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
fieldspecific 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 indepth
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, largescale 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 stellarmass black holes
form the rapidly variable xray 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 xray and gammaray background
radiation fields, the origin of gammaray 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, solidstate
chemistry, solidstate 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 "manmade" 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, tictactoe, hex, chess. Fixed points and
equilibria. Zerosum 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 subfields
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, timedependent 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, likelihoodbased
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,
GaussMarkov 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,
LehmannScheffe and RaoBlackwell 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 decisionmaking 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 boundaryvalue problem formulation via simple examples,
followed by the use of the finiteelement 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 boundarylayer 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, highlift devices
and highspeed 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
airbreathing propulsion systems. Introduces liquid and solidpropellant
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, betaplane 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; SturmLiouville 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 problemsolving
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, twophase, and nonNewtonian
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 nonideal reactor
concepts to system modeling; energetics and rates of intraphase
and interphase mass transport and reaction processes in surface
and groundwaters, 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. Handson experience in laboratory
sessions with communications, control and signal processing. Continuoustime
linear systems: convolution, Fourier and Laplace transforms, transfer
functions, poles and zeros, stability, sampling, introductions
to communications and feedback control. Discretetime linear systems:
Z transform, filters, Fourier transform, signal processing. State
space models of systems using finitestate 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; steadystate 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, contextfree 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: divideandconquer, 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 electromechanical 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, branchandbound, divideandconquer, dynamic
programming, greed, and randomization applied to polynomial and
NPhard 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, Multicollinearity 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 nonmeasure 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:
Primaldual algorithm. Resolution of degeneracy, upper bounding.
Variants of simplex method. Geometry of the simplex method, application
of adjacent vertex methods in nonlinear 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 QuasiNewton,
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,
outofkilter algorithm. Critical path networks, project cost
curves. Multicommodity 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, branchandbound 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 crosssection; shear
center and torsion of thinwalled sections; membrane stresses
in axisymmetric shells; elasticplastic 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.
Indepth 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 threedimensional
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 rigidbody and multibody 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 NavierStokes 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.
