in person

Engineering & Computational Mathematics

PhD in Engineering & Computational Mathematics

Whether you’re well into your engineering career or just beginning, the joint PhD in Engineering & Computational Mathematics broadens your understanding of the mathematical principles that underlie all engineering sub-disciplines and increases your professional value.

Combining the full resources of CGU’s Institute of Mathematical Sciences and the College of Engineering at California State University, Long Beach (CSULB), this joint degree program integrates advanced techniques in mathematical analysis with the latest in engineering innovation, research, and coursework. You’ll draw upon the expertise of faculty at two leading universities and study at a pace that fits your busy professional life. Flexibly designed to meet your individual needs, the joint PhD program in Engineering & Computational Mathematics offers ideal training for careers in aerospace, artificial intelligence, transportation, logistics, and more.

Program Highlights

Thanks to its flexible scheduling, this career-oriented program attracts students from well-known engineering and research firms, including Boeing, Northrup Grumman, and Raytheon.

With a joint degree from the CSULB/CGU program, you’ll be prepared to build a career in the growing fields of:

  • Operations research
  • Statistics
  • Computer science
  • Computational sciences
  • Biomechanics
  • Energy sustainability

Program At-a-glance

  • 72 units

    required units

  • PhD in Engineering & Computational Mathematics

    degree awarded

  • In Person

    modality

  • Spring, Summer, Fall

    program start

  • 7 years | full time*

    estimated completion time

Where You Can Find Our Alumni

Faculty

  • Portrait of John Angus

    John Angus

    Professor of Mathematics

    Research Interests

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

  • Portrait of Marina Chugunova

    Marina Chugunova

    Ellis Cumberbatch Professor of Mathematics
    Program Director, PhD in Engineering & Computational 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

  • Portrait of Hrushikesh Mhsakar

    Hrushikesh Mhaskar

    Distinguished Research Professor of Mathematics

    Research Interests

    Approximation theory, Computational harmonic analysis, Machine learning, Signal processing

  • Portrait of Ali Nadim

    Ali Nadim

    Professor of Mathematics

    Research Interests

    Fluid Dynamics, Mathematical Modeling, Scientific Computing

  • Portrait of Andrew Nguyen

    Andrew Nguyen

    Adjunct Professor of Mathematics

    Research Interests

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

  • Portrait of Qidi Peng

    Qidi Peng

    Research Associate Professor of Mathematics

    Research Interests

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

  • Portrait of Allon Percus

    Allon Percus

    Joseph H. Pengilly Professor of Mathematics
    Director, Institute of Mathematical Sciences

    Research Interests

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

  • Portrait of Claudia Rangel

    Claudia Rangel-Escareño

    Adjunct Professor of Mathematics

    Research Interests

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

  • Portrait of Henry Schellhorn

    Henry Schellhorn

    Professor of Mathematics
    Academic Director, Financial Engineering Program

    Research Interests

    Financial engineering, Credit risk, Stochastic analysis, Traffic models

Extended Faculty

  • Bahar Acu

    Pitzer College

    Research Interests

    Geometric topology, differential geometry

  • Konrad Aguilar

    Pomona College

    Research Interests

    Noncommutative/quantum metric geometry, functional analysis, operator algebras

  • Asuman G. Aksoy

    Claremont McKenna College

    Research Interests

    Analysis

  • David Bachman

    Pitzer College

    Research Interests

    Low-dimensional topology

  • Arthur Benjamin

    Harvey Mudd College

    Research Interests

    Combinatorics, game theory, operations research

  • Andrew Bernoff

    Harvey Mudd College

    Research Interests

    Applied dynamical systems, fluid mechanics, self-similarity and scaling

  • Sarah Cannon

    Claremont McKenna College

    Research Interests

    Randomized algorithms, Markov chains, stochastic processes, discrete geometry, statistical physics

  • Alfonso Castro

    Harvey Mudd College

    Research Interests

    Partial differential equations, variational methods, inverse-function theorems, water waves (solitons)

