Undergraduate Program Cognate Courses for Mathematics Concentrators The Pure and Honors mathematics concentration programs each require "one cognate course chosen from some field other than mathematics" while the Mathematical Sciences program requires "two additional advanced courses in mathematics or a related area." In each case courses from other departments should generally have numbers above 300 and contain "significant mathematical content, at least at the level of Math 215." The list below contains some courses which fulfill these requirements. This list should not be considered in any sense exhaustive but rather as providing some suggestions. We have omitted some courses which require several field-specific prerequisites that very few mathematics concentrators would satisfy, and frequently only the first course of a sequence is included; most subsequent courses would also qualify. As always, courses to be counted as fulfilling this requirement must be approved by a mathematics concentration advisor. Astronomy 402 Stellar Astrophysics Prerequisites: Math. 216, and prior or concurrent enrollment in Phys. 340 Credit: (3) Content: This course examines the appearance, structure, and evolution of stars. We examine the basic physical processes that cause stars to have their observed structures; a study of the energy generation through nucleosynthesis; the basic physical laws that lead to the structure of stars; the transfer of radiation through the outer parts of the star; how spectroscopic information informs us as to the composition and motion of stars; and an in-depth look at the late stages of stellar evolution and stellar death. Astro 403 Astrophysics of the Interstellar Medium. Prerequisites: Math. 216, and prior or concurrent enrollment in Phys. 240 (or 260) Credit: (3) Content: The interstellar medium (the gas between stars) comprises a wide variety of material that interacts closely, and often violently, with individual stars and the host galaxy. The underlying atomic and molecular physics is developed; we examine how gas is ionized by hot stars and supernova remnants; we analyze the content of the cold pervasive atomic and molecular gas in the galaxy, how it often lies in spiral arms, and why giant molecular clouds are the most active sites of star formation. Recent discoveries are highlighted. Astro 404 Galaxies and the Universe. Prerequisites: Math. 216, and prior or concurrent enrollment in Phys. 340 Credit: (3) Content: Examines the properties of galaxies, large-scale structure in the universe, and cosmological models. The basic aspects of galaxies are explained, orbital theory, spiral arms, the missing mass in galaxies, galaxy evolution, and the starburst phenomenon. The clustering of galaxies, the hot intracluster medium and the dynamical evolution of clusters. Expansion of the universe, the cosmic microwave background, the inflationary universe, Big Bang nucleosynthesis, and the origin and growth of structure in the universe. Astro 405 High Energy Astrophysics Prerequisites: Math. 216, and prior or concurrent enrollment in Phys. 340 Credit: (3) Content: Examines the accretion disk and jets of plasma around black holes and other compact objects. How stellar-mass black holes form the rapidly variable x-ray binary sources and how supermassive black holes at the centers of galaxies produce quasars. The explosions of massive stars (supernovae) and the possibly resulting neutron star or black hole. The origin of x-ray and gamma-ray background radiation fields, the origin of gamma-ray bursts, and the nature of cosmic rays. Astro 406 Computational Astrophysics Prerequisites: Math. 216, prior or concurrent enrollment in Phys. 240 (or 260), and some knowledge of programming. Credit: (3) Content: Develops a practical working knowledge of the most widely used numerical methods in astrophysics. Theory is put into practice by development and use of numerical routines (some already written) in the personal computer or workstation environment. Interpolation, curve fitting, root finding, quadrature, numerical integration of differential equations, and matrix solutions of sets of linear equations. Fourier methods. Numerical statistical analysis, with particular emphasis on the peculiarities and pitfalls associated with real astronomical data. BME 479 Biotransport Prerequisites: Math 115 - 215, BME 331 Credit: (4) Content: Course covers fundamentals of mass transport as they relate to living systems. convection, diffusion, active transport and osmosis will be considered. Conservation of momentum, mass and energy will be applied to a variety of biological transport phenomena, ranging im length scale from intracellular