Author | Title | |
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Michael Dunphy | |
Peter Stechlinski | |
Colin Phipps | |
Andree Susanto | |
Derek Steinmoeller | |
Venkata Manem | |
Alex Shum | |
PhD Theses 2013
Author | Title | |
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József Vass | |
Andrijana Burazin | |
Nancy Soontiens | |
Amenda Chow | |
Rasha Al Jamal | |
Wentao Liu | |
Minghua Lin | |
Killian Miller | |
PhD Theses 2012
Author | Title | |
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Rahul Rahul | |
Ruibin Qin | |
Dominique Brunet | |
Yasunori Aoki | |
Easwar Magesan | |
Christopher Ferrie | |
Dhanaraja Kasinathan | |
Wai Man NG | |
Matthew Johnston | |
PhD Theses 2011
Author | Title | |
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Raluca Jessop | |
Yufang Hao | |
Mohamad Alwan | |
Yanwei Wang | |
Christopher Subich | |
Timothy Rees | |
Volodymyr Gerasik | |
PhD Theses 2010
Author | Title | |
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Jun Liu | |
Kathleen Wilkie | |
Sean Speziale | |
Nataliya Portman | |
PhD Theses 2009
Author | Title | |
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Rudy Gunawan | |
Gibin George Powathil | |
Matthew Calder | |
PhD Theses 2008
Author | Title | |
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Gregory Mayer | |
Cedric Beny | |
Lijun Wang | |
Kahrizsangi Ebrahimi | |
Robert Martin | |
PhD Theses 2007
Author | Title | |
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Shannon Kennedy | |
Alexander Korobov | |
Qing Wang | |
Duncan Mowbray | |
Donald Campbell | |
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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Doctor of Philosophy in Mathematics
Department of Mathematics
Program Requirements | |
Select eight graduate-level subjects in Mathematics | 96 |
| Classroom Teaching in Mathematics | 12 |
| Graduate Thesis | 288-360 |
Total Units | 396-468 |
Note: Students in this program can choose to receive the Doctor of Philosophy or the Doctor of Science in Mathematics. Students receiving veterans benefits must select the degree they wish to receive prior to program certification with the Veterans Administration.
| . Either Internship in Mathematics or Research in Mathematics can be counted as one class toward this requirement but can only be taken once. |
| |
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The PDF includes all information on this page and its related tabs. Subject (course) information includes any changes approved for the current academic year.
PhD Applied Mathematics Research project proposal - Gianpiero Negri
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PhD Qualifying Exams
The requirements for the PhD program in Mathematics have changed for students who enter the program starting in Autumn 2023 and later.
Requirements for the Qualifying Exams
Students who entered the program prior to autumn 2023.
To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis.
Students who entered the program in Autumn 2023 or later
To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas:
- real analysis
- geometry and topology
- applied mathematics
The exams each consist of two parts. Students are given three hours for each part.
Topics Covered on the Exams:
- Algebra Syllabus
- Real Analysis Syllabus
- Geometry and Topology Syllabus
- Applied Mathematics Syllabus
Check out some Past and Practice Qualifying Exams to assist your studying.
Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the autumn. If they pass either or both of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.
Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn.
Students who started in Autumn 2023 and later
Students must choose and pass two out of the four qualifying exams by the autumn of their second year. Students take courses in algebra, real analysis, geometry and topology, and applied math in the autumn and winter quarters of their first year to prepare them for the exams. The exams are taken during the first week of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn.
Exam Schedule
Unless otherwise noted, the exams will be held each year according to the following schedule:
Autumn Quarter: The exams are held during the week prior to the first week of the quarter. Spring Quarter: The exams are held during the first week of the quarter.
The exams are held over two three-hour blocks. The morning block is 9:30am-12:30pm and the afternoon block is 2:00-5:00pm.
For the start date of the current or future years’ quarters please see the Academic Calendar
Upcoming Exam Dates
Autumn 2024.