  • Anie Chaderjian

    Scripps College

    Research Interests

    Combinatorics

  • Gabriel Chandler

    Pomona College

    Research Interests

    Statistics

  • Lisette G. de Pillis

    Harvey Mudd College

    Research Interests

    Computational fluid dynamics, numerical linear algebra, mathematical biology

  • Vin de Silva

    Pomona College

    Research Interests

    Computational topology, manifold learning

  • Christina Edholm

    Scripps College

    Research Interests

    Mathematical biology, epidemiological modeling

  • Lenny Fukshansky

    Claremont McKenna College

    Research Interests

    Number theory, discrete geometry

  • Stephan Garcia

    Pomona College

    Research Interests

    Complex symmetric operators, operator theory, complex function theory

  • Edray Goins

    Pomona College

    Research Interests

    Algebraic geometry, number theory, representation theory

  • Weiqing Gu

    Harvey Mudd College

    Research Interests

    Differential geometry, Grassman manifolds

  • Jamie Haddock

    Harvey Mudd College

    Research Interests

    Mathematical data science, optimization, applied convex geometry

  • Johanna Hardin

    Pomona College

    Research Interests

    Model-based clustering, outlier detection, robust clustering, analysis of microarray data

  • Mark Huber

    Claremont McKenna College

    Research Interests

    Computational probability

  • Mike Izbicki

    Claremont McKenna College

    Research Interests

    Machine learning, high-dimensional probability, computational geometry

  • Jon Jacobsen

    Harvey Mudd College

    Research Interests

    Nonlinear elliptic partial differential equations, fluid dynamics

  • Chiu-Yen Kao

    Claremont McKenna College

    Research Interests

    Numerical analysis and scientific computing

  • Gizem Karaali

    Pomona College

    Research Interests

    Lie & Hopf algebras, quantum groups, Poisson-Lie structures, combinatorial representation theory

  • Dagan Karp

    Harvey Mudd College

    Research Interests

    Algebraic geometry

  • Adam Landsberg

    Joint Science

    Research Interests

    Scientific modeling of complex systems

  • Ran Libeskind-Hadas

    Claremont McKenna College

    Research Interests

    Computational biology, cophylogenetics, design and analysis of algorithms

  • Haydee Lindo

    Harvey Mudd College

    Research Interests

    Commutative algebra, homological algebra, representation theory

  • Jemma Lorenat

    Pitzer College

    Research Interests

    History of mathematics, geometry

  • Susan Martonosi

    Harvey Mudd College

    Research Interests

    Operations research, applied probability, aviation security

  • John Milton

    Joint Science

    Research Interests

    Computational neuroscience

  • Sam Nelson

    Claremont McKenna College

    Research Interests

    Algebraic topology, knot theory

  • Mohamed Omar

    Harvey Mudd College

    Research Interests

    Combinatorial optimization, graph theory, algebraic geometry

  • Mike O’Neill

    Claremont McKenna College

    Research Interests

    Complex analysis and harmonic analysis

  • Michael Orrison

    Harvey Mudd College

    Research Interests

    Harmonic analysis on finite groups, algebraic voting theory

  • Winston Ou

    Scripps College

    Research Interests

    Harmonic analysis

  • Jeho Park

    Claremont McKenna College

    Research Interests

    High-performance computing, data science

  • Ami Radunskaya

    Pomona College

    Research Interests

    Dynamical Systems, stochastic processes, applications of dynamical systems to instrument modeling, sound generation, and interactive composition

  • Animesh Ray

    Keck Graduate Institute

    Research Interests

    Genomics, computational and systems biology

  • Adolfo Rumbos

    Pomona College

    Research Interests

    Nonlinear analysis, differential equations

  • Ghassan Sarkis

    Pomona College

    Research Interests

    Number theory and commutative algebra, p-adic formal group

  • Shahriar Shahriari

    Pomona College

    Research Interests

    Combinatorics, representation theory of finite groups

  • James Sterling

    Keck Graduate Institute

    Research Interests

    Bioengineering, microfluidics

  • Francis Su

    Harvey Mudd College

    Research Interests

    Geometric and topological combinatorics, game theory, mathematical economics

  • Chris Towse

    Scripps College

    Research Interests

    Arithmetic geometry, algebraic number theory, combinatorics

  • Talithia Williams

    Harvey Mudd College

    Research Interests

    Spatial-temporal modeling of rainfall data

  • Helen Wong

    Claremont McKenna College

    Research Interests

    Low-dimensional topology, applications to molecular biology, data analysis, and quantum computation

  • Darryl Yong

    Harvey Mudd College

    Research Interests

    Mathematics education, applied mathematics, perturbation theory, partial differential equations

  • Heather Zinn Brooks

    Harvey Mudd College

    Research Interests

    Applied mathematics, mathematical modeling, complex systems, nonlinear dynamics, network theory, social systems, mathematical biology

Curriculum

View All Mathematics Courses

Degree Requirements
A minimum of 72 units of course work, independent study, and research (including transfer credit) must be completed.