to organ level. Chemistry 417 / Physics 417 Dynamical Processes in Biophysics Prerequisites: Math. 216, and Phys. 340 or Chem. 463 Credit: (3) Content: The physical basis of diffusive processes in biology and biochemistry, and optical spectroscopic means for measuring its rates. Topics include: membrane electrical potentials, nerve impulses, synaptic transmission, the physics of chemoreception by cells, motion and reaction kinetics of membrane components, optical microscopy, visible and UV light absorption, fluorescence and phosphorescence, quasielastic light scattering, mathematics of random fluctuations, and chaotic processes in biology. Chem. 461 Physical Chemistry I Prerequisites: Chem. 260, Phys. 240 (or 260), and Math. 215 Credit: (3) Content: This is the second of a three term sequence in physical chemistry. This course builds on material introduced in Chemistry 260. The Schrodinger Equation is solved in 1, 2, and 3 dimensions for important chemical problems. Group theory and quantum chemistry are used to understand chemical bonding and advanced spectroscopy. Should be elected in the same term as Chem. 462. Geological Sciences 426 Quantum Geology Prerequisites: Math through 216, and one of: mineralogy, petrology, solid-state chemistry, solid-state physics, or materials science; or permission of instructor Credit: (3) Content: This course provides a foundation in basic physical principles for the interpretation of the state and behavior of earth materials in the field and laboratory, including fluids, minerals, and melts. Central geological concepts from mineral and fluid chemistry, thermodynamics, and transport are analyzed in terms of the underlying quantum and statistical mechanics. Geosci 477 Hydrogeology Prerequisites: Phys. 140 (or 160)/141, Chem. 125/130, and Math. 116; Math. 215/216 are recommended Credit: (4) Content: Introduction to physical and chemical hydrogeology, with emphasis on process and application to geological settings. Quantification of the hydrologic cycle and physical framework and properties of aquifer systems. Development of transport equations and examples of fluid, energy, and chemical transport in porous and fractures media. Geosci 483 Geophysics: Seismology. Prerequisites: Prior or concurrent election of Math. 215 and Phys. 240 (or 260) Credit: (4) Content: Elastic properties of rocks, elastic waves, seismological instruments and data, use of body wave travel times, surface wave dispersion, and periods of free vibrations to infer the structure and composition of the earth's interior; earthquake intensity and magnitude scales; spatial, temporal, and magnitude distribution of earthquakes, earthquake source mechanisms, seismological contributions to understanding of earth dynamics and global tectonics, moonquakes, underground nuclear explosions and "man-made" earthquakes, and earthquake prediction and control. Geosci 486 Geodynamics. Prerequisites: Geosci 420 and prior or concurrent election of Math. 215 and Phys. 240 (or 260) Credit: (3) Content: Analysis of dynamic problems in geology through application of continuum and thermal physics. Concepts of stress, strain and elasticity; flow of viscous fluids; and conduction and advection of heat are developed in geological contexts. Physical basis for plate tectonics considered in detail. Econ. 401 Intermediate Microeconomic Theory Prerequisites: Econ. 101 and 102 Math 115,116,121,156,175,185,186,215,295,or 296 with a C or better Credit: (4) Content: This course deals with the theoretical analysis of consumers, firms, markets, and price determination. The analysis is rigorous, using the tools of algebra, geometry, and elementary calculus in constructing models. Econ. 402 Intermediate Macroeconomic Theory Prerequisites: Econ. 101 and 102 and Math 115 Credit: (4) Content: This course in macroeconomics deals with the determination of broad economic aggregates such as national income, employment, the price level, and the balance of payments in both the short run and the long run. Rigorous analysis is used to understand the forces that determine these economic variables, and how they are affected by public policies. Econ. 406 Introduction to Econometrics Prerequisites: Econ. 405 or Statistics 426 Credit: (4) Content: This course, a continuation of Economics 405, is intended to prepare students to conduct empirical research in economics. The classical linear regression model is developed with special emphasis on the basic assumptions of the model, economic situations in which the assumptions are violated, and alternative estimation procedures that are appropriate in these cases. Econ. 409 Game Theory Prerequisites: Math. 217 Credit: (3) Content: