With a PhD in Mathematics from Claremont Graduate University, you will join a community of highly educated, capable scientists who excel at communicating knowledge to students, fellow mathematicians, and the global community.

CGU’s Institute of Mathematical Sciences (IMS) trains scientists in fundamental areas of mathematics and develops expertise in specialized areas of interest. You will learn to recognize significant research problems, formulate solutions, and transmit successful outcomes to others. Throughout the program, you will conduct collaborative research alongside faculty with extensive backgrounds in applied mathematics, computational science, statistics, financial engineering, industrial modeling, and more. Our mathematics graduates are ready to assume leadership roles in education, industry, government, technology, and more.

Program at a Glance

UNITS
72 units

COMPLETION TIME
3–5 years

COURSES BEGIN
Fall

DEGREE AWARDED
PhD in Mathematics

Featured Courses

MATH 452
Large-Scale Inference

Studies Bayesian hierarchical models and Empirical Bayesian approaches, as well as theory and application of multiple hypothesis testing such as false discovery rate.

MATH 368
Numerical Methods for Matrix Computations

Examines numerical linear algebra and the matrix computations that arise in solving linear systems, least-squares problems, and eigenvalue problems for both dense and sparse matrices.

MATH 294
Methods of Applied Mathematics

Examines broad range of subjects in applied mathematics, including quasilinear hyperbolic equations, Laplace, Poisson and Helmholtz equations, advection-diffusion equation, wave equation, and more.

MATH 337
Real & Functional Analysis I

Explores abstract measures, Lebesgue measure on Rn, and Lebesgue-Stieljes measures on R, as well as the Lebesgue integral and limit theorems, and more.

MATH 353
Asymptotic Methods in Statistics With Applications

Investigates modes of convergence for random variables and their distributions; central limit theorems; laws of large numbers; statistical large sample theory of functions of sample moments, sample quantiles, rank statistics, and more.

MATH 358
Mathematical Finance

Explores the theory of option pricing, with emphasis on Black-Scholes and interest rate models. Requires mature understanding of multivariable calculus and probability.

View All Mathematics Courses

Curriculum

Degree Requirements
General doctoral degree requirements can be found in the doctoral degrees section of the Bulletin.

A total of 72 units of coursework are required. These units must include one transdisciplinary course, per University policy.

Students must fulfill the CGU residency requirement: at least two semesters of full-time study within a two-year period or 48 units within a three-year period. It is recommended that coursework be completed on a full-time basis; while part-time attendance is an option, degree requirements should be fulfilled within a seven-year time frame.

Students who do not maintain a minimum overall grade point average of 3.0 in Mathematics courses are placed on academic probation. Students who remain on academic probation after taking an additional 8 units of Mathematics courses may be excluded from the program.

Students are assigned an academic advisor upon entering the program. As they reach the advanced stages of coursework, they select a research advisor, who assumes primary advising responsibilities. In order to advance to candidacy, students must select a PhD committee consisting of at least three Mathematics faculty members from within the Claremont Colleges, chaired by the research advisor.

Research Tools
The following two research tools, intended to help prepare students for independent research, are required:

  • 1. Research seminar requirement. Over a period of at least two semesters, each student must attend a mathematics research seminar regularly. This may be a CCMS research seminar, mathematics colloquium, faculty-organized topical seminar, or student-organized journal club. Completion of this research tool is required within one year of passing the written qualifying exam.

  • 2. Proficiency requirement. Each student must demonstrate proficiency in one of the following two categories. Completion of this research tool is required before advancing to candidacy.

    • Computational: A computer programming language, statistical research method, or other computational research tool approved by the advisor.

    • OR

    • Foreign language: French, German, or Russian.

Qualifying Examination
The written qualifying examination is given once per year, at the end of the Spring semester. Full-time students in the Mathematics PhD program take the exam immediately following the first year of coursework. Part-time students may wait until they have completed 16 units of CGU coursework. Students failing the exam on the first attempt must repeat the exam the following year. Failure to pass the exam on the second attempt results in dismissal from the program.

Students dismissed from the doctoral program in Mathematics for failure to pass the exam may, at the discretion of the faculty, qualify for a terminal master’s degree. However, they may not transfer to another doctoral program offered through the Institute of Mathematical Sciences.

Preliminary Examinations
Students are required to pass two preliminary examinations, within two years of passing the written qualifying exam, but no later than 3 months after the completion of 72 units of coursework. Unless there are mitigating circumstances, failure to complete the exams within the specified period is cause for dismissal from the program.

Advancement to Candidacy
After completing the qualifying and preliminary examinations, doctoral students must prepare a written dissertation proposal. In the advancement to candidacy examination, the student presents the proposed dissertation research. The examination should be scheduled within one year of completing the required 72 units of coursework.