  • Transfer credits of up to 24 units of related courses at the master’s level is permissible on approval of the program committee; this course work must have been completed with at least a grade of B or its equivalent at an accredited institution and must be directly related to the joint program and to the student’s PhD goals.
  • Of the 72 units, a minimum of 24 units must normally be completed in the graduate engineering program at CSULB and a minimum of 24 in the graduate mathematics program at CGU. Both sets of 24 units must conform to the area requirements of the relevant institution and must be approved by the Program Committee.
  • All degree requirements must be completed within seven years (or six with the transfer of 24 units according to CGU regulations) from the time a student begins graduate study.

Residency Requirement
The residency requirements for the PhD degree may be met either by two semesters of full-time study in a 24-month period or by the completion of 48 units of course work within a 48-month period, including work in the summer session, on either or both campuses.

Research Tool
A student in the joint PhD program must demonstrate proficiency in problem-solving ability using computer programs. This demonstration may take different forms depending on the student’s engineering sub-discipline, but it must include evidence that the student has used an appropriate computer language and an algorithmic method to solve a problem from an engineering discipline.

Preliminary Examinations
The student is required to pass written preliminary examinations. These examinations consist of two examination areas: one in engineering and one in mathematics.

Research Preparation
On completion of at least 48 units of course work (including transfer units) and completion of the preliminary examinations and research tool test, a student embarks on the research phase of the joint doctoral program. In preparation for the research phase, the student is expected to spend at least a semester in advanced graduate courses, seminars, or directed reading courses, where exposure to research material is emphasized.

Research Proposal and Qualifying Examination
The student will define an area of proposed research and prepare a written dissertation proposal containing an outline of the research to be undertaken and references to relevant source materials. The dissertation proposal is presented to the doctoral committee at least two weeks prior to the qualifying examination. The qualifying examination is an oral presentation to the doctoral committee by the student describing the research planned. The student is expected to present evidence both as to the mathematical content and to the engineering application of the proposed research, supporting such evidence with references to previous research work in both areas.

Advancement to Candidacy
After successful completion of the qualifying examination and certification that all other requirements are fulfilled, the student is advanced to candidacy.

Dissertation and Final Oral Examination
On completion of the research, the student will prepare the Dissertation in accordance with CGU regulations. A final draft of the dissertation will be presented to each member of the doctoral committee at least three weeks prior to the final oral examination. The oral defense will be held on the campus of the dissertation supervisor.

Application Guidelines

University Requirements
Application Fee

$80 (fee is non-refundable)

Official Transcripts

Undergraduate/graduate

Applicants must submit a sealed, official transcript from every undergraduate and graduate institution that has granted the applicant a degree. Electronic transcripts sent to admissions@cgu.edu are also accepted. For undergraduate coursework, applicants are required to submit proof of a completed bachelor’s degree from a regionally accredited college or university. Unofficial copies of transcripts are accepted for review purposes, but official copies will be required upon admission.

Applicants currently earning a degree that will be completed prior to attending CGU are required to submit a transcript showing work in progress for evaluation purposes. Once the degree has been granted, a final official transcript documenting the degree conferred must be submitted to CGU.

International applicants are advised to review the International Transcript Guidelines for additional information on submitting international transcripts.

English Proficiency Exam

Required (international applicants only)

A valid score on one of the following examinations TOEFL, IELTS, Pearson PTE, Duolingo English Test is required of all non-native English-speaking applicants. The examination is not required for the following applicants:

  • Citizens or permanent residents of countries where English is the sole official language of instruction, e.g., Australia, Bahamas, Barbados, Canada (except Quebec), England, Ghana, Ireland, Jamaica, Kenya, New Zealand, Nigeria, Scotland, St. Vincent and the Grenadines, Trinidad, Tobago, Uganda, and Wales (see the CGU Bulletin for a complete list of accepted countries).
  • Applicants who hold an undergraduate or advanced degree, or will have earned such a degree prior to enrolling at CGU, from an institution in the US or in countries where English is the sole official language of instruction (see above).
  • Applicants who have successfully completed an academic English pre-master’s or intensive graduate bridge program from a nationally recognized, regionally accredited four-year college or university in the United States in the last two years, with submitted evidence of successful completion, and subject to curriculum approval.
  • CGU allows for an English proficiency waiver if the applicant has received, or will receive prior to enrollment at CGU, an undergraduate or advanced degree from an institution where English is one of the primary languages of instruction for the majority of courses in the student’s program. To receive the waiver, documentation must be provided by the applicant to show that English is the language of instruction at their university/college.

