## Applied Mathematics

## 2014-15 Tuition

$29,500## Application deadlines

Fall, Jan. 15; no spring admission## Requirements summary

- all Graduate School Requirements, including the TOEFL Exam for Non-Native English Applicants
- three recommendations
- GRE general test (GRE subject test in mathematics advised)

## Degrees

- Ph.D.

## Subjects

- Applied Mathematics (Ph.D.)

## Major concentrations

- applied mathematics

The graduate program in applied mathematics is based on a solid foundation in pure mathematics, which includes the fundamentals of algebra and analysis. It involves a grounding in the methods of applied mathematics and studies of scientific areas in which significant applications of mathematics are made. The field has a broadly based interdepartmental faculty that can direct student programs in a large number of areas of the mathematical sciences.

Many specialized or interdisciplinary programs can be designed for individual students, including, for example, a variety of possibilities in biomathematics.

The dissertation is normally a mathematical contribution toward the solution of a problem arising outside mathematics.

Students who are interested in this field may also want to investigate the related fields listed under Mathematical Sciences in "Opportunities for Study," pages 7-8.

**Application: **

Applicants must have an undergraduate background that contains a substantial mathematical component. Applicants are required to submit GRE general test scores, and are advised to submit GRE mathematics subject test scores.

**Concentrations:**applied mathematics;

**Research interests:**algebraic combinatorics; discrete geometry

**Concentrations:**applied mathematics;

**Research interests:**numerical linear algebra; microelectromechanical systems; network tomography; finite element analysis; numerical software design

**Concentrations:**applied mathematics;

**Research interests:**linear programming; combinatorial optimization; networks and matroids

**Concentrations:**applied mathematics;

**Research interests:**markov processes; networks; market selection

**Concentrations:**applied mathematics;

**Research interests:**parallel numerical methods; matrix-based signal and image processing

**Concentrations:**applied mathematics;

**Research interests:**model selection and averaging (aggregation) in a variety of high dimensional parametric, semi-parametric and nonparametric models, machine learning and empirical processes theory

**Concentrations:**applied mathematics;

**Research interests:**computational fluid dynamics; aerodynamics

**Concentrations:**applied mathematics;

**Research interests:**nonlinear circuits and systems; power systems; artificial neural networks

**Concentrations:**applied mathematics;

**Research interests:**geometry of discrete structures; configuration spaces; topology

**Concentrations:**applied mathematics;

**Research interests:**theory of computing; applied logic; automated reasoning

**Concentrations:**applied mathematics;

**Research interests:**dynamical systems; control theory; stochastic systems; cognitive science

**Concentrations:**applied mathematics;

**Research interests:**

**Concentrations:**applied mathematics;

**Research interests:**turbulence; environmental and computational fluid mechanics

**Concentrations:**applied mathematics;

**Research interests:**computational solid mechanics; stochastic inverse problems

**Concentrations:**applied mathematics;

**Research interests:**theoretical population biology; evolutionary biology

**Concentrations:**applied mathematics;

**Research interests:**crystallography; quasicrystals; quasiperiodic minimal surfaces

**Concentrations:**applied mathematics;

**Research interests:**theoretical chemistry; chemical physics

**Concentrations:**applied mathematics;

**Research interests:**probability optimization; information theory; mathematical biology

**Concentrations:**applied mathematics;

**Research interests:**biomechanics of skeletal muscle, ligament and tendon; biomechanics of Glenohumeral joint

**Concentrations:**applied mathematics;

**Research interests:**quantum field theory; digital knowledge networks

**Concentrations:**applied mathematics;

**Research interests:**large-scale constraint reasoning and optimization; mathematical programming; machine learning

**Concentrations:**applied mathematics;

**Research interests:**diffusion processes, Monte Carlo simulation; non-Gaussian random functions; probabilistic models

**Concentrations:**applied mathematics;

**Research interests:**analysis over infinite dimensional manifolds

**Concentrations:**applied mathematics;

**Research interests:**dynamical systems; differential equations; mathematical biology

**Concentrations:**applied mathematics;

**Research interests:**wireless networks; mobile systems; ad hoc and sensor networks; modeling of communication systems; applications to bio-systems

