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PhD in Pure Mathematics and Mathematical Statistics

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This course is a three to four year programme culminating in the submission and examination of a single research thesis.  Students joining the course will often have completed prior study at a level comparable to our Part III (MMath/MASt) course and many have postgraduate experience. Our students, therefore, begin their PhD research with a good understanding of advanced material, which they build on in various ways throughout the course of their PhD studies.

Structure of the PhD

Students are required to undertake a minimum of nine full-time terms of research (ie three years). Students are not registered for the PhD in the first instance but are instead admitted on a probationary basis. All students are assessed for registration towards the end of their first year of full-time study (usually June). This assessment is based on a short written report which is reviewed by two assessors. In the fifth term, there may also be a further assessment of progress, for which students submit a longer piece of written work and receive an oral assessment.

Research areas

Research in DPMMS can be divided into the following broad areas: Algebra, Algebraic Geometry, Analysis and Partial Differential Equations, Combinatorics, Differential Geometry and Topology, Number Theory, Information and Finance, Probability, and Statistics. The boundaries between such areas are not rigid, however, and staff may contribute to more than one area.

Additional training and opportunities

Whilst there are no mandatory taught components to the PhD degree, students may wish to undertake specific courses or further training to expand their knowledge, either for personal interest or to directly assist with their PhD research. All students are encouraged to participate in and attend the wide range of lectures, seminars and events on offer within DPMMS and the Centre for Mathematical Sciences.

Many students submit a prize essay at the beginning of their fifth term. The best essays each year are of a scale and quality already adequate for a PhD thesis, incorporating work already, or about to be, published. We intend that our students publish their work in leading journals. Our PhD students might have written several papers before they submit their thesis, and can go on to win academic positions at leading institutions around the world.

DPMMS also promotes and encourages researcher development and transferable skills training. This can take the form of assisting with Part III preparatory workshops, attendance at skills-based training sessions, or presenting work at seminars and conferences. The University also offers training via the Researcher Development Programme .

There is no requirement for PhD students to teach but there are plenty of opportunities to do so, such as offering supervisions for third-year undergraduates (this involves the supervisor sitting with a pair of students for an hour, discussing their work). PhD students might help with running examples classes for Part III students, too.

The Postgraduate Virtual Open Day usually takes place at the end of October. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the  Postgraduate Open Day  page for more details.

See further the  Postgraduate Admissions Events  pages for other events relating to Postgraduate study, including study fairs, visits and international events.

Departments

This course is advertised in the following departments:

• Faculty of Mathematics
• Department of Pure Mathematics and Mathematical Statistics

Key Information

3-4 years full-time, 4-7 years part-time, study mode : research, doctor of philosophy, department of pure mathematics and mathematical statistics this course is advertised in multiple departments. please see the overview tab for more details., course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, michaelmas 2024.

Some courses can close early. See the Deadlines page for guidance on when to apply.

Funding Deadlines

These deadlines apply to applications for courses starting in Michaelmas 2024, Lent 2025 and Easter 2025.

Similar Courses

• Mathematics MPhil
• Mathematics (Applied Mathematics) MASt
• Mathematics (Mathematical Statistics) MASt
• Mathematics (Pure Mathematics) MASt
• Mathematics (Theoretical Physics) MASt

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The Ph.D. in Mathematics, with a Specialization in Statistics is designed to provide a student with solid training in statistical theory and methodology that find broad application in various areas of scientific research including natural, biomedical and social sciences, as well as engineering, finance, business management and government regulations. It aims to produce future researchers in contemporary statistics, both in academia and industry, who will contribute to satisfy the tremendous need for new statistics theory and methodology following the rapid growth of computing power, high throughput technology, and the explosion of digital data acquisition technologies.

Prospective students must apply to the  Ph.D. program in Mathematics  and select "Statistics" in the "Current Area of Interest" section of their on line application (this means the person is applying the Specialization in Statistics degree). Demonstration of computer literacy is highly desired; knowledge of a programming language such as Perl or C, and knowledge of a statistical computing package such as SAS, R, S-PLUS or STATA are also desirable. The program may admit students without this level of preparation with the understanding that the student will promptly make up any deficiencies by taking additional courses upon entering the program.

Program Requirements for the Specialization in Statistics

• The specialization requires completion of 72 units before advancement to Ph.D. candidacy.
• Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only.
• MATH 280A-B-C (Probability Theory)
• MATH 281A-B-C (Mathematical Statistics)
• MATH 282A-B (Applied Statistics)
• MATH 287A (Time Series Analysis)
• MATH 287B (Multivariate Analysis)
• MATH 287C (Advanced Time Series Analysis)
• MATH 287D (Statistical Learning)
• MATH 202A (Applied Algebra I)
• MATH 240A-B-C (Real Analysis)
• MATH 241A-B (Functional Analysis)
• MATH 261A-B-C (Probabilistic Combinatorics and Algorithms)
• MATH 270A-B (Numerical Analysis)
• MATH 271A-B-C (Numerical Optimization)
• MATH 283 (Statistical Methods in Bioinformatics)
• MATH 285 (Stochastic Processes)
• MATH 289A-B (Topics in Probability and Statistics)
• MATH 294 (The Mathematics of Finance)
• Candidates must acquire experience in statistical consulting and the practical analysis of data. To meet this requirement, students must participate in the MathStorm graduate student consulting seminar for one year. A project outside the consulting seminar can be substituted only if prior approval is obtained from the director of the consulting seminar and the student's advisor. Students should complete at least five quarters of coursework before taking the consulting seminar and are encouraged to fulfill the requirement in their third or fourth year.
• Students must pass two written qualifying exams. One of the required exams is in Mathematical Statistics (MATH 281A-B-C) the other is recommended to be in Real Analysis (MATH 240A-B-C). At least one of the exams should be passed at the Ph.D. level, and both exams should be passed at the provisional doctoral level or better.
• At least one of the exams should be passed at the provisional doctoral level before the start of the second year and both passed before the start of the third year, for the student to remain in the Ph.D. program.
• Before the start of the third year, the student is required to take Applied Statistics (MATH 282A-B) and pass the comprehensive exam in this subject.
• No foreign language requirement.

Advancement to Candidacy

It is expected that by the end of the third year (9 quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C. Phil. degree.

Dissertation and Final Defense

Students participating in the Ph.D. in Mathematics with a Specialization in Statistics must complete a dissertation and final defense that meets all requirements for the regular Ph.D. in mathematics.

Students who wish to switch between the regular Ph.D. program in Mathematics and the Specialization in Statistics must submit a written request to the graduate vice chair for consideration. Approval is not automatic, however.

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(858) 534-3590

Cornell University does not offer a separate Masters of Science (MS) degree program in the field of Statistics. Applicants interested in obtaining a masters-level degree in statistics should consider applying to Cornell's MPS Program in Applied Statistics.

Choosing a Field of Study

There are many graduate fields of study at Cornell University. The best choice of graduate field in which to pursue a degree depends on your major interests. Statistics is a subject that lies at the interface of theory, applications, and computing. Statisticians must therefore possess a broad spectrum of skills, including expertise in statistical theory, study design, data analysis, probability, computing, and mathematics. Statisticians must also be expert communicators, with the ability to formulate complex research questions in appropriate statistical terms, explain statistical concepts and methods to their collaborators, and assist them in properly communicating their results. If the study of statistics is your major interest then you should seriously consider applying to the Field of Statistics.

