# Cognate Courses

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.

### AEROSP 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.

### AEROSP 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.

### AEROSP 335 - Aerospace 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.

### AEROSP 347 - Space Flight Mechanics

• Prerequisites: ME 240, Math 216, and AE 201
• Credit: 3
• Content: Introduction to space flight mechanics. The two-body problem. Orbital transfers, maneuvers and orbital analysis. Ground tracks and relative motion in orbit. Gravity assist trajectories. Spacecraft attitude and rotational dynamics. Euler's and Poisson's equations. Stability analysis. Open loop attitude control momentum management using thrusters and reaction wheels.

### AEROSP 348 - Aircraft Dynamics and Control

• Prerequisites: AE 347
• Credit: 3
• Content: Introduction to the dynamics and control of atmospheric flight vehicles. Nonlinear equations of motion. Stability derivatives and linearized equations for longitudinal and lateral flight dynamics. Concepts from linear systems: state equations, transfer functions, stability, time response, frequency response. Fundamentals of feedback control, including root locus and Nyquist analysis applied to flight control.

### AEROSP 423 - Computational Methods for Aerospace Engineering

• Prerequisites: ENGR 101 or ENGR 151 and MATH 216 w/ minimum grade of C-
• Credit:  3
• Content: This course covers computational methods used in Aerospace engineering, including time integration techniques for ordinary differential equations, finite differences, finite volumes, finite elements, and probabilistic methods. Emphasis is placed on analysis and implementation of the underlying numerical methods. Computer programming in Matlab or a similar language is required.

### AEROSP 540 - Intermediate Dynamics

• Prerequisites: MECHENG 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.

### ASTRO 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.

### ASTRO 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.

### ASTRO 404 - Galaxies and the Universe

• Prerequisites: Math 216 plus prior or current enrollment in Physics 340 and 390; or instructor’s permission.
• Credit: 3
• Content: Examines the properties of galaxies, large-scale structure in the universe, and cosmological models. Considers orbit theory, spiral arms, the missing mass in galaxies, galaxy evolution, and the starburst phenomenon. Examines the clustering of galaxies, the hot intra-cluster medium, and the dynamical evolution of clusters. Addresses leading astronomy topics, such as expansion of the universe, the cosmic microwave background, 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 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.

### ASTRO 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.

### BIOMEDE 331 - Introduction to Biofluid Mechanics

• Prerequisites: BIOMEDE 231, MATH 215 and MATH 216
• Credit: 4
• Content: This course introduces the fundamentals of biofluid dynamics and continuum mechanics, and covers the application of these principles to a variety of biological flows. Fluid flow in physiology and biotechnology is investigated at a variety of scales, ranging from subcellular to whole body.

### BIOMEDE 332 - Introduction to Biosolid Mechanics

• Prerequisites: BIOMEDE 231, MATH 215 and MATH 216
• Credit: 4
• Content: This course covers the fundamentals of continuum mechanics and constitutive modeling relevant for biological tissues. Constitutive models covered include linear elasticity, nonlinear elasticity, viscoelasticity and poroelasticity. Structure-function relationships which link tissue morphology and physiology to tissue constitutive models will be covered for skeletal, cardiovascular, pulmonary, abdominal, skin, eye and nervous tissues.

### BIOMEDE 424/MECHENG 424 - Engineering Acoustics

• Prerequisites: MATH 216 and 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.

### BIOMEDE 479 - Biotransport

• Prerequisites: MATH 216, BIOMEDE 331 or MECHENG 330, or permission of instructor
• Credit: 4
• Content: Fundamentals of mass transport as it relates to biomedical systems. Convection, diffusion, osmosis and conservation of momentum, mass and energy will be applied to cellular and organ level transport. Examples of diffusion combined with reaction will also be examined.

### BIOMEDE 525/MICROB 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.

### CHEM 370/BIOPHYS 370/PHYSICS 370 - Physical and Chemical Principles Behind Biology and Medicine

• Prerequisites: MATH 215; and PHYSICS 235 or 240. (Prerequisites enforced at registration.) CHEM 130 or placement in 210.
• Credit: 3
• Content: This course is an introduction to the fundamental physical and chemical principles of biophysics. It covers quantum aspects of matter, thermodynamics, kinetics and statistical mechanics in the context of biological applications.

### CHEM 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 453 - Biophysical Chemistry I: Thermodynamics and Kinetics

• Prerequisites: CHEM 260 (or CHEM 261 and CHEM 330), CHEM 451, PHYSICS 240, and MATH 215 or CHEM 262
• Credit: 3
• Content: This course provides an introduction to quantum mechanics and its application to chemistry. It is the second of a 3-term sequence in physical chemistry and builds on material introduced in CHEM 260. The Schrodinger Equation is solved in one, two, and three dimensions for important chemical problems. Group theory and quantum chemistry are used to understand chemical bonding and advanced spectroscopy.

