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# Cognate Courses for Mathematics Majors

The Pure and Honors mathematics major 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 majors 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 major advisor.

### Astronomy 402—Stellar Astrophysics

**Prerequisites:**Math 216, and prior or concurrent enrollment in Physics 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.

### Astronomy 403—Astrophysics of the Interstellar Medium

**Prerequisites:**Math 216, and prior or concurrent enrollment in Physics 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.

### Astronomy 404—Galaxies and the Universe

**Prerequisites:**Math 216, and prior or concurrent enrollment in Physics 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.

### Astronomy 405—High Energy Astrophysics

**Prerequisites:**Math 216, and prior or concurrent enrollment in Physics 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.

### Astronomy 406—Computational Astrophysics

**Prerequisites:**Math 216, prior or concurrent enrollment in Physics 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 in length scale from intracellular to organ level.

### Chemistry 417 / Physics 417—Dynamical Processes in Biophysics

**Prerequisites:**Math 216, and Physics 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, Physics 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.

### Chem. 463—Physical Chemistry II

**Prerequisites:**Chem. 461/462**Credit:**3**Content:**This is the third of a three term sequence in physical chemistry and focuses on thermodynamics and kinetics. Both classical thermodynamics (entropy, phase and chemical equilibria) and statistical thermodynamics are discussed. The fundamental theories that govern macroscopic properties will be closely connected to motion and behavior of microscopic particles.

### EARTH 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.

### EARTH 477—Hydrogeology

**Prerequisites:**Physics 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.

### EARTH 483—Geophysics Seismology

**Prerequisites:**Prior or concurrent election of Math 215 and Physics 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.

### EARTH 486—Geodynamics

**Prerequisites:**Geosci 420 and prior or concurrent election of Math 215 and Physics 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:**Econ 401**Credit:**3**Content:**Game theory is the study of strategic interactions, where economic agents ("players" in a "game") affect each other through their actions, and make their decisions in light of what others are likely to choose. Game theory provides a unified framework for addressing questions about cooperation, conflict, and coordination. By formalizing the situations that players face, we can trace the logical implications of our assumptions on players' preferences, beliefs, and methods of reasoning.

### 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.

### Epidemiology 603—Introduction fo Mathematical Modeling in Epidemiology and Public Health

**Credit:**3**Content: This course addresses the following Epidemiology MPH Competencies (as listed in the Feb. 2012 CEPH Report): (1) Understand the nature and complexity of inter-individual variability at the molecular, cellular, organ, total body, and external environment (physical, social, economic, political, and cultural) levels as it affects and influences the study of a disease process. (2) Discuss population patterns of vital statistics, outbreaks, and health outcomes in terms of person, place and time. (9) Demonstrate written and oral communication skills related to epidemiological sciences within the context of public health.**

### 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:**Physics 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.

### Physics 390—Introduction to Modern Physics

**Prerequisites:**Physics 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.

### Physics 401—Intermediate Mechanics

**Prerequisites:**Physics 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.

### Physics 402—Light

**Prerequisites:**Physics 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.

### Physics 405—Intermediate Electricity and Magnetism

**Prerequisites:**Physics 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.

### Physics 406—Statistical and Thermal Physics

**Prerequisites:**Physics 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.

### Physics 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 415—Data Mining and Statistical Learning

**Prerequisites:**Math 215 and 217, and one of Stats. 401, 406, 412 or 426.**Credit:**4**Content:**This course covers the principles of data mining, exploratory analysis and visualization of complex data sets, and predictive modeling, Topics include: a) techniques and algorithms for exploratory data analysis and for discovering associations, patterns, changes, and anomalies in large data sets; and b) modern methods for multivariate analysis and statistical learning in regression, classification, and clustering. The presentation balances statistical concepts (such as model bias and over-fitting data, and interpreting results) and computational issues (including algorithmic complexity and strategies for efficient implementation). Students are exposed to algorithms, computations, and hands-on data analysis in weekly discussion sessions.

### 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.

### 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 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 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.

### 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 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 510Math 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 510Math 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 510Math 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 510Math 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.

### 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 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 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.