There are also several related fields that may fit even better with your interests and career goals. For example, if you are mainly interested in mathematics and computation as they relate to modeling genetics and other biological processes (e.g, protein structure and function, computational neuroscience, biomechanics, population genetics, high throughput genetic scanning), you might consider the Field of Computational Biology . You may wish to consider applying to the Field of Electrical and Computer Engineering if you are interested in the applications of probability and statistics to signal processing, data compression, information theory, and image processing. Those with a background in the social sciences might wish to consider the Field of Industrial and Labor Relations with a major or minor in the subject of Economic and Social Statistics. Strong interest and training in mathematics or probability might lead you to choose the Field of Mathematics . Lastly, if you have a strong mathematics background and an interest in general problem-solving techniques (e.g., optimization and simulation) or applied stochastic processes (e.g., mathematical finance, queuing theory, traffic theory, and inventory theory) you should consider the Field of Operations Research .

Residency Requirements

Students admitted to PhD program must be "in residence" for at least four semesters, although it is generally expected that a PhD will require between 8 and 10 semesters to complete. The chair of your Special Committee awards one residence unit after the satisfactory completion of each semester of full-time study. Fractional units may be awarded for unsatisfactory progress.

Your Advisor and Special Committee

The Director of Graduate Studies is in charge of general issues pertaining to graduate students in the field of Statistics. Upon arrival, a temporary Special Committee is also declared for you, consisting of the Director of Graduate Studies (chair) and two other faculty members in the field of Statistics. This temporary committee shall remain in place until you form your own Special Committee for the purposes of writing your doctoral dissertation. The chair of your Special Committee serves as your primary academic advisor; however, you should always feel free to contact and/or chat with any of the graduate faculty in the field of Statistics.

The formation of a Special Committee for your dissertation research should serve your objective of writing the best possible dissertation. The Graduate School requires that this committee contain at least three members that simultaneously represent a certain combination of subjects and concentrations. The chair of the committee is your principal dissertation advisor and always represents a specified concentration within the subject & field of Statistics. The Graduate School additionally requires PhD students to have at least two minor subjects represented on your special committee. For students in the field of Statistics, these remaining two members must either represent (i) a second concentration within the subject of Statistics, and one external minor subject; or, (ii) two external minor subjects. Each minor advisor must agree to serve on your special committee; as a result, the identification of these minor members should occur at least 6 months prior to your A examination.

Some examples of external minors include Computational Biology, Demography, Computer Science, Economics, Epidemiology, Mathematics, Applied Mathematics and Operations Research. The declaration of an external minor entails selecting (i) a field other than Statistics in which to minor; (ii) a subject & concentration within the specified field; and, (iii) a minor advisor representing this field/subject/concentration that will work with you in setting the minor requirements. Typically, external minors involve gaining knowledge in 3-5 graduate courses in the specified field/subject, though expectations can vary by field and even by the choice of advisor. While any choice of external minor subject is technically acceptable, the requirement that the minor representative serve on your Special Committee strongly suggests that the ideal choice(s) should share some natural connection with your choice of dissertation topic.

The fields, subjects and concentrations represented on your committee must be officially recognized by the Graduate School ; the Degrees, Subjects & Concentrations tab listed under each field of study provides this information. Information on the concentrations available for committee members chosen to represent the subject of Statistics can be found on the Graduate School webpage . 

Statistics PhD Travel Support

The Department of Statistics and Data Science has established a fund for professional travel for graduate students. The intent of the Department is to encourage travel that enhances the Statistics community at Cornell by providing funding for graduate students in statistics that will be presenting at conferences. Please review the Graduate Student Travel Award Policy website for more information. 

Completion of the PhD Degree

In addition to the specified residency requirements, students must meet all program requirements as outlined in Program Course Requirements and Timetables and Evaluations and Examinations, as well as complete a doctoral dissertation approved by your Special Committee. The target time to PhD completion is between 4 and 5 years; the actual time to completion varies by student.

Students should consult both the Guide to Graduate Study and Code of Legislation of the Graduate Faculty (available at www.gradschool.cornell.edu ) for further information on all academic and procedural matters pertinent to pursuing a graduate degree at Cornell University.

PhD Program

Advanced undergraduate or masters level work in mathematics and statistics will provide a good background for the doctoral program. Quantitatively oriented students with degrees in other scientific fields are also encouraged to apply for admission. In particular, the department has expanded its research and educational activities towards computational biology, mathematical finance and information science. The doctoral program normally takes four to five years to complete.

Doctoral Program in Statistics

Statistics phd minor.

Graduate Student Handbook (Coming Soon: New Graduate Student Handbook)

Phd program overview.

The PhD program prepares students for research careers in probability and statistics in academia and industry. Students admitted to the PhD program earn the MA and MPhil along the way. The first year of the program is spent on foundational courses in theoretical statistics, applied statistics, and probability. In the following years, students take advanced topics courses. Research toward the dissertation typically begins in the second year. Students also have opportunities to take part in a wide variety of projects involving applied probability or applications of statistics.

Students are expected to register continuously until they distribute and successfully defend their dissertation. Our core required and elective curricula in Statistics, Probability, and Machine Learning aim to provide our doctoral students with advanced learning that is both broad and focused. We expect our students to make Satisfactory Academic Progress in their advanced learning and research training by meeting the following program milestones through courseworks, independent research, and dissertation research:

By the end of year 1: passing the qualifying exams;

By the end of year 2: fulfilling all course requirements for the MA degree and finding a dissertation advisor;

By the end of year 3: passing the oral exam (dissertation prospectus) and fulfilling all requirements for the MPhil degree

By the end of year 5: distributing and defending the dissertation.

We believe in the Professional Development value of active participation in intellectual exchange and pedagogical practices for future statistical faculty and researchers. Students are required to serve as teaching assistants and present research during their training. In addition, each student is expected to attend seminars regularly and participate in Statistical Practicum activities before graduation.

We provide in the following sections a comprehensive collection of the PhD program requirements and milestones. Also included are policies that outline how these requirements will be enforced with ample flexibility. Questions on these requirements should be directed to ADAA Cindy Meekins at [email protected] and the DGS, Professor John Cunningham at [email protected] .

Applications for Admission

• Our students receive very solid training in all aspects of modern statistics. See Graduate Student Handbook for more information.
• Our students receive Fellowship and full financial support for the entire duration of their PhD. See more details here .
• Our students receive job offers from top academic and non-academic institutions .
• Our students can work with world-class faculty members from Statistics Department or the Data Science Institute .
• Our students have access to high-speed computer clusters for their ambitious, computationally demanding research.
• Our students benefit from a wide range of seminars, workshops, and Boot Camps organized by our department and the data science institute .
• Suggested Prerequisites: A student admitted to the PhD program normally has a background in linear algebra and real analysis, and has taken a few courses in statistics, probability, and programming. Students who are quantitatively trained or have substantial background/experience in other scientific disciplines are also encouraged to apply for admission.
• GRE requirement: Waived for Fall 2024.
• Language requirement: The English Proficiency Test requirement (TOEFL) is a Provost's requirement that cannot be waived.
• The Columbia GSAS minimum requirements for TOEFL and IELTS are: 100 (IBT), 600 (PBT) TOEFL, or 7.5 IELTS. To see if this requirement can be waived for you, please check the frequently asked questions below.
• Deadline: Jan 8, 2024 .
• Application process: Please apply by completing the Application for Admission to the Columbia University Graduate School of Arts & Sciences .
• Timeline: P.hD students begin the program in September only.  Admissions decisions are made in mid-March of each year for the Fall semester.