Dissertation Completion and Final Oral Examination
The dissertation must be completed within seven years from the semester in which the student was admitted. The dissertation defense may not occur earlier than six months after advancement to candidacy. The defense is a public event announced to the University’s academic community by the registrar’s office.

Resources

Engineering & Industrial Applied Mathematics Clinic
CGU’s internationally recognized Engineering & Industrial Applied Mathematics Clinic offers first-hand experience solving significant mathematical problems for industry and government clients.

Recent projects include:

  • Optimizing Transmission of Renewable Energy–Southern California Edison
  • Hardware-Software Codesign–Los Alamos National Laboratory
  • Data Cohort Analysis–Fair Isaac
  • Optimizing Smart Power Grids–Los Alamos National Laboratory
  • Credit Risk in a Network Economy–Fitch Rating
  • Isogeometric Analysis–Boeing
  • Gate to Base Capacitance Modeling for Nanoscale MOSFETs–USC Information Sciences Institute
  • Practical Semi-Analytic Model for the Substrate Current of Short Channel MOSFETs with LDDs–USC Information Sciences Institute

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Claremont Center for the Mathematical Sciences
Through the Claremont Center for the Mathematical Sciences (CCMS), you’ll have access to one of the largest mathematical science communities in California, as well as to workshops, conferences, and seminars, including:

  • Southern California Analysis Seminar
  • Math-in-Industry Workshop
  • Michael E. Moody Lecture Series
  • History and Philosophy of Mathematics Seminar
  • Claremont Mathematics Weekend
  • CCMS Software Lab
  • and more

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Faculty & Research
  • John Angus profile image

    John Angus

    Professor of Mathematics

    Research Interests

    Probability, Statistics, Computing, Algorithms, Navigation, Systems Engineering, Mathematical Finance

  • Marina Chugunova profile image

    Marina Chugunova

    Associate Professor of Mathematics
    Director, Institute of Mathematical Sciences
    Program Director, PhD in Engineering & Industrial Applied Mathematics

    Research Interests

    Surfactant-driven thin film flows in biomedical applications; Nonlinear parabolic equations; Stability problems in fluid dynamics; Scientific computations; Applied operator theory; Sturm-Liouville problems

  • Ellis Cumberbatch profile image

    Ellis Cumberbatch

    Professor of Mathematics Emeritus

    Research Interests

    Applied mathematics, Industrial modeling, Differential equations, Fluid mechanics, Wave propagation, Semi-conductors

  • Hrushikesh Mhaskar profile image

    Hrushikesh Mhaskar

    Research Professor of Mathematics

    Research Interests

    Approximation theory, Computational harmonic analysis, Mathematics of data, Query processing

  • Ali Nadim profile image

    Ali Nadim

    Professor of Mathematics
    Joseph H. Pengilly Chair in Mathematics

    Research Interests

    Fluid Dynamics, Mathematical Modeling, Scientific Computing

  • Andrew Nguyen profile image

    Andrew Nguyen

    Adjunct Professor of Mathematics

    Research Interests

    Stochastic processes, Statistics, Risk management, Financial derivatives, Actuarial sciences, Statistical software

  • Qidi Peng profile image

    Qidi Peng

    Research Assistant Professor of Mathematics

    Research Interests

    Statistical inferences, Stochastic differential equations, Stochastic modeling, Simulation, Machine learning, Approximation theory, Graph theory

  • Allon Percus profile image

    Allon Percus

    Professor of Mathematics

    Research Interests

    Discrete optimization; Network models; Statistical physics; Random combinatorial structures

  • Claudia Rangel-Escareño profile image

    Claudia Rangel-Escareño

    Adjunct Professor of Mathematics

    Research Interests

    Probabilistic methods in computational biology, Statistical inference of genetic networks, Bioinformatics

  • Henry Schellhorn profile image

    Henry Schellhorn

    Associate Professor of Mathematics
    Academic Director, Financial Engineering Program

    Research Interests

    Financial engineering, Credit risk, Interest rate models

Extended Faculty

In addition to CGU core faculty, you will have access to Math faculty across the Claremont Colleges, including Pomona, Scripps, Harvey Mudd, Claremont McKenna, Pitzer, and Keck Graduate Institute, as well as faculty who are part of the W.M. Keck integrated science department.

View Full Faculty List

Harvey Mudd
View Math Faculty

Pomona
View Math Faculty

Claremont McKenna
View Math Faculty

Scripps
View Math Faculty

Pitzer
David Bachman
Jim Hoste

W.M. Keck Integrated Science Department
(Claremont McKenna, Pitzer, Scripps)
Adam Landsberg
John Milton

Keck Graduate Institute
Animesh Ray
James Sterling

Where You Can Find Our Alumni

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Jake Campbell

Senior Assistant Director of Admissions and Veteran Outreach
T: 909-607-3024 (Direct)
T: 909-607-7811 (Central Admissions)
E: jake.campbell@cgu.edu