Computational Mathematics Physical Applied Mathematics

1 Applied Mathematics 1 Applied MATHEMATICSThe Department of Applied Mathematics in the College of Arts andSciences offers a range of courses and research opportunities in manyareas, including Computational Mathematics , mathematical biology,nonlinear phenomena, Physical Applied Mathematics , and probability andstatistics. Each of these areas is described codes for this program include APPM and MathematicsThe study of Computational Mathematics has grown rapidly over thepast 15 years and has allowed mathematicians to answer questionsand develop insights not possible only 20-30 years ago.

2 Moderncomputational methods require an in-depth knowledge of a variety ofmathematical subjects which include linear algebra, analysis, ordinaryand partial differential equations, asymptotic analysis, elements ofharmonic analysis, and nonlinear computers are invaluable tools for an Applied mathematician,students are expected to attain a highly professional level of computerliteracy and gain a substantial knowledge of operating systems Mathematics courses include the study of computationallinear algebra, optimization, numerical solution of ordinary and partialdifferential equations, solution of nonlinear equations as well asadvanced seminars in wavelet and multi-resolution BiosciencesRecent advances in our ability to quantitatively study biologicalphenomena have provided a tremendous number of excitingopportunities for Applied mathematicians.

3 The careful modeling, analysisand simulation of these systems using the standard tools of appliedmathematics has led to novel and non-intuitive insights into , deeper understanding of the inherently complex andmultiscale nature of biological systems, in many cases, requires thedevelopment of new mathematical tools, techniques and methodologies(a challenge to which Applied Mathematics is particularly well suited).Research areas in APPM encompass immunology, infectious diseases,cardiology, neuroscience, and population the Mathematical Biology Group page ( )Mathematical GeosciencesMathematical geosciences encompass quantitative modeling, analysisand simulation of all aspects of the Earth system.

4 Our faculty's researchintersects a broad range of geosciences: from the geodynamo to oceancirculation, from Computational methods for seismic imaging to theimpacts of weather on epidemiology, from tsunamis to stochasticweather generators. The complex and multiscale nature of geophysicalsystems, in many cases, requires the development of new mathematicalmodels and simulation strategies, a challenge to which appliedmathematics is particularly well coursework includes analysis and computation, probabilityand statistics, as well as background courses in one of the sciences orengineering fields in which one intends to do Waves and Dynamical SystemsIn recent years there has been an explosion of interest in the study ofnonlinear waves and dynamical systems with analytical results oftenmotivated by the use of computers.

5 The faculty in the Program is activelyand intensively involved in this growing field; research areas includeintegrable and near-integrable systems, conservative and dissipativechaos, as well as numerical of interest include solitons, dispersive shock waves, integrablesystems, cellular automata, pattern formation, qualitative structure andbifurcation theory, onset of chaos and turbulence, analytic dynamics andtransport phenomena. Program courses in this field include dynamicalsystems, nonlinear wave motion and many advanced background courses are: analysis, computation, partialdifferential equations and methods in Applied Mathematics .

6 Valuablesupplemental courses include mechanics and fluid Applied MathematicsPhysical Applied Mathematics is a term which generally refers to thestudy of mathematical problems with direct Physical area of research is intrinsically interdisciplinary. In addition tomathematical analysis, it requires a deep understanding of the underlyingapplications area, and usually requires knowledge and experience innumerical Program's affiliated faculty have a wide variety of expertise in variousareas of application, atmospheric and fluid dynamics, theoreticalphysics, plasma physics, genetic structure, etc.

7 The course requirementsof the Program are designed to provide students with a foundation fortheir study (analysis and computation).The Program also requires supplemental courses in one of the scienceor engineering fields which are needed to begin doing thesis research inphysical Applied the Dispersive Hydrodynamics Lab ( ) page, APPM's own fluid and Applied ProbabilityAlmost all natural phenomena in the technological, biological, physicaland social sciences have random components. Applied probability isthe application of probabilistic methods to understand the randomelements in real-life problems.

8 Statistics is the science of using data,which typically arises from the randomness inherent in nature, to gainnew areas of the Applied math and affiliated faculty exhibit thisinterplay between Mathematics and real-life problems. Areas of currentinterest include optimization of stochastic networks; the study ofstochastic processes and stochastic differential equations in hydrologyand telecommunications; probabilistic models and statistical tests basedon these models, in genetics and RNA sequencing; extreme value theoryin estimation of maximal wind coursework includes analysis, probability and statistics, aswell as background courses in one of the sciences or engineering fields inwhich one intends to do Applied MathematicsFor more information on courses and research opportunities, visit theDepartment of Applied Mathematics website ( ).

9 Master's Degrees Applied Mathematics - Master of Science (MS)( ) Applied Mathematics - Professional Master of Science (MSAM)( )Doctoral Degree Applied Mathematics - Doctor of Philosophy (PhD)( )FacultyWhile many faculty teach both undergraduate and graduate students,some instruct students at the undergraduate level only. For moreinformation, contact the faculty member's home , Mark J. ( )Professor; PhD, Massachusetts Institute of TechnologyAppel , Daniel E. ( )Associate Professor; PhD, KTH Royal Institute of Technology (Sweden)Bebernes, JerroldProfessor EmeritusBecker, Stephen R. ( )Assistant Professor; PhD, California Institute of TechnologyBeylkin, Gregory ( )Professor; PhD, New York UniversityBhat, Yermal Sujeet ( )Instructor; PhD, University of FloridaBortz, David Matthew ( )Associate Professor; PhD, North Carolina State UniversityBunn, Nancy Rodriguez ( )Assistant Professor; PhD, University of California, Los AngelesChang, Silva ( )Instructor; MS, Yale UniversityCole, Justin ; PhD, Florida State UniversityCorcoran, Jem ( )Associate Professor; PhD, Colorado State UniversityCurry, James H.

10 ( )Professor; PhD, University of California, BerkeleyDougherty, Anne Margaret ( )Associate Chair, Senior Instructor; PhD, University of Wisconsin MadisonDukic, Vanja ( )Professor; PhD, Brown UniversityEaston, RobertProfessor EmeritusFornberg, Bengt ( )Professor; PhD, University of Uppsala (Sweden)Gillman, Adrianna ( )Assistant Professor; PhD, University of Colorado BoulderGrooms, Ian G. ( )Assistant Professor; PhD, University of Colorado BoulderHoefer, Mark ( )Associate Professor; PhD, University of Colorado BoulderHuang, Yu-Jui ( )Assistant Professor; PhD, University of Michigan Ann ArborJulien, Keith ( )Chair, Professor; PhD, University of Cambridge (England)Kilpatrick, Zachary Peter ( )Assistant Professor, Visiting Assistant Professor; PhD, University of UtahKish, JonathanInstructor; PhD, University of Colorado BoulderKleiber, William Paul ( )Associate Professor.