Parlor games: nim, tic-tac-toe, hex, chess. Fixed points and equilibria. Zero-sum games. Chance and information. Poker. Coordination and cooperation. Bargaining. Evolution of cooperation. Econ. 435 Financial Economics. Prerequisites: Econ. 401, and 404 or 405 Credit: (4) Content: An introduction to the economic analysis of financial markets and financial decision making. Asset pricing theory, net present value, arbitrage strategies, portfolio management, and financial market behavior. Case studies of current policy. Philosophy 414 Mathematical Logic. Prerequisites: None Credit: (3) Content: An introduction to truth function theory and quantification theory, including the completeness of quantification theory. Physics 340 Waves, Heat, and Light Prerequisites: Phys. 240 or 260, and Math. 215 Credit: (3) Content: This is the third term of the introductory physics sequence. The topics covered in the course include thermodynamics, light and optics, the wave equation, and special relativity. Students should take the lab Physics 341 concurrently. Phys. 390 Introduction to Modern Physics Prerequisites: Phys. 340 and Math. 216 Credit: (3) Content: This course provides an introduction to the principles of quantum mechanics, followed by a survey of several of the sub-fields of physics, usually including atomic, solid state, nuclear, and particle physics. Phys. 401 Intermediate Mechanics. Prerequisites: Phys. 126/128 or 240 (or 260)/241, and Math. 216 Credit: (3) Content: Newtonian and Lagrangian mechanics: Kinematics and dynamics in one, two and three dimensions, vector analysis; motion under gravity, planetary motion; free and forced, damped and undamped harmonic oscillators; the conservation laws of mechanics; inertial and accelerated frames of reference, fictitious forces; rigid body mechanics; coupled oscillators. Phys. 402 Light Prerequisites: Phys. 126/128 or 240 (or 260)/241, and Math. 216 Credit: (3) Content: The phenomena of physical optics, reflection, refraction, dispersion, interference, diffraction, and polarization interpreted in terms of the wave theory of light. Phys. 405 Intermediate Electricity and Magnetism. Prerequisites: Phys. 126/128 or 240 (or 260)/241, and Math. 216 Credit: (3) Content: Emphasis is placed upon the basic physical principles including electrostatics, magnetostatics, time-dependent electromagnetic fields and the effect of fields on dielectric and magnetic media. An introduction to Maxwell's equations and electromagnetic radiation is included. Other topics may include AC circuits and superconductivity. Phys. 406 Statistical and Thermal Physics Prerequisites: Phys. 126/128 or 240 (or 260)/241, and Math. 216 Credit: (3) Content: Introduction to thermal processes including the classical laws of thermodynamics and their statistical foundations: basic probability concepts; statistical description of systems of particles; thermal interaction; microscopic basis of macroscopic concepts such as temperature and entropy; the laws of thermodynamics; and the elementary kinetic theory of transport processes. Phys. 451 Methods of Theoretical Physics I Prerequisites: Math. 215 and 216 Credit: (3) Content: Physics 451 and 452 constitute a two term sequence in mathematical methods of physics. Stats 406 Introduction to Statistical Computing Prerequisites: Math 215 Credit: (3) Content: Selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration. Stats 412 Introduction to Probability and Statistics Prerequisites: Stat. 405, 412, or 425 Credit: (4) Content: The objectives of this course are to introduce students to the basic ideas of probability and statistical inference and to acquaint students with some important data analytic techniques, such as regression and the analysis of variance. Examples will emphasize applications to the natural sciences and engineering. Stats 413 The General Linear Model and Its Applications Prerequisites: Stat. 350 and Math. 217; concurrent enrollment in Stat. 425 Credit: (4) Content: Introduces students to the general linear model and its assumptions, and covers such topics as the geometry of the model, projections, least squares estimation, residuals, normal distribution theory results, inference on parameters, diagnostic tools, and applications in analysis of variance, design, and time series. Stats 426 Introduction to Theoretical Statistics Prerequisites: Stat. 425 Credit: (3) Content: An introduction to theoretical statistics for students with a background in probability. Probability models for experimental and observational data, normal sampling theory, likelihood-based and Bayesian approaches to point estimation, confidence intervals, tests of hypotheses, and an introduction