Tuesday, September 17: Applied Math , Room 384I and Algebra , Room 384H
Wednesday, September 18: Real Analysis , Room 384H
Thursday, September 19: Geometry and Topology , Room 384H
Book series
Graduate Texts in Mathematics
About this book series.
- Patricia Hersh,
- Ravi Vakil,
- Jared Wunsch
Book titles in this series
Graph theory.
- Reinhard Diestel
- Copyright: 2025
Available Renditions
A Course in Real Algebraic Geometry
Positivity and Sums of Squares
- Claus Scheiderer
- Copyright: 2024
Fundamentals of Fourier Analysis
More Explorations in Complex Functions
- Richard Beals
- Roderick S.C. Wong
- Copyright: 2023
Random Walks on Infinite Groups
Publish with us
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Department of Mathematics
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PhD in Mathematics
The doctoral program in the Department of Mathematics offers the personalized attention of a small department while also providing a wide range of faculty who offer expertise to support dissertation research. The graduate student environment in the department is collaborative and rigorous, with many opportunities for mentorship, peer interaction and interdisciplinary opportunities across and outside the university.
PhD graduates go on to work as policy makers, consultants, data analysts, professors, researchers at internationally renowned institutions and much more.
Prospective Students
Apply to GW
Request More Information
Current Students
CCAS Doctoral Student Handbook
Graduate Student Resources
Teaching Assistantships and Funding
Full-time PhD students in mathematics are supported primarily through teaching assistantship (TA) positions. Students making acceptable progress in the PhD program are normally funded for at least five (and sometimes six) years.
While teaching assistant (TA) positions are usually offered to PhD students, master’s and part-time students are also invited to apply through the Office of Graduate Student Assistantships and Fellowships website .
- A stipend in the form of a GW fellowship
- Tuition credits (up to nine credit hours per semester)
- A salary in exchange for teaching work
PhD students apply for teaching assistantships as part of the general GW application process. Applications to the doctoral program completed before February 1 will receive full consideration for TA positions.
The duties of TAs may include teaching a course, conducting recitations, assisting in a computer lab, holding office hours, grading homework and proctoring and grading exams. Such duties typically take about 15 hours per week.
The graduate committee, in consultation with students' advisors, makes recommendations to CCAS for renewal of support; these recommendations are subject to the approval of the CCAS Associate Dean for Graduate Studies. Students making good progress toward earning a PhD and performing their teaching duties well usually receive at least five years of support. Requests for a sixth year of funding can be made when there is good evidence that the student is likely to complete the degree in the sixth year.
Several activities for new graduate students are held the week before the fall semester begins:
- a Graduate Teaching Assistant Program (GTAP) orientation organized by the GW Office of Graduate Student Assistantships and Fellowships ;
- an English test and interview for international students; and
- an orientation for mathematics graduate students, organized by the Department of Mathematics.
At the GTAP orientation, each new TA gives a five-minute sample presentation to a small group of peers and is evaluated for effective communication. All students, especially international students, are encouraged to discuss their presentation in advance with their academic advisor.
"I owe my success to my beginning days in the U.S. — to all the wonderful professors at GW. If not for their constant support, I would not have completed my PhD and all this would be moot!"
Sita Ramamurti PhD '95, 2020 Leo Schubert Teaching Award
Course Requirements
The following requirements must be fulfilled:
The general requirements stated under Columbian College of Arts and Sciences, Graduate Programs .
The requirements for the Doctor of Philosophy Program .
Pre-candidacy
Pre-candidacy requirements include satisfactory completion of 48 credits of coursework and achievement of a passing grade in the general examination.
After completing 36 credits of coursework, students may petition the graduate committee for approval to take MATH 6995 , but students may take no more than 12 credits in any combination of MATH 6995 and MATH 8999 in a single academic year.
Students wishing to take courses outside the department must petition and obtain the approval of the graduate committee. The committee may limit the number of such courses that students take.
