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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 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.
Programme 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 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.
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
Domestic
0 USD
International
0 USD
Scholarships
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Doctor of Philosophy (Ph.D.) in Mathematics
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48 monthsProgramme duration
MathematicsMain Subject Area
Programme overview
Main Subject
Mathematics
Study Level
PHD
Programme overview
Main Subject
Mathematics
Study Level
PHD
Admission Requirements
Domestic
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.
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How to get a full scholarship
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