# Mathematics PhD

*Major: **Mathematics*

*Degree Awarded: *Doctor of Philosophy (PhD)

*Calendar Type: Quarter*

Minimum Required Credits: 90.0

Co-op Option*: None*

*Classification of Instructional Programs (CIP) code:* 27.0101

*Standard Occupational Classification (SOC) code:* 15-2021; 15-2041

## About the Program

The Department of Mathematics is a broadly based academic unit offering instructional programs and carrying on research activities in mathematics.

Areas of research specialty among the faculty include applied mathematics, algebraic combinatorics, biomathematics, discrete mathematics, optics, analysis, number theory, numerical analysis, probability and statistics, matrix and operator theory, fluid mechanics and partial differential equations.

### Additional Information

For more information about these graduate programs, visit Department of Mathematics website.

## Admission Requirements

Applicants should hold a BS degree in mathematics or the equivalent and meet the University's graduate admission standards. In particular, the student should have had intensive exposure to proof oriented courses, such as real analysis and abstract algebra. Because many of the core courses are two- or three-term sequences beginning in the fall, new students are typically admitted to the programs only in the fall term.

For additional information on how to apply, visit Drexel University's Graduate Admissions website.

## Degree Requirements

Students must complete a minimum of 45 graduate credits for the PhD degree, in addition to the 45.0 required by the MS program for a total of 90.0 credits. Of the 45.0 credits of MS program courses, the following six are required:

Required Courses | ||

MATH 504 | Linear Algebra & Matrix Analysis | 3.0 |

MATH 505 | Principles of Analysis I | 3.0 |

MATH 506 | Principles of Analysis II | 3.0 |

MATH 533 | Abstract Algebra I | 3.0 |

MATH 630 | Complex Variables I | 3.0 |

MATH 633 | Real Variables I | 3.0 |

The remaining 27.0 credits, comprising the MS segment of the PhD program, may be any graduate mathematics courses. In some cases, course substitutions may be made with courses from other departments. Elective courses taken outside the department must receive prior departmental approval in order to be counted toward the degree.

The student must pass a written qualifying exam. The student is allowed two attempts. Students must take exam at the end of their first year, and have a second opportunity in September of their second year.

Students must take a PhD candidacy exam at the end of their second year. Additional coursework to reach the 90.0 credits required for the PhD will be agreed upon with the student's graduate advisor. Students should note that some departmental courses are foundation courses and do not contribute to the departmental requirements for the degree. They do count toward the University requirements for a degree.

## Program Level Outcomes

- Develop a thorough understanding through a range of fundamental graduate level topics in both required courses in analysis and algebra and in elective courses in core and applied mathematics
- Develop in-depth expertise through advanced graduate courses, participation in research seminar, and thesis research
- Develop the ability to work creatively and independently.
- Critically evaluate research articles in mathematics.
- Communicate sophisticated mathematics effectively at a professional level both in writing and in oral presentations.

## Mathematics Faculty

*(Duke University)*

*Associate Department Head, Mathematics*. Professor. Applied analysis and computing for systems of nonlinear partial differential equations, especially free-surface problems in fluid dynamics.

*(University of California at Berkeley)*. Associate Professor. Algebraic combinatorics, representation theory, and complexity theory.

*(Temple University)*. Assistant Teaching Professor.

*(University of Texas at Austin)*. Teaching Professor.

*(Drexel University)*. Associate Teaching Professor. Discrete mathematics and automata theory.

*(Drexel University)*. Associate Teaching Professor.

*(Massachusetts Institute of Technology)*. Assistant Professor. Algebraic Combinatorics, Noncommutative Algebra, Symmetric Functions, Hopf Algebras, Enumerative Combinatorics, Invariant Theory

*(Massachusetts Institute of Technology)*. Associate Professor. Intersection of physics, engineering, applied mathematics and computational science.

*(University of California at Berkeley)*. Associate Teaching Professor. Function theory and operator theory, harmonic analysis, matrix theory.

*(University of Pittsburgh)*. Associate Professor. Biomathematics, dynamical systems, ordinary and partial differential equations and math education.

*(University of Pennsylvania)*

*Undergraduate Advisor*. Professor. Geometry; optics; computer vision.