to regression and the analysis of variance. Stats 430 Applied Probability Prerequisites: Stat. 425 Credit: (3) Content: Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distributions; introduction to Brownian motion. Selected applications such as branching processes, financial modeling, genetic models, the inspection paradox, inventory and queuing problems, prediction, and/or risk analysis. Stats 500 Applied Statistics I Prerequisites: Mathematics 417 and a course in statistics (Statistics 426 or permission) Credit: (3) Content: Linear models: Definition, fitting, identifiability, multicollinearity, Gauss-Markov theorem, variable selection, diagnostics, transformations, influential observations, robust procedures, ANOVA and analysis of covariance, interpretation of results, meaning of regression coefficients. Randomized block, factorial designs. Stats 510 Mathematical Statistics I Prerequisites: Math. 450 or 451, and a course in probability or statistics Credit: (3) Content: Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential families, inequalities and a central limit theorem. Introduction to decision theory including: models, parameter spaces, decision rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems, and various types of estimators. Stats 550 Bayesian Decision Analysis Prerequisites: Stat. 425 Credit: (3) Content: Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; applications to a variety of decision-making situations. Stats 575 Econometric Theory I. Prerequisites: Math. 417 and 425 or Econ. 653, 654, 673, and 674 Credit: (3) Content: A course in econometric theory stressing the statistical foundations of the general linear model. The course involves a development of the required theory in mathematical statistics; and derivations and proofs of main results associated with statistical inference in the general linear model. Aerospace Engineering 315 Aircraft and Spacecraft Structures Prerequisites: Aero 285 and Math 216 Credit: (4) Content: Concepts of displacement, strain, stress, compatibility, equilibrium, and constitutive equations as used in solid mechanics. Emphasis is on boundary-value problem formulation via simple examples, followed by the use of the finite-element method for solving problems in vehicle design. Aero 325 Aerodynamics Prerequisites: Math 216 and Aero 225 Credit: (4) Content: Fundamental concepts in aerodynamics. Students learn how airfoils produce lift and how the pressure distribution about an airfoil can be calculated. Introduces the boundary-layer concept, how boundary layers lead to drag, and what makes them prone to instability and turbulence or separation. Effects of the wing platform shape on lift and drag. Introduction to airfoil design, high-lift devices and high-speed aerodynamics. Aero 335 Aircraft and Spacecraft Propulsion Prerequisites: Aero 225 and Math 216 Credit: (4) Content: Air breathing propulsion, rocket propulsion, and an introduction to modern advanced propulsion concepts. Includes thermodynamic cycles as related to propulsion and the chemistry and thermodynamics of combustion. Students analyze turbojets, turbofans and other air-breathing propulsion systems. Introduces liquid- and solid-propellant rockets and advanced propulsion concepts such as Hall thrusters and pulsed plasma thrusters. Students also learn about the environmental impact of propulsion systems and work in teams to design a jet engine. Aero 345 Flight Dynamics and Control Prerequisites: Math 216, Aero 245, and ME 240 Credit: (4) Content: An introduction to dynamics and control of aircraft and spacecraft. Introduces concepts from linear systems theory (state equations, transfer functions, stability, time and frequency response). Includes aircraft longitudinal and lateral flight dynamics and control systems. Also includes spacecraft attitude dynamics and control. Involves a team design project. Aero 351 Computational Methods in Aerospace Vehicle Analysis and Design Prerequisites: Aero 245, Math 216 Credit: (3) Content: Students learn to use computational methods for solving problems in aerospace engineering, in the areas of aerodynamics, structures, flight mechanics, and propulsion. Lectures cover the engineering analysis and design methods, basic numerical methods, and programming techniques necessary to solve these problems. AOSS 305 Introduction to Atmospheric, Oceanic and Space Dynamics Prerequisites: AOSS 304, Math 215 Credit: (4) Content: Fluid kinematics and thermodynamics; equations of motion; hydrostatic and geostrophic approximations; convective instability; atmospheric boundary layer; Gulf Stream theory; wave motions; barotropic and baroclinic instability; introductory