Research in Applied Mathematics
Faculty and students interested in the applications of mathematics are an integral part of the Department of Mathematics; there is no formal separation between pure and applied mathematics, and the Department takes pride in the many ways in which they enrich each other. We also benefit tremendously from close collaborations with faculty and students in other departments at UC Berkeley as well as scientists at Lawrence Berkeley National Laboratory and visitors to the Mathematical Sciences Research Institute.
The Department regularly offers courses in ordinary and partial
differential equations and their numerical solution, discrete applied
mathematics, the methods of mathematical physics, mathematical biology,
the mathematical aspects of fluid and solid mechanics, approximation
theory, scientific computing, numerical linear algebra, and mathematical
aspects of computer science. Courses in probability theory, stochastic
processes, data analysis and bioinformatics are offered by
the Department of Statistics, while courses in combinatorial and convex
optimization are offered by the Department of Industrial
Engineering and Operations Research. Our students are encouraged to
take courses of mathematical interest in these and many other
departments.
Topics explored intensively by our faculty and students in recent years
include scientific computation and the mathematical aspects of quantum
theory, computational genomics, image processing and medical imaging,
inverse problems, combinatorial optimization, control, robotics, shape
optimization, turbulence, hurricanes, microchip failure, MEMS,
biodemography, population genetics, phylogenetics, and computational approaches to historical linguistics. Within the department we also have a Laboratory for Mathematical and Computational Biology.
Courses
Undergraduate upper division courses
Math C103. Introduction to Mathematical Economics.
Math 104, H104. Introduction to analysis.
Math 105. Second course in analysis.
Math 110, H110. Linear algebra.
Math 113, H113. Introduction to abstract algebra.
Math 118. Fourier analysis, wavelets, and signal processing.
Math121A,B. Mathematical Tools for the Physical Sciences.
Math 123. Ordinary Differential Equations.
Math 126. Introduction to Partial Differential Equations.
Math 127. Mathematical and Computational Methods in Molecular Biology.
Math 128A,B. Numerical Analysis.
Math 170. Mathematical Methods for Optimization.
Math 172. Combinatorics.
Math 185, H185. Introduction to Complex Analysis.
Math 189. Mathematical Methods in Classical and Quantum Mechanics.
Course Descriptions
Courses offered by the Statistics Department
Courses offered by the Computer Science Department
Courses offered by the Industrial Engineering and Operations Research Department
Graduate courses
Math 202A,B. Introduction to Topology and Analysis.
Math 203. Asymptotic Analysis in Applied Mathematics.
Math 204. Ordinary Differential Equations.
Math 205. Theory of Functions of a Complex Variable.
Math C218A,B. Probability Theory.
Math 220. Methods of Applied Mathematics.
Math 221. Advanced Matrix Computations.
Math 222A,B. Partial Differential Equations.
Math C223A,B. Stochastic Processes.
Math 224A,B. Mathematical Methods for the Physical Sciences.
Math 228A,B. Numerical Solution of Differential Equations.
Math 239. Discrete Mathematics for the Life Sciences.
Math 258. Classical Harmonic Analysis.
Math 273. Topics in Numerical Analysis.
Math 275. Topics in Applied Mathematics.