CGU’s school code for the TOEFL exam is 4053.

International applicants are encouraged to visit our International Applicants page for more information, including score requirements.

Resume

Applicants must submit an up-to-date copy of their resume.

Program Requirements
Statement of Purpose

Please submit a 2-3 page statement of purpose that details your academic and/or professional achievements, your specific areas of research interest within your desired field of study, why you are a strong candidate for graduate studies at CGU, and your career goals.

Academic Prerequisites

To be admitted to the Engineering & Computational Mathematics doctoral program, an applicant must have received a bachelor’s or master’s degree in science, engineering, or mathematics from a regionally accredited institution.

Letter of Recommendation

2 letters required

When filling out the online application, please enter references acquainted with your potential for success who will submit a written recommendation on your behalf. In most academic departments, references from faculty members who can speak to your academic ability are preferred; applicants with substantial work experience may request professional references. Please do not enter family members as references.

You will be required to input information for your recommenders (whether they are submitting online or not) in the “Recommendations” section of the online application. Please follow the directions in this section carefully before clicking on “Recommendation Provider List” to input the names and contact information for each recommender. You will have an opportunity to indicate if the reference writer will be submitting online. These reference writers will receive an email from CGU with instructions on submitting an online recommendation.

Recommenders who are indicated as offline will not receive an email from CGU with instructions to submit. These reference writers can submit via traditional mail and should use the supplemental New Student Recommendation Form. Recommenders can also email their letter of recommendation to the Office of Admissions at admissions@cgu.edu.

Download the Recommendation Form

Standardized Test Scores

GRE or GMAT required

GMAT or GRE examination scores must be dated within the past five years. Request that an official GMAT or GRE score be sent to admissions directly from Educational Testing Service (ETS).

Scores must be sent directly to CGU by the testing agency.

CGU’s school codes:
GMAT DZK-QS-08
ETS (GRE and TOEFL) 4053

In order to be considered for admission, applicants must submit separate and complete applications to both Cal State Long Beach and Claremont Graduate University. Both application fees are required.

You can also visit the Cal State Long Beach program page for program information and faculty listings.

Key Dates & Deadlines

CGU operates on a priority deadline cycle. Applicants are strongly encouraged to submit complete applications by the priority dates in order to assure maximum consideration for both admission and fellowships.

Once the priority deadlines have passed, the University will continue to review applications for qualified candidates on a competitive, space-available basis. The final deadlines listed are the last date the University can accept an application in order to allow sufficient time to complete the admissions, financial aid, and other enrollment processes.

Spring 2025
Priority Deadline – November 1, 2024
Final Deadline (International) – November 15, 2024
Final Deadline (Domestic) – December 1, 2024
Classes begin – January 21, 2025

Fall 2025
Priority Deadline – February 1, 2025
Final Deadline (International) – July 5, 2025
Final Deadline (Domestic) – August 1, 2025
Classes begin – August 25, 2025

Apply Now

Cost & Aid

ESTIMATED TUITION (CALIFORNIA RESIDENTS, NON-RESIDENTS, INTERNATIONAL)
Program 72 units
Tuition per unit* $2,020

*Based on 2024-2025 tuition rates.

 

STUDENT FEES (PER SEMESTER)
$245 Student Fee
$150 Technology Fee
International Student Services Fee*: $661 fall semester, $776 spring semester
**Applies to all international students (F-1 visa only) who are registered in coursework, doctoral study, or continuous registration. The fee is assessed each fall and spring semester for annual ISO accident and sickness plans and administrative fees. Subject to change.

For estimates of room & board, books, etc., please download CGU’s Cost of Attendance 2024-2025.

review financial aid

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Resources

Engineering & Computational Mathematics Clinic
CGU’s internationally recognized Engineering & Computational 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

Learn More

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

Learn More

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