kinetic theory; electromagnetic forces. AOSS 401 Geophysical Fluid Dynamics Prerequisites: Physics 240, preceded or accompanied by Aero 350 or Math 450 Credit: (3) Content: Dynamics of the oceans and atmosphere. Equations of motion in spherical coordinates, beta-plane approximation, wave properties in the oceans and atmosphere. AOSS 407 Mathematical Methods in Geophysics Prerequisites: Math 216 Credit: (3) Content: Vector calculus and Cartesian tensors; Sturm-Liouville systems, Green's functions, and solution of boundary value problems; Fourier series, Fourier and Laplace transforms, discrete Fourier transform, fast Fourier transforms, and energy spectra. AOSS 408 Environmental Problem Solving with Computers Prerequisites: Eng 103, Math 216 Credit: (3) Content: Solution of meteorological, oceanographic, and general environmental problems using computers. Applications of numerical analysis, statistics, and data handling to geophysics and environmental numerical output in terms of observed phenomena. AOSS 422 Micrometeorology I Prerequisites: Physics 240 or Math 215 Credit: (3) Content: Physical processes responsible for the thermal and moisture conditions in the air layer near the ground. Components of net radiation exchange, heat transfer in soil, wind structure and turbulence near the ground, turbulent transfer of sensible heat and water vapor, evapotranspiration; forest climatologic, transitional microclimates. AOSS 430 Thermodynamics of the Atmosphere Prerequisites: preceded or accompanied by Math 216 Credit: (3) Content: Physical principles of thermodynamics with emphasis on atmospheric applications. Topics include atmospheric statics; first and second principles of thermodynamics; adiabatic processes; thermodynamics of moist air; equilibrium with droplets and crystals; fundamentals of cloud and precipitation processes. AOSS 432 Environmental Radiative Processes Prerequisites: Math 216, Physics 240 Credit: (3) Content: The nature of electromagnetic radiation. Solar and terrestrial radiation. The transfer of radiation including absorption, emission and scattering. Radiation and climate. Satellite observations and remote sounding. AOSS 458 Principles and Applications of Visible and Infrared Remote Sensing Prerequisites: Math 216, Physics 140 or equivalent Credit: (3) Content: Principles of visible and infrared remote sensing AOSS 459 : Principles and Applications of Radio and Active Remote Sensing Prerequisites: Math 216, Physics 140 Credit: (3) Content: Principles of radio and lidar remote sensing are discussed, beginning with electromagnetic wave propagation, emission, absorption and scattering, followed by air and spacecraft instruments. These principles are applied to case studies in environmental science and protection, global change, urban metabolism, military surveillance and treaty monitoring as well as law enforcement. AOSS 479 Atmospheric Chemistry Prerequisites: Chem 130, Math 216 Credit: (3) Content: Thermochemistry, photochemistry, and chemical kinetics of the atmosphere; geochemical cycles, generation of atmospheric layers and effects of pollutants are discussed. AOSS 480 The Planets: Composition, Structure, and Evolution Prerequisites: Math 216, Physics 240, Chem 130 Credit: (3) Content: Origin of the solar system, composition and radial distribution of material in planets and satellites; relationship of gravity fields to shape and density distribution; magnetism; origin and significance of topography; structure of planetary atmospheres; energetics and dynamics of interiors and atmospheres, thermal histories and evolution of interiors, devolatization, origin, and evolution of atmospheres. AOSS 555 Spectral Methods Prerequisites: Math 216, Eng 103 or knowledge of FORTRAN Credit: (4) Content: An introduction to numerical methods based on Fourier Series, Chebyshev polynomials, and other orthogonal expansions. Although the necessary theory is developed, the emphasis is on algorithms and practical applications in geophysics and engineering, especially fluid mechanics. Many homework assignments will be actual problem-solving on the computer. Biomedical Engineering 525 Cellular and Molecular Networks Prerequisites: Biol 105 or Biol 112 and Math 215 Credit: (3) Content: This course is designed to equip the student with appropriate concepts and techniques for the quantitative analysis of the integrated behavior of complex biochemical systems. A general approach is developed from the basic postulates of enzyme catalysis and is illustrated with numerous specific examples, primarily from the microbial cell. Chemical Engineering 341 Fluid Mechanics Prerequisites: Physics 140, preceded or accompanied by ChemE 230 and