**Concentrations:**applied mathematics;

**Research interests:**reasoning about knowledge and uncertainty; qualitative reasoning; (fault-tolerant) distributed computing logic; game theory

**Concentrations:**applied mathematics;

**Research interests:**nonlinear elasticity; nonlinear analysis; equivariant bifurcation theory

**Concentrations:**applied mathematics;

**Research interests:**visual communication; application-specific image and video processing and compression; multirate coding; joint optimization of network and coding parameters

**Concentrations:**applied mathematics;

**Research interests:**discrete-event simulation; simulation and optimization; applications in radiation oncology

**Concentrations:**applied mathematics;

**Research interests:**econometric theory; economics of China

**Concentrations:**applied mathematics;

**Research interests:**robust geometric algorithms; modeling and simulation; and information capture and access

**Concentrations:**applied mathematics;

**Research interests:**ordinary differential equations; iterations; fractals

**Concentrations:**applied mathematics;

**Research interests:**fracture mechanics; high-temperature crack propagation; geomechanics; asymptotic methods

**Concentrations:**applied mathematics;

**Research interests:**geometric and physical algorithms; computer graphics and animations; haptic rendering; deformable models

**Concentrations:**applied mathematics;

**Research interests:**continuum mechanics; biomechanics; mechanics of granular materials

**Concentrations:**applied mathematics;

**Research interests:**physical modeling of semiconductor devices and processes; numerical solvers for hybrid systems (EM, mechanical, and thermal)

**Concentrations:**applied mathematics;

**Research interests:**design and analysis of algorithms, especially randomized and online algorithms for networked systems and electronic markets

**Concentrations:**applied mathematics;

**Research interests:**algorithms; combinatorial optimization; computational geometry; computational biology

**Concentrations:**applied mathematics;

**Research interests:**fluid dynamics; stochastic processes in suspensions

**Concentrations:**applied mathematics;

**Research interests:**uncertainty quantification; stochastic simulation; random heterogeneous materials; multiscale analysis and formulations; Bayesian inferencing

**Concentrations:**applied mathematics;

**Research interests:**theory of computation; computational complexity; program logic and semantics

**Concentrations:**applied mathematics;

**Research interests:**ecology, epidemiology, and evolutionary theory; mathematical biology

**Concentrations:**applied mathematics;

**Research interests:**variational analysis and nonsmooth optimization with particular interest in eigenvalue optimization

**Concentrations:**applied mathematics;

**Research interests:**fluid dynamics; nonlinear water waves

**Concentrations:**applied mathematics;

**Research interests:**chemical applications of equilibrium and nonequilibrium statistical mechanics

**Concentrations:**applied mathematics;

**Research interests:**asynchronous VLSI design; computer architecture; concurrency theory

**Concentrations:**applied mathematics;

**Research interests:**quantitative genetics/genomics; statistical genetics; computational biology; pathway modeling; molecular evolution

**Concentrations:**applied mathematics;

**Research interests:**Andrea is a second year Assistant Professor in ORIE. She works in mathematical finance, in non-traditional directions. Her works deals with aspects of finance related to optimal control, queuing theory, interacting particle systems, etc.