*(Warsaw University)*. Professor. Probability theory and its applications to analysis, combinatorics, wavelets, and the analysis of algorithms.

*(Duke University)*. Assistant Teaching Professor. Rare Event Simulation, Dynamical Systems, Numerical Analysis and Mathematical Biology

*(Boston University)*. Professor. Ordinary and partial differential equations, mathematical neuroscience.

*(Federal University of Rio de Janeiro)*. Assistant Professor. Analysis of Partial Differential Equations, Fluid Dynamics, Stochastic Processes

*(Rutgers University)*. Professor. Partial differential equations and numerical analysis, including homogenization theory, numerical methods for problems with rough coefficients, and inverse problems.

*(Omsk State University)*. Teaching Professor. Math education; geometrical modeling.

*(Drexel University)*. Assistant Teaching Professor.

*(University of North Carolina)*. Assistant Teaching Professor. Commutative Algebra

*(University of California at Berkeley)*. Associate Professor. Applied mathematics, numerical analysis, symbolic computation, differential geometry, mathematical physics.

*(Drexel University)*. Associate Teaching Professor.

*(University of Pennsylvania)*. Professor. Probabilistic combinatorics, asymptotic enumeration.

*(Rutgers University)*. Associate Professor. Discrete optimization, combinatorics, operations research, graph theory and its application in molecular biology, social sciences and communication networks, biostatistics.

*(Columbia University)*. Associate Professor. Partial differential equations, scientific computing and applied mathematics.

*(University of Kansas)*. Associate Professor. Stochastic Calculus, Large Deviation Theory, Theoretical Statistics, Data Network Modeling and Numerical Analysis.

*(Boston University)*. Associate Teaching Professor.

*(Physical Research Laboratory)*. Instructor.

*(Penn State University)*. Assistant Teaching Professor.

*(Vrije Universiteit, Amsterdam)*. Professor. Matrix and operator theory, systems theory, signal and image processing, and harmonic analysis.

*(Boston University)*

*Department Head*. Professor. Partial and lattice differential equations, specifically nonlinear waves and their interactions.

*(Cornell University)*. Associate Teaching Professor. Dynamical systems, neurodynamics.

*(Stanford University)*. Professor. Multiscale mathematics, wavelets, applied harmonic analysis, subdivision algorithms, nonlinear analysis, applied differential geometry and data analysis.

*(University of South Carolina)*. Assistant Teaching Professor. Functional Analysis, Operator Algebras, Semigroups, Mathematical Physics

## Emeritus Faculty

*(Polytechnic Institute of Brooklyn)*. Professor Emeritus.

*(University of Washington)*. Professor Emeritus. Functional analysis, wavelets, abstract harmonic analysis, the theory of group representations.

*(University of Pennsylvania)*. Professor Emeritus. Functional analysis, C*-algebras and the theory of group.

*(University of Pennsylvania)*. Professor Emeritus. Functional analysis, C*-algebras and group representations, computer science.

*(Temple University)*

*Dean Emeritus*. Professor Emeritus. Mathematics education, curriculum and instruction, minority engineering education.

*(Ohio State University)*. Associate Professor Emeritus. Number theory, approximation theory and special functions, combinatorics, asymptotic analysis.

*(Drexel University)*. Teaching Professor Emerita.

*(University of Pennsylvania)*. Professor Emeritus. Lie algebras; theory, applications, and computational techniques; operations research.

*(University of California at Davis)*. Professor Emeritus. Probability and statistics, biostatistics, epidemiology, mathematical demography, data analysis, computer-intensive methods.

*(University of California at Berkeley)*. Associate Professor Emerita. Applied mathematics, computed tomography, numerical analysis of function reconstruction, signal processing, combinatorics.

*(Courant Institute, New York University)*. Professor Emeritus. Applied mathematics, scattering theory, mathematical modeling in biological sciences, solar-collection systems.

*(Courant Institute, New York University)*. Professor Emeritus. Homotopy theory, operad theory, quantum mechanics, quantum computing.

*(University of Edinburgh)*. Professor Emeritus. Applied mathematics, special factors, approximation theory, numerical techniques, asymptotic analysis.

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