Math 216 Credit: (4) Content: Fluid mechanics for chemical engineers. Mass, momentum, and energy balances on finite and differential systems. Laminar and turbulent flow in pipes, equipment, and porous media. Polymer processing and boundary layers. Potential, two-phase, and non-Newtonian flow. ChemE 507 Mathematical Modeling in Chemical Engineering Prerequisites: ChemE 344, Eng 303 Credit: (3) Content: Formulation of deterministic models from conservation laws, population balances; transport and reaction rates. Formulation of boundary and initial conditions. Dimensional analysis, analytical and numerical methods. CEE480 Dynamics of Environmental Systems Prerequisites: Chem 130, CEE 280, Math 216 Credit: (3) Content: Dynamics of transformation processes in natural and engineered environmental systems; application of ideal and non-ideal reactor concepts to system modeling; energetics and rates of intraphase and interphase mass transport and reaction processes in surface and ground-waters, treatment operations, and other systems of concern in environmental engineering. EECS 306 Signals and Systems II Prerequisites: EECS 206, 215 and Math 216 Credit: (4) Content: Theory and practice of signals and systems engineering in continuous and discrete time. Hands-on experience in laboratory sessions with communications, control and signal processing. Continuous-time linear systems: convolution, Fourier and Laplace transforms, transfer functions, poles and zeros, stability, sampling, introductions to communications and feedback control. Discrete-time linear systems: Z transform, filters, Fourier transform, signal processing. State space models of systems using finite-state machines. EECS 314 Circuit Analysis and Electronics Prerequisites: Math 216, Physics 240 Credit: (4) Content: A survey of electrical and electronic circuits for students not in EE or CE. Formulation of circuit equations; equivalent circuits; frequency response ideas; steady-state and transient response; introduction to amplifiers; operational amplifiers; survey of electronic devices and circuits. Use of computer simulations for analysis of more advanced circuits. EECS 376 Foundations of Computer Science Prerequisites: EECS 203 or 280 Credit: (4) Content: An introduction to computation theory: finite automata, regular languages, pushdown automata, context-free languages, Turing machines, recursive languages and functions, and computational complexity. EECS 475 Introduction to Cryptography Prerequisites: EECS 203 or Elementary Algebra at the level of Math 312. Programming experience in a high level language (for example as in EECS 280) or in mathematical packages such as MAPLE or MATHEMATICA.. Credit: (4) Content: This course will study fundamental concepts, algorithms, encryption schemes, and protocols in cryptography. Main topics include: symmetric (private key) encryption, public key encryption, hash functions, digital signatures, and key distribution. The course emphasizes a rigorous mathematical study of the various cryptographic schemes and their security in terms of algorithmic complexity. A nontrivial part of the course will be devoted to algorithmic and mathematical background from number theory, algebra, and probability theory needed to gain a solid understanding of cryptography. Popular cryptographic schemes such as AES and RSA will be highlighted and their security will be rigorously investigated. EECS 477 Introduction to Algorithms Prerequisites: EECS 281 Credit: (4) Content: Fundamental techniques for designing efficient algorithms and basic mathematical methods for analyzing their performance. Paradigms for algorithm design: divide-and-conquer, greedy methods, graph search techniques, dynamic programming. Design of efficient data structures and analysis of the running time and space requirements of algorithms in the worst and average cases. EECS 550 Information Theory Prerequisites: EECS 501 Credit: (3) Content: The concepts of source, channel, rate of transmission of information. Entropy and mutual information. The noiseless coding theorem. Noisy channels; the coding theorem for finite state zero memory channels. Channel capacity. Error bounds. Parity check codes. Source encoding. EECS 567 Introduction to Robotics: Theory and Practice Prerequisites: EECS 281 Credit: (3) Content: Introduction to robots considered as electro-mechanical computational systems performing work on the physical world. Data structures representing kinematics and dynamics of rigid body motions and forces and controllers for achieving them. Emphasis on building and programming real robotic systems and on representing the work they are to perform. EECS 586 Design and Analysis