Frequently Asked Questions

• What is the application deadline? What is the deadline for financial aid? Our application deadline is January 5, 2024 .
• Can I meet with you in person or talk to you on the phone? Unfortunately given the high number of applications we receive, we are unable to meet or speak with our applicants.
• What are the required application materials? Specific admission requirements for our programs can be found here .
• Due to financial hardship, I cannot pay the application fee, can I still apply to your program? Yes. Many of our prospective students are eligible for fee waivers. The Graduate School of Arts and Sciences offers a variety of application fee waivers . If you have further questions regarding the waiver please contact  gsas-admissions@ columbia.edu .
• How many students do you admit each year? It varies year to year. We finalize our numbers between December - early February.
• What is the distribution of students currently enrolled in your program? (their background, GPA, standard tests, etc)? Unfortunately, we are unable to share this information.
• How many accepted students receive financial aid? All students in the PhD program receive, for up to five years, a funding package consisting of tuition, fees, and a stipend. These fellowships are awarded in recognition of academic achievement and in expectation of scholarly success; they are contingent upon the student remaining in good academic standing. Summer support, while not guaranteed, is generally provided. Teaching and research experience are considered important aspects of the training of graduate students. Thus, graduate fellowships include some teaching and research apprenticeship. PhD students are given funds to purchase a laptop PC, and additional computing resources are supplied for research projects as necessary. The Department also subsidizes travel expenses for up to two scientific meetings and/or conferences per year for those students selected to present. Additional matching funds from the Graduate School Arts and Sciences are available to students who have passed the oral qualifying exam.
• Can I contact the department with specific scores and get feedback on my competitiveness for the program? We receive more than 450 applications a year and there are many students in our applicant pool who are qualified for our program. However, we can only admit a few top students. Before seeing the entire applicant pool, we cannot comment on admission probabilities.
• What is the minimum GPA for admissions? While we don’t have a GPA threshold, we will carefully review applicants’ transcripts and grades obtained in individual courses.
• Is there a minimum GRE requirement? No. The general GRE exam is waived for the Fall 2024 admissions cycle. 
• Can I upload a copy of my GRE score to the application? Yes, but make sure you arrange for ETS to send the official score to the Graduate School of Arts and Sciences.
• Is the GRE math subject exam required? No, we do not require the GRE math subject exam.
• What is the minimum TOEFL or IELTS  requirement? The Columbia Graduate School of Arts and Sciences minimum requirements for TOEFL and IELTS are: 100 (IBT), 600 (PBT) TOEFL, or 7.5 IELTS
•  I took the TOEFL and IELTS more than two years ago; is my score valid? Scores more than two years old are not accepted. Applicants are strongly urged to make arrangements to take these examinations early in the fall and before completing their application.
• I am an international student and earned a master’s degree from a US university. Can I obtain a TOEFL or IELTS waiver? You may only request a waiver of the English proficiency requirement from the Graduate School of Arts and Sciences by submitting the English Proficiency Waiver Request form and if you meet any of the criteria described here . If you have further questions regarding the waiver please contact  gsas-admissions@ columbia.edu .
• My transcript is not in English. What should I do? You have to submit a notarized translated copy along with the original transcript.

Can I apply to more than one PhD program? You may not submit more than one PhD application to the Graduate School of Arts and Sciences. However, you may elect to have your application reviewed by a second program or department within the Graduate School of Arts and Sciences if you are not offered admission by your first-choice program. Please see the application instructions for a more detailed explanation of this policy and the various restrictions that apply to a second choice. You may apply concurrently to a program housed at the Graduate School of Arts and Sciences and to programs housed at other divisions of the University. However, since the Graduate School of Arts and Sciences does not share application materials with other divisions, you must complete the application requirements for each school.

How do I apply to a dual- or joint-degree program? The Graduate School of Arts and Sciences refers to these programs as dual-degree programs. Applicants must complete the application requirements for both schools. Application materials are not shared between schools. Students can only apply to an established dual-degree program and may not create their own.

With the sole exception of approved dual-degree programs , students may not pursue a degree in more than one Columbia program concurrently, and may not be registered in more than one degree program at any institution in the same semester. Enrollment in another degree program at Columbia or elsewhere while enrolled in a Graduate School of Arts and Sciences master's or doctoral program is strictly prohibited by the Graduate School. Violation of this policy will lead to the rescission of an offer of admission, or termination for a current student.

When will I receive a decision on my application? Notification of decisions for all PhD applicants generally takes place by the end of March.

Notification of MA decisions varies by department and application deadlines. Some MA decisions are sent out in early spring; others may be released as late as mid-August.

Can I apply to both MA Statistics and PhD statistics simultaneously?  For any given entry term, applicants may elect to apply to up to two programs—either one PhD program and one MA program, or two MA programs—by submitting a single (combined) application to the Graduate School of Arts and Sciences.  Applicants who attempt to submit more than one Graduate School of Arts and Sciences application for the same entry term will be required to withdraw one of the applications.

The Graduate School of Arts and Sciences permits applicants to be reviewed by a second program if they do not receive an offer of admission from their first-choice program, with the following restrictions:

• This option is only available for fall-term applicants.
• Applicants will be able to view and opt for a second choice (if applicable) after selecting their first choice. Applicants should not submit a second application. (Note: Selecting a second choice will not affect the consideration of your application by your first choice.)
• Applicants must upload a separate Statement of Purpose and submit any additional supporting materials required by the second program. Transcripts, letters, and test scores should only be submitted once.
• An application will be forwarded to the second-choice program only after the first-choice program has completed its review and rendered its decision. An application file will not be reviewed concurrently by both programs.
• Programs may stop considering second-choice applications at any time during the season; Graduate School of Arts and Sciences cannot guarantee that your application will receive a second review.
• What is the mailing address for your PhD admission office? Students are encouraged to apply online . Please note: Materials should not be mailed to the Graduate School of Arts and Sciences unless specifically requested by the Office of Admissions. Unofficial transcripts and other supplemental application materials should be uploaded through the online application system. Graduate School of Arts and Sciences Office of Admissions Columbia University  107 Low Library, MC 4303 535 West 116th Street  New York, NY 10027
• How many years does it take to pursue a PhD degree in your program? Our students usually graduate in 4‐6 years.
• Can the PhD be pursued part-time? No, all of our students are full-time students. We do not offer a part-time option.
• One of the requirements is to have knowledge of linear algebra (through the level of MATH V2020 at Columbia) and advanced calculus (through the level of MATH V1201). I studied these topics; how do I know if I meet the knowledge content requirement? We interview our top candidates and based on the information on your transcripts and your grades, if we are not sure about what you covered in your courses we will ask you during the interview.
• Can I contact faculty members to learn more about their research and hopefully gain their support? Yes, you are more than welcome to contact faculty members and discuss your research interests with them. However, please note that all the applications are processed by a central admission committee, and individual faculty members cannot and will not guarantee admission to our program.
• How do I find out which professors are taking on new students to mentor this year?  Applications are evaluated through a central admissions committee. Openings in individual faculty groups are not considered during the admissions process. Therefore, we suggest contacting the faculty members you would like to work with and asking if they are planning to take on new students.