**Concentrations:**applied mathematics;

**Research interests:**economic growth; infinite horizon dynamic optimization; chaotic dynamical systems

**Concentrations:**applied mathematics;

**Research interests:**systems biology; complex systems; computational science

**Concentrations:**applied mathematics;

**Research interests:**logic; recursive functions and computability; theoretical computer science; hybrid systems

**Concentrations:**applied mathematics;

**Research interests:**digital signal processing; image enlargement, enhancement, and restoration

**Concentrations:**applied mathematics;

**Research interests:**cryptography and its interplay with computational complexity; game theory

**Concentrations:**applied mathematics;

**Research interests:**probability models of the failure of materials

**Concentrations:**applied mathematics;

**Research interests:**turbulence; combustion; computational fluid mechanics; stochastic processes

**Concentrations:**applied mathematics;

**Research interests:**differential equations; dynamical systems; biomechanics

**Concentrations:**applied mathematics;

**Research interests:**complexity of algorithms; mathematical programming

**Concentrations:**applied mathematics;

**Research interests:**applied probability; extreme values; data network modeling; heavy tails and long range dependence

**Concentrations:**applied mathematics;

**Research interests:**analysis; potential theory; stochastic processes

**Concentrations:**applied mathematics;

**Research interests:**applied probability; stable processes; long-range dependence; communication networks; financial models; risk theory

**Concentrations:**applied mathematics;

**Research interests:**numerical analysis; partial differential equations

**Concentrations:**applied mathematics;

**Research interests:**artificial intelligence and experimental computer science

**Concentrations:**applied mathematics;

**Research interests:**theoretical condensed-matter physics; materials science; spatially extended dynamical systems

**Concentrations:**applied mathematics;

**Research interests:**algorithms for perturbative protein folding and dynamics

**Concentrations:**applied mathematics;

**Research interests:**economic theory; mathematical economics

**Concentrations:**applied mathematics;

**Research interests:**analysis of algorithms; combinatorial optimization; approximation algorithms; computational biology

**Concentrations:**applied mathematics;

**Research interests:**numerical optimization; stochastic dynamic programming; heuristic optimization; applications to environmental systems

**Concentrations:**applied mathematics;

**Research interests:**large-scale 3D reconstruction from 2D images; analysis of large graphs derived from massive image collections

**Concentrations:**applied mathematics;

**Research interests:**risk analysis; stochastic hydrology; water resource systems

**Concentrations:**applied mathematics;

**Research interests:**hydrodynamic stability; nonlinear fluid dynamics

**Concentrations:**applied mathematics;

**Research interests:**algebraic geometry; computational algebra and algebraic geometry; commutative algebra

**Concentrations:**applied mathematics;

**Research interests:**nonlinear dynamics; applications to physics, engineering, and biology

**Concentrations:**applied mathematics;

**Research interests:**communication networks; control and dynamical systems optimization; game theory and applications; stochastic processes and networks

**Concentrations:**applied mathematics;

**Research interests:**design and analysis of algorithms, with emphasis on problems in combinatorial optimization and their applications to various problems

**Concentrations:**applied mathematics;

**Research interests:**continuous optimization; interior-point methods; mathematical programming

**Concentrations:**applied mathematics;

**Research interests:**statistical signal processing; communication systems and networking; adaptive receiver design-estimation theory

**Concentrations:**applied mathematics;

**Research interests:**stochastic programming; approximate dynamic programming; stochastic approximation algorithms

**Concentrations:**applied mathematics;

**Research interests:**discrete optimization; parallel computing

**Concentrations:**applied mathematics;

**Research interests:**applied mathematics; numerical methods; dynamic systems; nonlinear PDEs; control theory

**Concentrations:**applied mathematics;

**Research interests:**information theory; communication and compression; networking; computational linguistics; security

**Concentrations:**applied mathematics;

**Research interests:**fluids in physics and biology; biomathematics; statistical physics; scientific computing and modeling

**Concentrations:**applied mathematics;

**Research interests:**Classification, Copula Modeling, Learning Theory, Empirical Process Theory, Matrix Estimation and Completion, Model Selection and Aggregation, Nonparametric estimation

**Concentrations:**applied mathematics;

**Research interests:**wireless information networks; digital communication systems; error control coding

**Concentrations:**applied mathematics;

**Research interests:**combinatorial optimization; approximation algorithms; information networks

**Concentrations:**applied mathematics;

**Research interests:**life history theory; models of dispersal

**Concentrations:**applied mathematics;

**Research interests:**computational mathematics; stochastic and statistical multiscale modeling; uncertainty quantification; materials science