of Algorithms Prerequisites: EECS 281 Credit: (3) Content: Design of algorithms for nonnumeric problems involving sorting, searching, scheduling, graph theory, and geometry. Design techniques such as approximation, branch-and-bound, divide-and-conquer, dynamic programming, greed, and randomization applied to polynomial and NP-hard problems. Analysis of time and space utilization. IOE 310 Introduction to Optimization Methods Prerequisites: Math 216, IOE 201 and Engr 101 or EECS 100 Credit: (4) Content: Introduction to deterministic models with emphasis on linear programming; simplex and transportation algorithms, engineering applications, relevant software. Introduction to integer, network, and dynamic programming, critical path methods. IOE 465 Design and Analysis of Experiments Prerequisites: IOE 366 Credit: (4) Content: Linear Models, Multi-collinearity and Robust Regression, Comparative Experiments, Randomized Blocks and Latin Squares, Factorial Designs, Confounding, Mixed Level Fractional Factorials, Random and Mixed Models, Nesting and Split Plots, Response Surface Methods, Taguchi Contributions to Experimental Design. IOE 512 Dynamic Programming Prerequisites: IOE 510, IOE 316 Credit: (3) Content: The techniques of recursive optimization and their use in solving multistage decision problems, applications to various types of problems, including an introduction to Markov decision processes. IOE 515 Stochastic Processes Prerequisites: IOE 316 or Stat 310 Credit: (3) Content: Introduction to non-measure theoretic stochastic processes. Poisson processes, renewal processes, and discrete time Markov chains. Applications in queuing systems, reliability, and inventory control. IOE 610 Linear Programming II Prerequisites: IOE 510(Math 561) Credit: (3) Content: Primal-dual algorithm. Resolution of degeneracy, upper bounding. Variants of simplex method. Geometry of the simplex method, application of adjacent vertex methods in non-linear programs, fractional linear programming. Decomposition principle, generalized linear programs. Linear programming under uncertainty. Ranking algorithms, fixed charge problem. Integer programming. Combinatorial problems. IOE 611 Nonlinear Programming Prerequisites: IOE 510(Math 561) Credit: (3) Content: Modeling, theorems of alternatives, convex sets, convex and generalized convex functions, convex inequality systems, necessary and sufficient optimality conditions, duality theory, algorithms for quadratic programming, linear complementary problems, and fixed point computing. Methods of direct search, Newton and Quasi-Newton, gradient projection, feasible direction, reduced gradient; solution methods for nonlinear equations. IOE 612 Network Flows Prerequisites: IOE 510(Math 561) Credit: (3) Content: Flow problems on networks. Maximum flow minimum cut theorem. Labeling algorithms. Circulation and feasibility theorems. Sensitivity analysis. Incidence matrices. Shortest routes. Minimum cost flows, out-of-kilter algorithm. Critical path networks, project cost curves. Multi-commodity flow problem, biflows. Matching problems in graph theory. IOE 614 Integer Programming Prerequisites: IOE 510(Math 561) Credit: (3) Content: Modeling with integer variables, total unimodularity, cutting plane approaches, branch-and-bound methods, Lagrangian relaxation, Bender's decomposition, the knapsack, and other special problems. MacroSE 418 Structural Macromolecular Prerequisites: Math 216, Physics 242 or permission Credit: (3) Content: An intensive study of macromolecular structural problems and their solutions: thermodynamics and statistical mechanics of chain molecules; conformational influencing conformational transitions; denaturation; statistical nature of physical properties; nature of general organization and folding in macromolecules; case studies of structural problems in bio and macromolecules. MSE 430 Thermodynamics of Materials Prerequisites: Chem 210, Phys 140/141, Math 215 or Math 285, MSE 350 Credit: (4) Content: The laws of thermodynamics and their consequences. Applications to solid and liquid materials. Mass and energy balances. Gas reactions. Phase diagrams. Ellingham, Pourbaix and stability diagrams. Defects in solids. Interfaces. Statistical thermodynamics. MSE 435 Kinetics and Transport in Materials Engineering Prerequisites: Math 216, MSE 150 or 220 or MSE 250 Credit: (4) Content: Principles of reaction kinetics. Fluid, energy, and mass transport, with applications to materials systems. ME 311 Strength of Materials Prerequisites: ME 211, Math 216 Credit: (3) Content: Energy methods; buckling of columns, including approximate methods; bending of beams of unsymmetrical cross-section; shear