Seminars
Applied Mathematics Seminar (Chorin, Strain, Wilkening)
Matrix Computations and Scientific Computing Seminar (Demmel, Gu, Parlett)
Computational Biology Seminar (Pachter, Sturmfels)
Probability Seminar (Chatterjee, Bhadimi)
Interdisciplinary Stochastic Processes Colloquium (Aldous)
Senate Faculty
| Name | Title | Research Interests |
|---|---|---|
| Robert M. Anderson | Professor | Mathematical economics, Nonstandard analysis, Probability theory |
| Grigory I. Barenblatt | Professor Emeritus | Applied mathematics, Solid mechanics, Fluid mechanics, Similarity methods asymptotics, Mechanics of deformable solids |
| Elwyn R. Berlekamp | Professor Emeritus | Combinatorial game theory, Algebraic coding theory, Electrical engineering, Computer science |
| Paul L. Chambré | Professor Emeritus | Applied mathematics |
| Alexandre J. Chorin | University Professor | Applied mathematics, Numerical methods, Computational physics |
| Paul Concus | Professor Emeritus | Fluid mechanics, Numerical analysis, Applied mathematics |
| James W. Demmel | Professor | Numerical analysis, Applied control theory |
| Stephen P.L. Diliberto | Professor Emeritus | Ordinary differential equations, Celestial mechanics |
| F. Alberto Grünbaum | Professor | Analysis, Probability, Integrable systems, Medical imaging |
| Ming Gu | Professor | Numerical linear algebra, Scientific computing |
| Ole H. Hald | Professor | Numerical analysis |
| Olga Holtz | Professor | Matrix analysis, approximation theory, analysis of algorithms |
| William M. Kahan | Professor Emeritus | Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems |
| Richard Karp | University Professor | Computer science and bioengineering |
| C. Keith Miller | Professor Emeritus | Partial differential equations, Numerical methods for PDE's |
| John C. Neu | Professor | Applied mathematics |
| Lior Pachter | Professor | Mathematical and computational biology |
| Beresford N. Parlett | Professor Emeritus | Numerical analysis, Scientific computation |
| Yuval Peres | Adjunct Professor | Probability theory and Hausdorff dimension |
| Per-Olof Persson | Assistant Professor | Applied Mathematics, Numerical Methods, Computational Fluid and Solid Mechanics |
| Rainer K. Sachs | Professor Emeritus | Mathematical biology |
| James A. Sethian | Professor | Applied mathematics, Computational physics, Partial differential equations |
| Chris Shannon | Professor | Mathematical economics |
| Stephen Smale | Professor Emeritus | Algorithms, Numerical analysis, Global analysis |
| John Strain | Professor | Applied mathematics, Numerical analysis, Fast algorithms, Materials science |
| Jon Wilkening | Associate Professor | Applied mathematics, Materials science, and Scientific computing |
Visiting Faculty
| Name | Title | Research Interests |
|---|---|---|
| Santiago Canez | Lecturer | Symplectic geometry and mathematical physics |
| Benjamin Johnson | Lecturer | Economics of Information Security |
| Svante Linusson | Visiting Scholar | Probabilistic combinatorics, electoral systems |
Postdocs
| Name | Title | Research Interests |
|---|---|---|
| Sharon Aviran | Postdoctoral Fellow | Computational biology, applied mathematics |
| Valerie Hower | Postdoctoral Fellow | computational biology, topological and probabilistic methods in data analysis |
| August Johansson | Miller Research Fellow | Finite element methods |
| Kate Poirier | RTG Postdoctoral Fellow | String topology |
| Chris H. Rycroft | Morrey Assistant Professor | Applied mathematics, high performance computing, granular flow |
| Benjamin Stamm | Morrey Assistant Professor | Numerical analysis, partial differential equations, discontinuous Galerkin methods, stabilization strategies, reduced basis method, electrical field integral equations, and a posteriori estimates |
Faculty with Related Research Interests
| Name | Title | Research Interests |
|---|---|---|
| Mina Aganagic | Associate Professor | String theory |
| David Aldous | Professor | Theoretical and applied probability |