### CHEM 461 - Physical Chemistry I

• Prerequisites: CHEM 260 (or CHEM 261 and CHEM 330), CHEM 451, PHYSICS 240, and MATH 215 or CHEM 262
• Credit: 3
• Content: First in a two-semester Biophysical Chemistry sequence for biochemistry concentrators. Emphasis on topics and applications relevant to biochemistry and modern biophysical chemistry, building on CHEM 260. Rigorous mathematical theory of classical thermodynamics will be developed, including applications to entropy, heat engines, solution properties, and phase and chemical equilibrium. Modern statistical thermodynamics, modern theories of fundamental reaction rates and enzyme kinetics and molecular transport theories will be described and developed.

### CHE 341 - Fluid Mechanics

• Prerequisites: Preceded by Physics 140 and Math 215, preceded or accompanied by CHE 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.

### CHE 342 - Mass and Heat Transfer

• Prerequisite: CHE 230, CHE 341, and Math 216
• Credit: 4
• Content: Theories and applications of mass and heat transport phenomena. Fick's law. Steady and unsteady diffusion. Mass transfer coefficeients. Simultaneous momentum and mass transfer. Fourier's law. Steady and unsteady thermal conduction. Heat transfer coefficients. Heat exchangers. Condensation and boiling. Radiation. Kirchoff's law and view factors.

### CHE 540 - Mathematical Methods for Biological Network Analysis

• Prerequisite: Senior or graduate standing, permission by instructor
• Credit: 3
• Content: This course focuses on methods and applications. Methods include ordinary differential equations, mathematical programming, Bayesian networks and statistical analysis, etc. Applications to the modeling of various biological systems are discussed and students perform a critical evaluation of current literature as well as hands-on computational projects using high level computing languages

### CHE 554/MATSCIE 554 - Computational Methods in MS&E and CHE`

• Prerequisite: none
• Credit: 3
• Content: Broad introduction to the methods of numerical problem solving in Materials Science and Chemical Engineering. Topics include numerical techniques, computer algorithms and the formulation and use of computational approaches for the modeling and analysis of phenomena peculiar to these disciplines.

### CHE 557/MATSCIE 557 - Computational Nanoscience of Soft Matter

• Prerequisites: Differential equations course, and a statistical thermodynamics or statistical mechanics course.
• Credit: 3
• Content: Provides an understanding of strategies, methods, capabilities and limitations of computer simulation as it pertains to the modeling and simulation of soft materials at the nanoscale. The course consists of lectures and hands-on, interactive simulation labs using research codes and commercial codes. Ab initio, molecular dynamics, Monte Carlo and mesoscale methods.

### CEE 412 - Matrix Structural Analysis

• Prerequisite: Math 216 and CEE 312 or equivalent
• Credit: 3
• Content: Displacement-based linear analysis of truss, beam, frame, and cable structures, including axial loading and structural pre-tension effects. Analytical derivation of stiffness equations from first principles. Matrix assembly techniques and implementation of computational solution techniques. Approximate stability analysis. Elementary plasticity analysis, using incremental loading techniques. Introduction to structural dynamics.

### CEE 450 - Introduction to Transportation Engineering

• Prerequisite: MATH 215 and Physics 240 or graduate standing.  Minimum grade of "C" required for enforced prerequisites.
• Credit: 4
• Content: Fundamentals of planning, design and operation of highway transportation facilities. Topics covered include driver and vehicle performance characteristics, highway geometric design principles, basics of traffic analysis, traffic signal operations, transportation planning, connected and automated vehicle technologies and their impacts to the transportation infrastructure.

### CEE 480 - Design of Environmental Engineering Systems

• Credit:
• Content: Design and theoretical understanding of environmental processes; biological, physical and chemical processes and reactor configurations commonly used for water quality control; applications to the design of specific water and wastewater treatment operations; discussion of pollution prevention and green engineering options.

### CLIMATE 321/SPACE 321/EARTH 321 - Earth and Space Systems Dynamics

• Prerequisites: CLIMATE/SPACE 320, MATH 215 and MATH 216
• Credit: 3
• Content: This course will describe the major wind systems and ocean currents that are important to climate studies. The primary equations will be developed and simple solutions derived that will explain many of these motions. The relations among the dynamics and other parameters in the climate system will be illustrated by examples from both paleo and present day systems.

### CLIMATE 350/SPACE 350/EARTH 350 - Atmospheric Thermodynamics

• Prerequisites: MATH 216 or equivalent. Minimum grade of "C" required for enforced prerequisite.
• Credit: 3
• Content: Fundamentals of thermodynamics are presented, including the First, Second and Third Laws, ideal gases, adiabatic processes, phase changes, vapor pressure, humidity and atmospheric stability. The Kinetic Theory of Gases provides a molecular perspective on the various forms of atmospheric water substance and on macroscopic phenomenology in general.

### SPACE 370/EARTH 370 - Solar Terrestrial Relations

• Prerequisite: MATH 216, Physics 240.
• Credit: 4
• Content: Introduction to solar terrestrial relations with an overview of solar radiation and its variability on all time-scales. The effects of this variability on the near-Earth space environment and upper atmosphere are considered, as well as effects on the lower and middle atmosphere with connections to weather and climate. Subjects are approached through extensive data analysis, including weekly computer lab sessions.