For more information please contact us at [email protected] .

For more information please contact us at  [email protected]

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Requirements: Students must complete their primary program’s degree requirements along with the IDPS requirements. Statistics requirements must not unreasonably impact performance or progress in a student’s primary degree program.

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Statistics and Data Science, PhD

Wharton’s PhD program in Statistics and Data Science provides the foundational education that allows students to engage both cutting-edge theory and applied problems. These include problems from a wide variety of fields within Wharton, such as finance, marketing, and public policy, as well as fields across the rest of the University such as biostatistics within the Medical School and computer science within the Engineering School.

Major areas of departmental research include:

• analysis of observational studies;
• Bayesian inference, bioinformatics;
• decision theory;
• game theory;
• high dimensional inference;
• information theory;
• machine learning;
• model selection;
• nonparametric function estimation; and
• time series analysis.

Students typically have a strong undergraduate background in mathematics. Knowledge of linear algebra and advanced calculus is required, and experience with real analysis is helpful. Although some exposure to undergraduate probability and statistics is expected, skills in mathematics and computer science are more important. Graduates of the department typically take positions in academia, government, financial services, and bio-pharmaceutical industries.

For more information: https://statistics.wharton.upenn.edu/programs/phd/curriculum/

View the University’s Academic Rules for PhD Programs .

The total course units required for graduation is 13.

Electives must include suitable courses numbered 9000 and above, when offered.

The degree and major requirements displayed are intended as a guide for students entering in the Fall of 2023 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.

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Department of statistics and applied probability - uc santa barbara, phd in statistics and applied probability.

Our doctoral program in Statistics and Applied Probability prepares graduate students to expand the boundaries of statistical theory and practice for use in real-world problem solving. Graduates are trained for a career in academics or industry where they are working in and contributing to the forefront of new methods and technology. This program provides rigorous mathematical training in statistics and probability that can be used to develop real-world methodologies applicable to a wide range of interdisciplinary fields including finance, environmental science, computer science, and biomedical science. Recent dissertations have been written in the areas of smoothing splines, spatial statistics, micro-array analysis, functional data models, empirical processes, mathematical and statistical finance, Bayesian inference, and bootstrap estimation methods.

Admission Requirements

Our doctoral program in Statistics and Applied Probability is open to those who hold a bachelor’s degree in Statistics, Mathematics, or other fields with strong quantitative requirements. Students must have a minimum overall grade point average of 3.0; one year of statistical theory that includes hypothesis testing, confidence intervals, best statistics and most powerful tests, regression and ANOVA concepts; and one course in linear algebra that includes vector spaces, bases in vector spaces, eigenvalues, and eigenvectors.

For further admissions requirements and procedures, please visit our admissions page .

Normative Time to Degree

The normative time to advancement to candidacy is 3 years. The normative time for completion of the PhD program is 5 years. Students are expected to have their core courses completed and written qualifying exams passed within the first 2 years.

Registration Expectations

In addition to department requirements, every UC Santa Barbara graduate student is required to follow University policy with regards to degree requirements and registration expectations. You can read over these requirements on the Graduate Division website: here.

Sample Study-Plan

Every full-time student at UC Santa Barbara is required to take 8 units of coursework per quarter. Financial support is contingent on normal progress towards the degree objective.

The following would be a typical program for a well-prepared student seeking a Ph.D. objective with no optional degree emphasis.

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PhD, Mathematical Statistics With a Concentration in Biostatistics and Bioinformatics

Explore statistical techniques for public health, medical and biological research

Biostatistics/Bioinformatics is an important and emerging research field in statistics with immensely broad applications in public health, medical and biological research. The Bioinformatics/Biostatistics (STAT-BB) concentration addresses the increasing research opportunities and the educational needs of this burgeoning field.

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Perfect for...

Students who plan to learn:

• Theories, techniques, methods in epidemiology
• Design, analysis and evaluation of epidemiologic studies
• Causal analysis and control of biases
• Development intervention and prevention strategies
• Presentations of findings in academic journals and conferences

Career Paths

• Private sector

Program Overview

The STAT-BB concentration is administered by the Statistics (STAT) Program within the Mathematics Department. Its faculty includes professors in the STAT Program, in the Department of Epidemiology and Biostatistics (EPIB) and in the Center for Bioinformatics and Computational Biology (CBCB) at UMCP. The program also includes the participation of the Division of Biostatistics and Bioinformatics (DBB) faculty at the University of Maryland School of Medicine (SOM). STAT faculty and EPIB faculty collaborate on program admissions decisions, academic policies and creating qualifying exams.

A Master’s degree is not required for admission to the Ph.D. program. A doctoral student must complete a minimum of 36 hours of formal courses (at least 27 at the 600/700 level) with at least a B average (3.0 on a 4.0 scale); at least 18 of the graduate credits must be taken in Statistics. In addition, the University requires at least 12 hours of STAT 899 or EPIB 899 (Doctoral research) given by any participating faculty member as the major advisor.

Ph.D. students must satisfy the Ph.D. qualifying requirements (see below). Full-time students must satisfy all qualifying requirements by the middle of the third year. Part-time students must satisfy all qualifying requirements by the end of the fourth year. If successful in the written examinations, the student must pass an oral exam. Administered by the faculty under this proposed joint program, the oral exam usually takes place a year after the student passes the written examination. This exam serves as a test of the student's in-depth preparation in the area of specialization and research potential. Successful completion of the oral exam indicates that the student is ready to begin writing the doctoral dissertation. In addition, the Department requires a reading competence in one foreign language for the Ph.D. To be admitted to candidacy, the Ph.D. student must pass the written examinations and the oral examination. The final step in completion of the doctoral study for a student is to pass the final oral exam on the dissertation.

The following courses are required:

• STAT 410 Introduction to Probability Theory
• STAT 650 Applied Stochastic Processes
• STAT 700 Mathematical Statistics I
• STAT 701 Mathematical Statistics II
• STAT 705 Computational Statistics
• STAT 740 Linear Statistical Models I
• STAT 741 Linear Statistical Models II (STAT 740 is the prerequisite)
• STAT 770 Analysis of Categorical Data
• STAT 702 Survival Analysis
• STAT 899 or EPIB 899 Doctoral Research (12 credits)

Each student is required to take at least three additional courses  in STAT, EPIB  or CMSC )with the approval of the Advisory Committee). For students who focus their studies on Biostatistics, it is required to take at least two of the following three courses:

• EPIB 652 Categorical Data Analysis
• EPIB 653 Applied Survival Data Analysis
• EPIB 655 Longitudinal Data Analysis

Students interested in bioinformatics will complete the required coursework and can select specialized courses such as CMSC 423 Bioinformatic Algorithms, Databases and Tools; CMSC 701 Computational Genomics or CMSC 702 Computational Systems Biology. Interested students can then select a faculty advisor with expertise in computational biology. Interested students will be expected to have a solid background in computer science for this option.