| Paul R. Chernoff | Professor Emeritus | Functional analysis, Operator theory |
| L. Craig Evans | Professor | Partial differential equations |
| Steven N. Evans | Professor | Probability and stochastic processes |
| Michael J. Klass | Professor | Probability theory, Combinatorics |
| Hendrik W. Lenstra, Jr. | Professor Emeritus | Algebraic number theory, Algorithms |
| James Pitman | Professor | Probability, stochastic processes, combinatorics, machine learning |
| Nicolai Reshetikhin | Professor | Mathematical physics, Low-dimensional topology, Representation theory |
| Fraydoun Rezakhanlou | Professor | Probability theory, Partial differential equations |
| John L. Rhodes | Professor Emeritus | Algebra, Semigroups, Automata |
| Marc A. Rieffel | Professor | Non-commutative harmonic analysis, Operator algebras, Quantum geometry |
| Bernd Sturmfels | Professor | Combinatorics, Computational algebraic geometry |
| Alan D. Weinstein | Professor Emeritus, Professor of the Graduate School | Symplectic geometry, Mathematical physics |
| Mariusz Wodzicki | Professor | Non-commutative and algebraic geometry, Analysis, K-theory |
| Maciej Zworski | Professor | Partial differential equations, Mathematical physics |
Graduate Students
| Name | Dissertation Supervisor |
|---|---|
| David G. Anderson | |
| Natth Bejraburnin | Lior Pachter |
| Jue Chen | |
| Jeffrey Donatelli | James A. Sethian |
| Maryam Farahmand-asil | |
| Bradley Froehle | Jon Wilkening |
| Erica Isaacson | Jon Wilkening |
| David C. Kaspar | Fraydoun Rezakhanlou |
| Michael Kazi | James A. Sethian |
| Aaron Kleinman | Lior Pachter |
| Jakub Kominiarczuk | Alexandre J. Chorin |
| Trevor Potter | Jon Wilkening |
| Darsh Ranjan | Jonathan Richard Shewchuk, EECS |
| Robert I. Saye | James A. Sethian |
| Vladislav Voroninski | John Strain, Emmanuel Candes |
| Luming Wang | Per-Olof Persson |
| Christopher A. Wong | |
| Cinna Julie Wu | Ming Gu |
| Junjie Zhou | Chris Shannon |
Recent Ph.D.s
| Name | Dissertation Title | Dissertation Supervisor | Year |
|---|---|---|---|
| Shaowei Lin | Algebraic Methods for Evaluating Integrals in Bayesian Statistics | Bernd Sturmfels | 2011 |
| John Yiran Zhu | Sticky Incentives and Dynamic Agency | Robert Anderson | 2011 |
| Anne Shiu | Algebraic Methods for Biochemical Reaction Network Theory | Bernd Sturmfels, Lior Pachter | 2010 |
| Jia Yu | A Local Construction of the Smith Normal Form of a Matrix Polynomial and Time-Periodic Gravity Driven Water Waves | Jon Wilkening | 2010 |
| Ian Sammis | Implicit and fourth-order semi-Lantrangian contouring for geometric moving interface problems | John Strain | 2009 |
| Tianbing Chen | Piecewise-Polynomial Discretization and Krylov-Accelerated Multigrid for Elliptic Interface Problems | John Strain | 2008 |
| Aubrey Clayton | Mutation-Selection Balance for Polynomial Selection Costs and Matrix-Valued Orthogonal Polynomials | Steven Evans | 2008 |
| Peter McKinley Huggins | Polytopes in Computational Biology | Lior Pachter, Bernd Sturmfels | 2008 |
| Radu Horia Mihaescu | Distance Methods in Phylogeny | Lior Pachter, Satish Rao | 2008 |
| Asaf Nachmias | Critical Percolation on Finite Graphys | Yuval Peres | 2008 |
| Jomy Joseph Alappatu | An Anlysis of Randomized Algorithms on Trees | James Pitman | 2007 |
| Maria Kourkina Cameron | Seismic Velocity Estimation from Time Migration | James Sethian | 2007 |
| Elizabeth Jenny Chester | Fast Methods for Computing All-to-All Geodesic Paths for the Eikonal Equation | James Sethian | 2007 |
| Jae-Seok Huh | Implicit Interface Finite Element Method | James Sethian | 2007 |
| Kay Kirkpatrick | Rigorous Derivation of the Landau Equation in the Weak Coupling Limit | Fraydoun Rezakhanlou | 2007 |
| Ying Shan | Solving Partial Differential Equations on Irregular Domains with Moving Interfaces, with Applications to Superconformal Electodeposition in Semiconductor Manufacturing | James Sethian | 2007 |
| Jonathan Quincy Weare | Efficient Conditional Path Sampling of Stochastic Differential Equations | Alexandre J Chorin | 2007 |