### CLIMATE 380/SPACE 380/EARTH 381 - Introduction to Atmospheric Radiation

• Prerequisites: MATH 216 or equivalent. Minimum grade of "C" required for enforced prerequisite.
• Credit: 3
• Content: Basic concepts and processes of radiative transfer including radiometric quantities, electromagnetic spectrum, absorption, emission and scattering. The physics laws governing these processes including the Planck Law and the Kirchhoff Law. Radiative properties of atmospheric constituents. Reflection and refraction. Introductory-level descriptions of relevant applications in atmospheric sciences and climate physics.

### CLIMATE 401/EARTH 401 - Geophysical Fluid Dynamics

• Advised Prerequisites: Physics 240, MATH 215, MATH 216, CLIMATE 323, SPACE 323.
• Credit: 4
• Content: Dynamics of the oceans and atmosphere. Equations of motion in spherical coordinates, beta-plane approximation, wave properties in the oceans and atmosphere.

### CLIMATE 411/EARTH 411 - Cloud and Precipitation Processes

• Advised Prerequisites: CLIMATE 350, SPACE 350, MATH 216
• Credit: 3
• Content: The special nature of water substance; nucleation of phase changes in the free atmosphere; the structure and content of clouds; the development of physical characteristics of precipitation; and the dynamics of rain systems.

### CLIMATE 450/SPACE 450 - Geophysical Electromagnetics

• Credit: 4
• Content: The fundamentals of electricity, magnetism and electrodynamics in the context of the Earth. The first segment will cover electrostatics, the electric structure and circuit of the Earth, electricity in clouds and lightning. The second segment will cover magnetostatics, currents, the magnetic field and magnetic dynamo of the Earth, and the Earth's magnetosphere. The third segment will cover electrodynamics, electromagnetic waves, radiation in the Earth environment, waveguides and radiation from sources.

### CLIMATE 451/ENSCEN 451/EARTH 457 - Atmospheric Dynamics I

• Advised Prerequisites: CLIMATE 401 or MATH 450
• Credit:
• Content: Quasi-geostrophic energetics; fronts; the mean circulation; planetary and equatorial waves: overview of the dynamics of the middle atmosphere; wave-mean flow interaction; spectral methods; and tropical meteorology.

### CLIMATE 463/ENSCEN 463 - Air Pollution Meteorology

• Prerequisite: MATH 215
• Credit: 3
• Content: Weather and motion systems of the atmosphere; topographic influences on winds, atmospheric stability and inversions; atmospheric diffusion; natural cleansing processes; meteorological factors in plant location, design and operation.

### CLIMATE 479/ENSCEN 479 - Atmospheric Chemistry

• Prerequisite: CHEM 130, MATH 216
• Credit: 4
• Content: Thermochemistry, photochemistry and chemical kinetics of the atmosphere; geochemical cycles, generation of atmospheric layers and effects of pollutants are discussed.

### CLIMATE 480/NRE 480 - Climate Change: The Move to Action

• Credit: 3
• Content: All sectors of society are affected by climate change: science, policy, business, economics, public health, energy, ecosystems, environmental engineering, journalism, religion, etc. This course explores the intersections of these communities and exposes students the factual and contextual elements that will allow effective participation in the adaption to climate change.

### SPACE 545 - High Energy Density Physics

• Prerequisite: MATH 450, Physics 405 & Physics 406
• Credit: 3
• Content: Introduces students to fundamental tools and discoveries of high-energy density physics, where pressures are above a million atmospheres. Discusses fundamental physical models, equations of state, hydrodynamics including shocks and instabilities, radiation transport, radiation hydrodynamics, experimental technique, inertial fusion, experimental astrophysics and relativistic systems.

### CLIMATE 551/SPACE 551 - Fluid Dynamics for Climate and Space Sciences

• Advised prerequisites: MATH 215, MATH 216, and MATH 450
• Credit: 4
• Content: Covers the fundamentals of fluid dynamics.  The purpose of the course is to provide fundamental grounding in fluid dynamics and in fundamental mathematical technique at the level required to do serious quantitative graduate research that involves fluid dynamics effects.  The emphasis of the examples is on geophysical and space applications.

### CLIMATE 580/SPACE 580 - Remote Sensing and Geographic Information System Project Laboratory

• Prerequisite: MATH 216, Physics 140
• Credit: 2
• Content: Lectures and hands-on demonstrations train students in acquiring and processing remote sensing and field data using computer based image processing and geographic information systems. Students apply this knowledge in individual and small team projects oriented toward student interests. Research project results are communicated in formal presentations and written reports.

### 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.

### 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 445 - Introduction to Machine Learning

• Prerequisites: EECS 281, completed with a minimum grade of C or better
• Credit: 4
• Content: Theory and implementation of state of the art machine learning algorithms for large-scale real-world applications. Topics include supervised learning (regression, classification, kernal methods, neural networks, and regularization) and unsupervised learning, (clustering, density estimation, and dimensionality and reduction).

### 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.

### EPID 603 - Intro to 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.

### 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### MECHENG 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.

### Naval Architecture & Marine Engineering

• 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.

### PHIL 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 417/CHEM 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.

### 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.