechanical Response Of Materials Credit Hours: 3.00. This course encompasses deformationbased microscopic mechanisms, including dislocation motion, diffusion, and viscoplasticity. Macroscopic mechanical response of metals, ceramics, polymers, and composites will be related to elasticity and plasticity concepts for single crystal, polycrystalline, and amorphous materials. Practical design considerations for deformation will be included as well as an introduction to fracture mechanisms. Typically offered Spring. 


MSE 38299  Professional Practice CoOp II Credit Hours: 0.00. To obtain practice with qualified employers within industry, government, or small business. Permission of Department required. Typically offered Fall Spring Summer. 


MSE 38399  Professional Practice CoOp III Credit Hours: 0.00. To obtain practice with qualified employers within industry, government, or small business. Permission of Department required. Typically offered Fall Spring Summer. 


MSE 39000  Materials Engineering Seminar Credit Hours: 0.00. Presentation and discussion of current topics in materials engineering. Typically offered Fall Spring. 


MSE 39300  Industrial Practice III Credit Hours: 0.00. Practice in industry and comprehensive written reports of this practice. For cooperative program students only. Typically offered Fall Spring Summer. 


MSE 39399  Professional Practice Extensive CoOp III Credit Hours: 0.00. Professional experience in Materials Engineering. Program coordinated by school with cooperation of participating employers. Students submit summary report and company evaluation. Professional Practice students only. Permission of department required. Typically offered Fall Spring Summer. 


MSE 39400  Industrial Practice IV Credit Hours: 0.00. Practice in industry and comprehensive written reports of this practice. For cooperative program students only. Typically offered Fall Spring Summer. 


MSE 39499  Professional Practice Extensive CoOp IV Credit Hours: 0.00. Professional experience in Materials Engineering. Program coordinated by school with cooperation of participating employers. Students submit summary report and company evaluation. Professional Practice students only. Permission of department required. Typically offered Fall Spring Summer. 

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