**Concentrations:**applied mathematics;

**Research interests:**signal and image processing; optimization; algorithms

**Learning Goals, Proficiencies and Assessment for the PhD****program in Applied Mathematics**

**I. Learning Goals**

Graduate Program in Applied Mathematics is one of the most broad and interdisciplinary programs at Cornell, with 95 members of the graduate fields representing 13 different departments. The research interests of the members of the Center of Applied Mathematics (CAM) range over mathematical biology, probability theory, nonlinear dynamics, numerical analysis, network theory, optimization, mathematical finance, signal processing, mathematical physics, game theory, and the list goes on and on. The uniting theme is deep mathematical analysis of applied problems, including development of new mathematical tools of attacking these problems.

The very flexible and interdisciplinary nature of the graduate program in Applied Mathematics determines the learning goals for a PhD student. The student is expected to acquire both excellent general mathematical background and background in the specific area of application the student is working in. The student is expected to learn to think as a mathematician. This means taking nothing for granted, until proved to be true. This means searching for new routes for solutions of problems, for bringing together ideas from different branches of mathematics. This means thinking originally, and using the work of others as a stepping stone, instead of following in their

footsteps. Finally, the student is expected to develop deep interest in applied problems and ability to translate the acquired mathematical knowledge into a framework for solving an applied problem.

A student in the graduate program in Applied Mathematics is expected to learn to communicate effectively technical ideas to his/her peers, students and lay audiences by developing written and presentation skills. These skills may be developed through coursework, writing papers and proposals, and by giving technical talks in both informal and formal setups. Finally, a student in the graduate program in Applied Mathematics is expected to learn to adhere to highest ethical standards in conducting and communicating research, teaching and professional community service.

**II. Proficiencies**

A graduate student in Applied Mathematics is expected to demonstrate both mastery of knowledge in mathematics and its applications, and ability to create new mathematical knowledge and innovative ways to apply mathematical tools to important problems in science, industry and society. Each student is expected to demonstrate the following proficiencies.

- Make substantial original contributions to applied mathematics. This includes ability to identify new important and promising research problems; ability to think independently, critically and creatively;ability to complete research work by bringing it to the stage where it can be published and be used by the others.

- Maintain ability to acquire new knowledge by keeping up with the new developments in the field through professional publications and professional meetings.

- Ability to communicate effectively research findings and plans. This includes ability to present results in the format of technical papers and have them published in professional journals and conference proceedings; ability to explain complex ideas to peers in technical presentations; being aware of funding opportunities and ability to write effective research proposals and obtain research funding.

- Dedication to advancing science through effective teaching, advising, mentoring and service to professional community.

- Awareness of the ethical standards in the field, and ability to maintain and advance these standards.

**III. Assessment of Learning Outcomes**

There are several components to assessment of how graduate students in Applied Mathematics reach the learning outcomes of the program. The first component is the coursework and exams associated with this coursework. This component allows the Special Committee members and the

Director of CAM to assess the specific outcome of learning in the classroom environment.

The second component is the Admission to Candidacy Examination (the A exam). This exam is administered by student’s Special Committee. Due to the highly interdisciplinary nature of the Graduate Field for Applied Mathematics, the exact nature of the A exam depends somewhat on the specific field in which the student is planning to conduct research. Invariably, this oral exam allows the members of the Special Committee to assess the general knowledge of the student in mathematics and the selected applied field, as well as to assess the appropriateness and feasibility of the PhD research the student is planning to conduct. It also allows the committee members to make an assessment of the oral presentation skills of the student.

The third, and final, component is the B exam (thesis defense). This exam allows the members of the Special Committee to assess the completed PhD work of the student and to evaluate the resulting thesis. The B exam has a public part, that allows the faculty members and the graduate students to listen a presentation by the candidate and ask him/her questions. This allows another assessment of the presentation skills of the student.