center and torsion of thin-walled sections; membrane stresses in axisymmetric shells; elastic-plastic bending and torsion; axisymmetric bending of circular plates. ME 330 Thermal and Fluid Sciences II Prerequisites: ME 230, ME 240, and Math 216 Credit: (4) Content: Fluid statics. Control volume analysis; mass, momentum, energy. Bernoulli equation. Dimensional analysis; similarity in fluid dynamics and convective heat transfer. Simple viscous flows with heat transfer. Internal and external flows with heat transfer; boundary layers, skin friction, heat transfer coefficient, heat exchangers, lift, drag, correlations, introduction to computational approaches. ME 336 Thermodynamics II Prerequisites: ME 235 or ME 230 Credit: (3) Content: Thermodynamic power and refrigeration systems; availability and evaluation of thermodynamic properties; general thermodynamic relations, equations of state, and compressibility factors; chemical reactions; combustion; gaseous dissociation; phase equilibrium. Design and optimization of thermal systems. ME 360 Modeling, Analysis and Control of Dynamic Systems Prerequisites: ME 240 Credit: (4) Content: Unified approach to abstracting real mechanical, fluid, and electrical systems into proper models in graphical and state equation form to meet engineering design and control system objectives. Introduction to system analysis (eigenvalues, time and frequency response) and linear feedback control. Synthesis and analysis by analytical and computer methods. ME 424 Engineering Acoustics Prerequisites: Math 216 and EECS 230 or Physics 240 Credit: (3) Content: Vibrating systems; acoustic wave equation; plane and spherical waves in fluid media; reflection and transmission at interfaces; propagation in lossy media; radiation and reception of acoustic waves; pipes, cavities, and waveguides; resonators and filters; noise; selected topics in physiological, environmental and architectural acoustics. ME 437 Applied Energy Conversion Prerequisites: ME 230 and Math 216 Credit: (3) Content: Quantitative treatment of energy resources, conversion processes, and energy economics. Consideration of fuel supplies, thermodynamics, environmental impact, capital and operating costs. Emphasis is placed on issues of climate change and the role of energy usage. In-depth analysis of automobiles to examine the potential of efficiency improvement and fuel change. ME 440 : Intermediate Dynamics and Vibrations Prerequisites: ME 240 Credit: (4) Content: Newton/Euler and Lagrangian formulations for three-dimensional motion of particles and rigid bodies. Linear free and forced responses of one and two degree of freedom systems and simple continuous systems. Applications to engineering systems involving vibration isolation, rotating imbalance and vibration absorption. ME 501 Analytical Methods in Mechanics Prerequisites: ME 211, ME 240, Math 216 Credit: (3) Content: An introduction to the notation and techniques of vectors, tensors, and matrices as they apply to mechanics. Emphasis is on physical motivation of definitions and operations, and on their application to problems in mechanics. Extensive use is made of examples from mechanics. ME 502 Methods of Differential Equations in Mechanics Prerequisites: Math 454 Credit: (3) Content: Applications of differential equation methods of particular use in mechanics. Boundary value and eigenvalue problems are particularly stressed for linear and nonlinear elasticity, analytical dynamics, vibration of structures, wave propagation, fluid mechanics, and other applied mechanic topics. ME 540 Intermediate Dynamics Prerequisites: ME 240 Credit: (3) Content: Newton/Euler and Lagrangian formulations for three dimensional motion of particles and rigid bodies. Principles of dynamics applied to various rigid-body and multi-body dynamics problems that arise in aerospace and mechanical engineering. NA 320 Marine Hydrodynamics I Prerequisites: ME 211 or ME 240 or permission Credit: (4) Content: Concepts and basic equations of marine hydrodynamics. Similitude and dimensional analysis, basic equations in integral form, continuity, and Navier-Stokes equations. Ideal fluid flow, Euler's equations, Bernoulli equation, free surface boundary value problems. Laminar and turbulent flows in pipes and around bodies. NERS 311 Elements of Nuclear Engineering and Radiological Sciences I Prerequisites: NERS 211, Physics 240, preceded or accompanied by Math 450 Credit: (4) Content: Photons, electrons, neutrons, and protons. Particle and wave properties of radiation. Introduction to quantum mechanics and special relativity. Properties and structure of atoms and nuclei. Introduction to interactions of radiation with matter.