Dr. Jamie Trevitt Assistant Clinical Professor & Director of Graduate Studies [email protected]

Department of Mathematics and Statistics

College of natural and mathematical sciences, ms and phd programs in applied mathematics or statistics.

The Department of Mathematics and Statistics offers graduate programs leading to the Master’s (MS) and Doctor of Philosophy (PhD) degrees in both Applied Mathematics and Statistics . The department has had an active graduate program in applied mathematics since 1970. It expanded to include a full graduate program in statistics in 1984. The strength of these programs lies in its graduate faculty, who are actively engaged in research in applications of mathematics and statistics in a wide variety of real-world problems, as well as in investigations of fundamental and theoretical questions. The faculty designs and implements courses and curricula with emphasis on innovative research directed toward practical applications, as mandated by the charter from the University System of Maryland Board of Regents.

Both the Applied Mathematics and Statistics programs are intended for those students who are interested in pursuing an advanced degree and who have earned the equivalent of a bachelor’s or master’s degree in mathematics, statistics or in other mathematically oriented disciplines. Students who already hold a master’s degree may apply and enter the doctoral program directly. The doctoral programs provide training suitable for employment in academia, industrial research and development organizations, as well as research-oriented government agencies. The master’s degree programs provide training in applications of mathematics and statistics in areas suitable for employment in industry or government agencies. They also can serve as preparatory steps toward advancing to a PhD program.

Please note: Applications for admission should be submitted through the Graduate School’s site at https://gradschool.umbc.edu/ . The department can only process complete applications submitted to that site.

Individuals wishing to benefit from the department’s course offerings without enrolling as degree-seeking students may do so by filing a non-degree seeking student application form. For students who do not already hold an undergraduate degree, a combined BS+MS program leading to a master’s degree in either applied mathematics or statistics is also offered by the department.

Tracks/options toward the MS degree

To serve the students’ varying range of backgrounds and goals, the department has instituted several tracks/options within its master’s degree programs, as listed below. Each track defines a set of well-focused graduation requirements. Students who intend to continue to the doctoral programs should consider the traditional tracks in Applied Mathematics or Statistics. A student whose final goal is a master’s degree in statistics may consider the applications-oriented track in statistics. Most graduate courses are offered in the late afternoon or in the evening to enable the participation of those who hold full-time employment.

• Comprehensive examination option
• Thesis option
• Traditional track with comprehensive examination option
• Traditional track with thesis option
• Applications-oriented track: Environmental Statistics with comprehensive examination option
• Applications-oriented track: Environmental Statistics with thesis option
• Applications-oriented track: Biostatistics with comprehensive examination option
• Applications-oriented track: Biostatistics with thesis option

The comprehensive examination options require taking 30 credits of courses and passing a written comprehensive examination. The thesis options requires taking 24 credits of courses plus 6 credits of master’s thesis research. Please consult the Graduate Catalog for the details.

The PhD degree programs

The department offers doctoral study in a broad spectrum of both classical and modern applied mathematics and statistics. Admission to these programs presupposes a strong background in mathematics and/or statistics. Doctoral students continue with advanced study and dissertation research, with specialization in any of the departmental fields or in an interdisciplinary area.

Particular emphasis is given to the following areas in applied mathematics: differential equations and applications, numerical analysis and scientific computation, dynamical systems, stochastic processes, mathematical biology, optimization theory and algorithms.

In statistics, the areas of emphasis are: Bayesian analysis, biostatistics, data mining, design of experiments, environmental statistics, nonparametric statistics, reliability, spatial statistics and image analysis, statistical decision theory and inference, survival analysis, time series analysis.

A rough outline of the programs’ requirements is:

• Completing the course work;
• Passing the written Master’s comprehensive examination.
• Passing the written PhD qualifying examination;
• Passing the oral PhD qualifying examination;
• Admission to candidacy;
• Completing residency requirements of the university;
• Completing and successfully defending a doctoral dissertation.

Please consult the Graduate Catalog for the details of the requirements.

Policies and Procedures Handbook

The Policies and Procedures handbook describes policies and procedures pertaining to graduate students in the Department of Mathematics and Statistics at UMBC. It adds, expands and clarifies the requirements set forth in the Graduate Catalog, which is the Graduate School’s official manual for UMBC’s graduate students.

The focus of the handbook is on full-time students who receive financial support from the department. Many, but not all, of the policies described here apply to part-time and independently-supported students as well. If in doubt, please consult the Graduate Program Director for clarification.

Samples of Comprehensive Exams

To help students with preparing for the Master’s and PhD Comprehensive Examinations, the department makes available a selection of exams given in the past. These should give you an indication of the level of preparation expected in these exams.

Pre-application form

If you are interested in applying for admission to the graduate program in Applied Mathematics or Statistics, you may want to submit a pre-application form for a no-cost, no-obligation informal feedback about how well your educational background fits the demands of the program.

For further information regarding graduate programs in Applied Mathematics and Statistics please contact:

Dr. Andrei Draganescu Graduate Program Director Program in Applied Mathematics Phone: 410–455–3237 Email: [email protected]

Dr. DoHwan Park Graduate Program Director Program in Statistics Phone: 410–455–2408 Email: [email protected]

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Ph.D. in Statistics

Our doctoral program in statistics gives future researchers preparation to teach and lead in academic and industry careers.

Program Description

Degree type.

approximately 5 years

The relatively new Ph.D. in Statistics strives to be an exemplar of graduate training in statistics. Students are exposed to cutting edge statistical methodology through the modern curriculum and have the opportunity to work with multiple faculty members to take a deeper dive into special topics, gain experience in working in interdisciplinary teams and learn research skills through flexible research electives. Graduates of our program are prepared to be leaders in statistics and machine learning in both academia and industry.

The Ph.D. in Statistics is expected to take approximately five years to complete, and students participate as full-time graduate students.  Some students are able to finish the program in four years, but all admitted students are guaranteed five years of financial support.  

Within our program, students learn from global leaders in statistics and data sciences and have:

20 credits of required courses in statistical theory and methods, computation, and applications

18 credits of research electives working with two or more faculty members, elective coursework (optional), and a guided reading course

Dissertation research

Coursework Timeline

Year 1: focus on core learning.

The first year consists of the core courses:

• SDS 384.2 Mathematical Statistics I
• SDS 383C Statistical Modeling I
• SDS 387 Linear Models
• SDS 384.11 Theoretical Statistics
• SDS 383D Statistical Modeling II
• SDS 386D Monte Carlo Methods

In addition to the core courses, students of the first year are expected to participate in SDS 190 Readings in Statistics. This class focuses on learning how to read scientific papers and how to grasp the main ideas, as well as on practicing presentations and getting familiar with important statistics literature.

At the end of the first year, students are expected to take a written preliminary exam. The examination has two purposes: to assess the student’s strengths and weaknesses and to determine whether the student should continue in the Ph.D. program. The exam covers the core material covered in the core courses and it consists of two parts: a 3-hour closed book in-class portion and a take-home applied statistics component. The in-class portion is scheduled at the end of the Spring Semester after final exams (usually late May). The take-home problem is distributed at the end of the in-class exam, with a due-time 24 hours later. 