Subject to the approval of the graduate committee (requested via petition), students may take up to 12 credits of courses offered by other institutions in the Consortium of Universities of the Washington Metropolitan Area . Students wishing to take such courses must petition and obtain the approval of the graduate committee.
Subject to the approval of the graduate committee (requested via petition) and the agreement of the instructor, students may take up to 12 credits from the following upper-level undergraduate courses for graduate credit, provided that additional graduate-level coursework is completed in these classes.
Course List Code | Title | Credits |
MATH 3613 | Introduction to Combinatorics | |
MATH 3632 | Introduction to Graph Theory | |
MATH 3710 | Introduction to Mathematical Logic | |
MATH 3720 | Axiomatic Set Theory | |
MATH 3730 | Computability Theory | |
MATH 3740 | Computational Complexity | |
MATH 3848 | Differential Geometry | |
MATH 4239 | Real Analysis I | |
MATH 4240 | Real Analysis II | |
MATH 4981 | Seminar: Topics in Mathematics | |
General examination
The general examination consists of two preliminary examinations. One examination is in two to four subjects selected from algebra, analysis, topology, and applied math, and the other is a specialty examination in a research area approved by the department.
Post-candidacy requirements
Post-candidacy requirements include the successful completion of an additional 24 credits of graduate coursework, including at least 6 credits of MATH 8999 ; the completion of the dissertation; and the successful defense of the dissertation in a final oral examination.
No more than 15 credits in any combination of MATH 6995 and MATH 8999 may be among the student's final 18 credits of required coursework.
Once a student successfully completes 24 post-candidacy credits, they must register for 1 credit of CCAS 0940 each subsequent fall and spring semester until they have successfully defended their dissertation, thereby completing the degree program.
Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.
Learn more about Harvard’s Math community and our statement on diversity and inclusion.
The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers diversity resources and student affinity groups for graduate students.
The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.
open. The application deadline is December 15, 2021. -->
The pure math PhD admissions application is open. The application submission deadline is December 15, 2024.
For information on admissions and financial support , please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.
Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.
Note for Harvard College Undergraduates
Since it is better for a student’s mathematical development to learn mathematics at different institutions so as to be exposed to a broader range of mathematical perspectives, ordinarily applications for the mathematics PhD program from Harvard College undergraduates are not considered. If exceptional circumstances warrant an application from a Harvard undergraduate, an advisor or mentor of that student should seek approval from the Director of Graduate Studies before the student submits an application.
IMAGES
VIDEO
COMMENTS
Mathematics PhD theses. A selection of Mathematics PhD thesis titles is listed below, some of which are available online: ... (PDF-29.1MbB) G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB) 2008. C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.
UNIVERSITÀ DEGLI STUDI DI MILANO DEPARTMENT OF MATHEMATICS PhD Thesis in Mathematics On the p-Laplace operator on Riemannian manifolds Date: 27th January, 2014 Author: Daniele Valtorta ID number R08513 e-mail:[email protected] Supervisor: Alberto Giulio Setti This thesis is available onarXiv arXiv:1212.3422v3 [math.DG] 24 Jan 2014
pdf. bio-mathematics: introduction to the mathematical model of the hepatitis c virus, lucille j. durfee. pdf. analysis and synthesis of the literature regarding active and direct instruction and their promotion of flexible thinking in mathematics, genelle elizabeth gonzalez. pdf.
graduate,I wasthe leastexperienced with the material,but I alsohad lessexperience organizing my talks, presentingeffectivel y,andaddressingquestions. I wasable to learnfrom people who werealmost exactly whereI wantedto bein two,four, or sixyears.Their specific topics were extremely engaging, and indicated
graduate students at the University of Illinois at Urbana-Champaign, pri-marily physics students but also some from other branches of the physical sciences. The courses aim to introduce students to some of the mathematical methods and concepts that they will nd useful in their research. We have
Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ...
