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Fields include real analysis, complex analysis, functional analysis, classical and modern harmonic analysis; linear and nonlinear partial differential equations; dynamical systems and ergodic theory; geometric analysis; kleinian groups, low dimensional... Read more topology and geometry; differential geometry; finite and infinite groups; geometric group theory; finite and infinite dimensional Lie algebras, Lie groups, and discrete subgroups; representation theory; auto orphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; numerical analysis; combinatory and discrete mathematics. All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) pass qualifying examinations on their general mathematical knowledge; (3) submit a dissertation prospectus; (4) participate in the instruction of undergraduates; (5) be in residence for at least three years; and (6) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Doctor of Philosophy (Ph.D.) program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)?(5) and obtaining an adviser.Read less
Program overview
Main Subject
Mathematics
Study Level
PHD
Fields include real analysis, complex analysis, functional analysis, classical and modern harmonic analysis; linear and nonlinear partial differential equations; dynamical systems and ergodic theory; geometric analysis; kleinian groups, low dimensional... Read more topology and geometry; differential geometry; finite and infinite groups; geometric group theory; finite and infinite dimensional Lie algebras, Lie groups, and discrete subgroups; representation theory; auto orphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; numerical analysis; combinatory and discrete mathematics. All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) pass qualifying examinations on their general mathematical knowledge; (3) submit a dissertation prospectus; (4) participate in the instruction of undergraduates; (5) be in residence for at least three years; and (6) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Doctor of Philosophy (Ph.D.) program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)?(5) and obtaining an adviser.Read less
Admission Requirements
7+
A Bachelor's degree (or equivalent) prior to matriculation at Yale. Other English language Requirements: Yale?s most competitive applicants will have TOEFL scores of at least the following, 600 on the paper-based TOEFL, 250 on the computer-based TOEFL.
Jan-2000
Tuition fees
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0 USD
International
0 USD
Scholarships
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Doctor of Philosophy (Ph.D.) in Mathematics
# 29QS Subject Rankings
48 monthsProgram duration
MathematicsMain Subject Area
Program overview
Main Subject
Mathematics
Study Level
PHD
Read more topology and geometry; differential geometry; finite and infinite groups; geometric group theory; finite and infinite dimensional Lie algebras, Lie groups, and discrete subgroups; representation theory; auto orphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; numerical analysis; combinatory and discrete mathematics. All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) pass qualifying examinations on their general mathematical knowledge; (3) submit a dissertation prospectus; (4) participate in the instruction of undergraduates; (5) be in residence for at least three years; and (6) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Doctor of Philosophy (Ph.D.) program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)?(5) and obtaining an adviser. Read less
Program overview
Main Subject
Mathematics
Study Level
PHD
Read more topology and geometry; differential geometry; finite and infinite groups; geometric group theory; finite and infinite dimensional Lie algebras, Lie groups, and discrete subgroups; representation theory; auto orphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; numerical analysis; combinatory and discrete mathematics. All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) pass qualifying examinations on their general mathematical knowledge; (3) submit a dissertation prospectus; (4) participate in the instruction of undergraduates; (5) be in residence for at least three years; and (6) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Doctor of Philosophy (Ph.D.) program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first two years. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)?(5) and obtaining an adviser. Read less
Admission Requirements
Tuition fees
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International
Scholarships
Selecting the right scholarship can be a daunting process. With countless options available, students often find themselves overwhelmed and confused. The decision can be especially stressful for those facing financial constraints or pursuing specific academic or career goals.
To help students navigate this challenging process, we recommend the following articles:
How to get a full scholarship
Looking for a fully-funded scholarship to see you into university? Find out how to boost your chances of getting one.
Scholarships to study abroad
Find scholarships to study abroad with our lists of international scholarships – categorized by country, by subject, and by type of student.
Scholarship Applications: Frequently Asked Questions
Get answers to all your questions about scholarship applications, including tips on how to find scholarships and chances of success.
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