Year 2: Transitioning from Student to Researcher

In the second year of the program, students take the following courses totaling 9 credit hours each semester:

• Required: SDS 190 Readings in Statistics (1 credit hour)
• Required: SDS 389/489 Research Elective* (3 or 4 credit hours) in which the student engages in independent research under the guidance of a member of the Statistics Graduate Studies Committee
• One or more elective courses selected from approved electives ; and/or
• One or more sections of SDS 289/389/489 Research Elective* (2 to 4 credit hours) in which the student engages in independent research with a member(s) of the Statistics Graduate Studies Committee OR guided readings/self-study in an area of statistics or machine learning. 
• Internship course (0 or 1 credit hour; for international students to obtain Curricular Practical Training; contact Graduate Coordinator for appropriate course options)
• GRS 097 Teaching Assistant Fundamentals or NSC 088L Introduction to Evidence-Based Teaching (0 credit hours; for TA and AI preparation)

* Research electives allow students to explore different advising possibilities by working for a semester with a particular professor. These projects can also serve as the beginning of a dissertation research path. No more than six credit hours of research electives can be taken with a single faculty member in a semester.

Year 3: Advance to Candidacy

Students are encouraged to attend conferences, give presentations, as well as to develop their dissertation research. At the end of the second year or during their third year, students are expected to present their plan of study for the dissertation in an Oral candidacy exam. During this exam, students should demonstrate their research proficiency to their Ph.D. committee members. Students who successfully complete the candidacy exam can apply for admission to candidacy for the Ph.D. once they have completed their required coursework and satisfied departmental requirements. The steps to advance to candidacy are:

• Discuss potential candidacy exam topics with advisor
• Propose Ph.D. committee: the proposed committee must follow the Graduate School and departmental regulations on committee membership for what will become the Ph.D. Dissertation Committee
•   Application for candidacy

Year 4+: Dissertation Completion and Defense

Students are encouraged to attend conferences, give presentations, as well as to develop their dissertation research. Moreover, they are expected to present part of their work in the framework of the department's Ph.D. poster session.

Students who are admitted to candidacy will be expected to complete and defend their Ph.D. thesis before their Ph.D. committee to be awarded the degree. The final examination, which is oral, is administered only after all coursework, research and dissertation requirements have been fulfilled. It is expected that students will be prepared to defend by the end of their fifth year in the doctoral program.

General Information and Expectations for All Ph.D. students

• 2023-24 Student Handbook
• Annual Review At the end of every year (due May 1), students are expected to fill out the Annual Progress Review . 
• Seminar Series All students are expected to attend the SDS Seminar Series
• SDS 189R Course Description (when taken for internship)
• Internship Course Registration form
• Intel Corporation
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Attending Conferences 

Students are encouraged to attend conferences to share their work. All research-related travel while in student status require prior authorization.

• Request for Travel Authorization (both domestic and international travel)
• Request for Authorization for International Travel  

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College of Engineering and Mathematical Sciences

Department of mathematics & statistics, mathematical science (ph.d).

The Department offers the degree of Doctor of Philosophy in Mathematical Sciences in three areas of concentration: Pure Mathematics, Applied Mathematics, and Statistics. This document focuses on the first two: Pure and Applied Mathematics. A reference to a document on the PhD degree in Statistics is found in the next paragraph. Research interests of the Mathematics faculty include: algebraic geometry, algebraic and computational topology, arithmetic geometry, combinatorics/graph theory, complex systems, computational social science, Fourier/harmonic analysis, logic, mathematical cryptography, network science, number theory, topological data analysis, biomathematics, fluid mechanics, numerical methods for, and analytical theories of, partial differential equations.

The Department also supports Master’s degree programs in Mathematics, Statistics, and Biostatistics as well as Doctoral and Master’s degree programs in Complex Systems and Data

Why choose UVM?

• Our Department is large enough to offer classes and research experiences in a broad range of mathematical subjects, while small enough to give students ample opportunity to interact with our active research faculty. 
• Applied mathematics: complex systems, differential equations, Fourier analysis, mathematical modeling, mathematical biology, numerical analysis,…
• Pure mathematics: algebra, real/complex analysis, combinatorics, cryptography, geometry, number theory, algebraic and computational topology, topological data analysis, …
• We have a regular Department Colloquium and regular seminars, such as the Combinatorics Seminar and the Quebec-Vermont Number Theory Seminar, as well as seminars in related departments, such as complex systems, computer science, engineering, physics and statistics.
• Burlington, Vermont has been ranked as a top college town by the New York Times. Find out more about living in Burlington here .

Admission Requirements

• Bachelor's degree with a major in mathematics or a closely related discipline (e.g., statistics, engineering, or physics, with a substantial mathematics foundation).
• Please review the Application Instructions for graduate admission to UVM. The information listed below supplements some of the general instruction on that page. 
• The is no GRE score requirement. However, if you have taken the GRE test(s), we encourage you to submit your official score(s). 
• Resume/CV is required . 
• No Writing Sample is required. 
• Please try to contain your Statement of Purpose to about 600 words, which is approximately one page. 
• Which of the Department faculty you plan on doing your thesis with (you may include more than one faculty member here), and 
• How your background has prepared you for that.

Your statement about being interested to work with particular faculty member(s) will not constitute a commitment to do so; you will be free to explore the opportunities to work with any of our faculty as your thesis advisor if you join UVM. However, your being specific in your narrative will help the Admissions Committee to select candidates who can best fit into our program.  You may also include any other information about yourself that you consider relevant, such as your teaching and research experience. We encourage you to emphasize specific facts rather than make generic or emotional statements. 

• Please see the link to Application Fee Waiver Requests in Application Instructions by UVM. 
• In addition, the Department of Mathematics & Statistics will provide a very limited number of application fee waivers. To be considered for this highly selective pool of applicants, please send to the Graduate Program Director,  Joan (Rosi) Rosebush ,  the following documents by December 20 as separate pdf files: 
• An unofficial copy of your academic transcript;
• An unofficial copy of your general GRE score (which is not required for fee-paying applicants);
• And a draft of the Statement of Purpose addressing the two requirements listed in its description above. (It does not need to contain anything except your answers to those two questions.);
• International applicants must provide an unofficial copy of their English Proficiency examination. 

Applicants for the Application Fee Waiver by the Department will be notified of the decision by January 15. 

• International students are to satisfy English Proficiency requirements; further information can be found on this webpage . 
• The application deadlines are found on this webpage (click on the link for Mathematical Sciences). 
• Everyone applying for Fall admission will be automatically considered for financial support in the form of Graduate Teaching Assistantship. No financial support is available for Spring admission.  
• All applications must be completed online .

University-wide Requirements for the Doctor of Philosophy degree

UVM requirements for the Doctor of Philosophy Degree

Requirements specific to Doctoral degree in Mathematical Sciences

• A total of at least 75 credit hours as combination of course work and dissertation research;
• Successful completion of two written qualifying examinations;
• A comprehensive examination, consisting of a written and oral presentation, on a topic chosen in consultation with the candidate’s research studies committee;
• >Writing a doctoral dissertation and passing its oral defense.