Ph.D. THESIS MATHEMATICS A STUDY ON CYCLES IN GRAPHS Thesis submitted to the UNIVERSITY OF CALICUT for the award of the Degree of DOCTOR OF PHILOSOPHY in MATHEMATICS under the Faculty of Science by ANNIE SABITHA PAUL under the guidance of Prof.(Dr.) RAJI PILAKKAT Department of Mathematics, University of Calicut Kerala, India 673 635. October 2021
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid. PhD Theses 2022. Author. Title. James Petrie. Decentralized contact tracing protocols and a risk analysis approach to pandemic control. Yiming Meng. Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties.
The Mathematics PhD program consists of at least 75 credit hours of course work beyond the bachelor's degree, of which a minimum of 39 hours of formal course work, exclusive of independent study, and 15 credit hours of dissertation research (7980) are required. The program requires 18 credit hours of core courses, and 6 to 12
Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact. Digital Accessibility. Legacy Department of Mathematics Website. Associated Center.
9. Total Credits: 18. Year 1 courses will train students to develop a common solid foundation on basic graduate mathematics. The Ph.D. student is required to pass all 6 courses, and to pass qualifying exams in Algebra and Real Analysis. The qualifying exams will be given in May of each year, shortly after finals week.
Mathematics research is fun, engaging, di cult, frustrating, and di erent than most 9-5 jobs. This article is meant to provide some tips on making the major transition from mathematics student to independent researcher. Imagine you are a graduate student in a math Ph.D. program and you have just nished your qualifying exams.
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 ...
5000-Level Mathematics Courses (21+ hours) In addition to MATH 5624 & 5634, PhD students must complete at least 21 credit hours of 5000-level mathematics courses. MATH 4225 & 4226 (Abstract Algebra), 4124 (Real Analysis), and 4445 (Numerical Analysis) should be taken if not in the student's background.
undergraduate and graduate programs offered by the College of Science and the other colleges of RIT in providing and discovering new knowledge. A new Ph.D. program would create an infusion of new research projects and research teams from across many fields. Because mathematics is so central to many other disciplines, the proposed
Graduate Thesis 2. 288-360. Total Units. 396-468. Note: Students in this program can choose to receive the Doctor of Philosophy or the Doctor of Science in Mathematics. Students receiving veterans benefits must select the degree they wish to receive prior to program certification with the Veterans Administration. 1. Select subjects in Mathematics.
Abstract. PhD in Applied Mathematics - Research Proposal Scope of the research project: development of a game theory-based mathematical model for an autonomous machine decision-making system, with ...
Eva Thanheiser Director, Ph.D. Program in Mathematics Education Fariborz Maseeh Hall Room 468-E [email protected]. Sean Larsen Faculty (Ph.D. Program Committee Member) Fariborz Maseeh Hall Room 464-K [email protected]. Steven Boyce Faculty (Ph.D. Program Committee Member) Fariborz Maseeh Hall Room 468-J [email protected].
Graduate Programs and Fellowships in Mathematics If exploring mathematics is your life's calling, then a graduate Ph. D. program in mathematics is your next step towards that end. This document is meant as a primer for applying to these programs. The topics covered are: o CHOOSING THE RIGHT PH.D. PROGRAM o THE ADMISSIONS PROCESS
Students who entered the program in Autumn 2023 or later. To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: algebra. real analysis. geometry and topology. applied mathematics. The exams each consist of two parts. Students are given three hours for each part.
Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.
an orientation for mathematics graduate students, organized by the Department of Mathematics. At the GTAP orientation, each new TA gives a five-minute sample presentation to a small group of peers and is evaluated for effective communication. All students, especially international students, are encouraged to discuss their presentation in ...
The pure math PhD admissions application is open. The application submission deadline is December 15, 2024. For information on admissions and financial support, please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.. Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. . Applicants can determine eligibility for ...