More information can be found in the Mathematics Graduate Handbook

Graduate Teaching Assistantship and Comprehensive fee

• The majority of Graduate Teaching Assistants (GTA) teach for 9 months (September – May); their stipend is $20,958 for the 2021/22 Academic Year. In exceptional cases, an experienced GTA may be assigned to teach in the Summer, in which case their stipend will be proportionally increased.
• Graduate Teaching Assistantship also covers 9 credit hours of tuition per semester and also the Student Health Insurance premium.
• Information on tuition and fees is found on this website . In particular, all graduate students are required to pay a Mandatory comprehensive fee, which covers access to the UVM gymnasium and medical and mental health services; in the 2022/23 Academic Year it will be $1018 per semester. 

Please email the Mathematics Graduate Director,  Joan (Rosi) Rosebush , if you have any questions or would like further information.

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

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PhD projects

Several School members offer supervision for PhD research projects in the School of Mathematics and Statistics.

Navigate via the tabs below to view project offerings by School members in the areas of Applied Mathematics, Pure Mathematics and Statistics. (This list was updated September 2022.)

Please note that this is not an exhaustive list of all potential projects and supervisors available in the School. 

Information about PhD research offerings and potential supervisors can be found in various locations. It's worth browsing the current research students list to see what research our PhD students are currently working on, and with whom.

There is also a past research students list which provides links to the theses of former students and the names of their supervisors. 

It's also recommended to browse our Staff Directory , where our staff members' names are linked to their research profiles which provide details about their areas of research and often include the topics they are open to supervising students in.

We host PhD information sessions in the School of Mathematics and Statistics twice a year. Keep an eye on our events page for session information. 

• Applied mathematics
• Pure mathematics
• Real world problem solving using dynamical systems, stochastic modelling and queueing theory for stochastic transport and signalling in cells. 
• Real & Computational Algebraic Geometry: Possible subjects include nonnegativity of real polynomials, polynomial system solving, semialgebraic sets, and algorithmic aspects of real algebraic & convex geometry.
• Polynomial & Convex Optimization: Potential topics include convex relaxations, designing algorithms, exploiting structure (e.g. sparsity), and applications in science & engineering.
• Dynamical Systems and Ergodic Theory: Projects that combine techniques from nonlinear dynamics, ergodic theory, functional analysis, differential geometry, or machine learning and can range from pure mathematical theory through to numerical techniques and applications (including ocean/atmosphere/fluids/blood flow), depending on the student.
• Optimisation: Projects are occasionally available in optimisation, mainly using either techniques from mixed integer programming to solve applied problems (e.g. transport, medicine,…) or mathematical problems arising from dynamics.
• Modelling and analysis of ocean biogeochemical cycles including isotope dynamics, inverse modelling of hydrographic data to detect climate-driven circulation changes, and analysis of large-scale ocean transport. PhD students should be highly motivated, have a strong background in applied mathematics and/or theoretical physics, and will have the opportunity to contribute to shaping their project.
• Data-Driven Multi-stage Robust Optimization: The aim of this study is to develop mathematical principles for multi-stage robust optimization problems, which can identify true optimal solutions and can readily be validated by common computer algorithms, to design associated  data-driven numerical methods to locate these solutions and to provide an advanced optimization framework to solve a wide range of real-life optimization models of multi-stage technical decision-making under evolving uncertainty.
• Semi-algebraic Global Optimization: The goal of this study is to examine classes of semi-algebraic global optimization problems, where the constraints are defined by polynomial equations and inequalities. These problems have numerous locally best solutions that are not globally best. We develop mathematical principles and numerical methods which can identify and locate the globally best solutions.
• Detection and cloaking of surface water waves created by submerged objects
• Decomposition of ocean currents into wave-like and eddy-like components
• Theory and application of Quasi-Monte Carlo methods: for high dimensional integration, approximation, and related problems.
• Computational Mathematics: with specialised topics in radial basis functions, random fields, uncertainty quantification, partial differential equations on spheres and manifolds, stochastic partial differential equations. 
• Discrete Integrable Systems: These are birational maps with particularly ordered dynamics and their study is a nice motivation for using algebraic geometry, symmetry, ideal theory and number theory in the study of dynamical systems.
• Arithmetic Dynamics:  This field is the study of iterated rational maps over the integers or rationals or over finite fields, rather than the complex or real numbers. I am particularly interested in how the usual structures present in dynamical systems over the continuum manifest themselves over discrete spaces.
• Convex geometry: Focused on the study of the facial structure of convex sets and the relations between the geometry of convex optimisation problems and performance of numerical methods. The project can be oriented towards convex algebraic geometry, experimental mathematics or classical convex analysis.
• Algebraic and Geometric Aspects of Integrable Systems: The ubiquitous nature of integrable systems is reflected in their (apparent or disguised) presence in a wide range of areas in both mathematics and (mathematical) physics. Projects focus on the algebraic and/or geometric aspects of discrete and/or continuous integrable systems, depending on the individual student's background and preferences. 
• Analysis of multiscale problems in stochastic systems: These projects will involve an analytical study of certain multiscale problems arising in Markov chains and stochastic differential equations. These projects are suited for those interested in both analysis and probability, and will employ tools from differential equations, functional analysis and stochastic processes.
• Numerical methods for sampling constrained distributions: These projects are aimed at sampling problems arising in molecular dynamics. They will deal with designing and analysing numerical schemes to sample constrained probability distributions using stochastic differential equations.  
• Fluid flow in channels with porous walls
• Mathematics education
• Nonlinear differential equations
• Difference equations
• Dynamic equations on time scales
• How many oceans are there? Using novel statistical and machine learning techniques to characterise oceanic zones and provide a blueprint for quantifying the ocean's role in a changing climate.
• How does heat get into the ocean? An investigation of the physical mechanisms that control the ocean's uptake of heat and its effect on climate.
• Making climate models work better: Developing new methods to validate and improve the inner workings of numerical climate models and improve their projections of global warming and its impacts.
• Will it mix? New perspectives on turbulence in rotating fluid flows and how we estimate mixing from observations. 
• Combinatorics
• Graph theory
• Coding theory
• Extremal set theory
• Operator algebras (von Neumann algebras)
• Mathematical physics (quantum field theory)
• Group theory
• Jones subfactor theory
• Vaughan Jones' connection between conformal field theory, Richard Thompson's groups and knot theory.
• Noncommutative algebra
• Algebraic geometry
• Quantum groups/supergroups
• The Schur-Weyl duality
• Representation Theory
• Random graphs
• Asymptotic enumeration
• Randomized combinatorial algorithms

Extremal and probabilistic combinatorics: Possible subjects therein include Ramsey theory, random graphs, positional games and hypergraphs.

• Unlikely Intersection in Number Theory and Diophantine Geometry: These are problems of showing that arithmetic “correlations" between specialisations of algebraic functions are rare unless there is some obvious reason why they happen. These “correlations” may refer to common values or to values factored into essentially the same set of prime ideals and similar. 
• Arithmetic Dynamics: This area is concerned with algebraic and arithmetic aspects of iterations of rational functions over domains of number theoretic interest. 
• Isometries, conformal mappings, and other special mappings on metric Lie groups
• Complex structures on Lie groups and their Lie algebras
• Counting integral and rational solutions to Diophantine equations and congruences. The goal is to obtain upper bounds on the number of integer solutions to some multivariate equations and congruences in variables from a given interval [M, M+N]. Similarly, for rational solutions one restricts both numerators and denominators to certain intervals.
• Kloostermania: Kloosterman and Salie sums and their applications. A classical direction in analytic number theory where the goal is to obtain new bounds on bilinear sums of Kloosterman and Salie sums and apply them to various arithmetic problems, such as the Dirichlet divisor problem in progressions.

Exponential sums and applications. This topic is about understanding the behaviour (e.g. extreme and typical values) of some most important exponential sums, in particular of Weyl sums.  

• Non-commutative functional analysis and its applications to non-commutative geometry, particularly those related to quantised calculus and index theorems.
• Singular (Dixmier) traces and their applications
• Non-commutative integration theory
• Non-commutative probability theory
• Various aspects of Banach space geometry and its applications
• Algebraic geometry (birational geometry and moduli)
• Hodge theory
• Transcendental methods in algebraic geometry 
• Motivic cohomology and algebraic K-theory - an intersection of algebraic geometry and algebraic topology
• Equivariant algebraic topology
• Extreme Value Analysis: Projects available on the modelling of the dependence of multivariate and spatial extremes, spatio-temporal modelling, high-dimensional inference. Interests in environmental/climate applications. 
• Symbolic Data Analysis: Projects available on symbol design, distributional symbols and others. Applications in big and complex data analysis.
• Ancient river systems and landscape dynamics with Bayeslands framework
• Bayesian inference and machine learning for reef modelling 
• Deep learning for the reconstruction of 3D ore-bodies for mineral exploration 
• Bayesian deep learning for protein function detection  
• COVID-19 modelling with deep learning
• Variational Bayes for surrogate assisted deep learning
• Bayesian deep learning for incomplete information
• Computational Statistics
• Event sequence data analysis
• Hidden Markov Models and State-Space Models and their inference and applications
• Financial data analysis and modelling
• Point processes and their inference and applications
• Semi- and non-parametric inference
• Bayesian statistical inference
• Computational statistics and algorithms
• Approximate Bayesian inference
• Quantile regression method
• Statistical text analyses
• Applications to climate science, social science, image analyses

*Yanan Fan is an Adjunct A/Prof in the School and is able to co-supervise students (not as primary supervisor)

• Nonparametric and semiparametric statistics: Nonparametric dependence modelling (copulas) and nonparametric functional data analysis.
• Social network analysis for epidemiology, social sciences, defence, national security, and other areas
• Statistical models for dependent categorical data
• Survey sampling (design and inference), particularly for network data
• Statistical computing, particularly MCMC-based methods
• Dependence measures
• Complex-valued random variables
• Goodness-of-fit tests
• Machine learning (with potential applications in medical imaging)
• Time series analysis
• Real-time analytics with the Raspberry Pi
• For some examples of my current projects, have a look at my  personal webpage .
• Fast and efficient model selection for high-dimensional data
• Development of efficient estimation and sampling algorithms for random graphs and spatial point processes
• Development of model compression methods for deep neural networks.

Topics include regression to the mean, interrupted time series, meta-analysis, and population attributable fractions.

Monte Carlo and Uncertainty Quantification 

• Projects on the stochastic analysis and development of modern Monte Carlo methods for uncertainty quantification, sequential Bayesian inference, high dimensional sampling, particle based Variational Inference (knowledge/experience with stochastic analysis and SDE & PDE theory highly desired).

Machine learning and generative modelling 

• Projects with a focus on (but not restricted to) medical imaging and machine learning methods for uncertainty quantification of image segmentation
• Theoretical analysis of modern machine learning methods (knowledge/experience with functional and stochastic analysis highly desired).

Mathematics of sustainability 

• Projects on stochastic games, agent based models, network science and their applications in sustainability science.
• Automating data analyses via natural language queries
• Bayesian statistics, algorithms and applications
• Building software tools, services and packages
• Data privacy and synthetic data
• Data science, theory and application
• Defence applications (nationality restrictions may apply)
• Extreme value theory and applications
• Machine learning 
• Symbolic data analysis
• Developing statistical methods for point processes
• Financial data modeling
• Computational statistics
• Analysis of capture-recapture data
• Estimation of animal abundance
• Measurement error modelling
• Model selection for multivariate data
• Non-parametric smoothing
• Statistical ecology
• High-dimensional data analysis
• Simulation-based inference
• Eco-Stats project ideas

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College of Liberal Arts and Sciences

Department of Statistics

Yu-bo wang ’16 phd has been promoted to associate professor at clemson university..

Yu-Bo Wang ’16 PhD has been promoted to Associate Professor at Clemson University. He was also chosen as the recipient of the School of Mathematical and Statistical Sciences Teaching Award for 2023-2024.

Mathematics, PHD

On this page:, at a glance: program details.

• Location: Tempe campus
• Second Language Requirement: No

Program Description

Degree Awarded: PHD Mathematics

The PhD program in mathematics is intended for students with exceptional mathematical ability. The program emphasizes a solid mathematical foundation and promotes innovative scholarship in mathematics and its many related disciplines.

The School of Mathematical and Statistical Sciences has very active research groups in analysis, number theory, geometry and discrete mathematics.

Degree Requirements

84 credit hours, a written comprehensive exam, a prospectus and a dissertation

Required Core (3 credit hours) MAT 501 Geometry and Topology of Manifolds I (3) or MAT 516 Graph Theory I (3) or MAT 543 Abstract Algebra I (3) or MAT 570 Real Analysis I (3)

Other Requirements (3 credit hours) MAT 591 Seminar (3)

Electives (24-39 credit hours)

Research (27-42 credit hours) MAT 792 Research

Culminating Experience (12 credit hours) MAT 799 Dissertation (12)

Additional Curriculum Information Electives are to be chosen from math or related area courses approved by the student's supervisory committee.

Students must pass:

• two qualifying examinations
• a written comprehensive examination
• an oral dissertation prospectus defense

Students should see the department website for examination information.

Each student must write a dissertation and defend it orally in front of five dissertation committee members.

Admission Requirements

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics or a closely related area from a regionally accredited institution.

Applicants must have a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in the last 60 hours of their first bachelor's degree program or a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in an applicable master's degree program.

All applicants must submit:

• graduate admission application and application fee
• official transcripts
• statement of education and career goals
• three letters of recommendation
• proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

Additional eligibility requirements include competitiveness in an applicant pool as evidenced by coursework in linear algebra (equivalent to ASU course MAT 342 or MAT 343) and advanced calculus (equivalent to ASU course MAT 371), and it is desirable that applicants have scientific programming skills.

Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, application deadlines, learning outcomes.

• Address an original research question in mathematics.
• Able to complete original research in theoretical mathematics.
• Apply advanced mathematical skills in coursework and research.

Career Opportunities

Graduates of the doctoral program in mathematics possess sophisticated mathematical skills required for careers in many different sectors, including education, industry and government. Potential career opportunities include:

• faculty-track academic
• finance and investment analyst
• mathematician
• mathematics professor, instructor or researcher
• operations research analyst
• statistician

Program Contact Information

If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below.

• [email protected]
• 480/965-3951