PhD in Mathematics - Analysis in Santa Barbara United States | University of California, Santa Barbara

University of California, Santa Barbara | Santa Barbara United States
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Qualification
Doctor of Philosophy
Languages
English
Delivery Mode
On-Campus
Tuition (2025)
USD 29,118
Attendance
Full-time
Full-time Duration
48 months

Mathematical Analysis first emerged from the need to study geometric shapes and physical motion through infinitesimal methods. Following the remarkable achievements of differential and integral calculus, mathematicians recognized that examining collections of functions rather than individual ones provided deeper insights and extended classical theories. This realization gave rise to Functional Analysis approximately a hundred years ago, profoundly impacting various branches of modern mathematics and yielding significant applications across scientific disciplines.

Our department's analysts specialize exclusively in functional analysis. Their research focuses on infinite-dimensional spaces involving functions, operators, representations, and dynamical systems. Key pursuits include solving equations, optimizing functionals, and investigating operator algebras. Their work finds diverse applications ranging from traditional continuum mechanics and information theory to contemporary fields like image processing, knot theory, and quantum computation. Throughout the year, the department hosts multiple research seminars on these topics, which draw both graduate students and renowned visiting scholars.


Destination of Study

Subjects of Study

Language Requirements

English
IELTS 7.0

Qualification Requirements

Applicants who have conducted their post-secondary education outside of the United States must have completed an undergraduate degree program equivalent to a University of California bachelor's degree by the beginning of their graduate program at UCSB. Equivalent undergraduate degrees usually include a minimum four years of university work and above-average scholarship. The degree must be awarded by an accredited institution. To be considered for admission, you must have received a bachelor's degree or its equivalent from an accredited university prior to the quarter for which you seek admission, and have at least a B average (3.0 GPA) in your undergraduate coursework. Satisfaction of minimal standards does not, however, guarantee admission, since the number of qualified applicants far exceeds the number of spaces available. An excellent command of written and spoken English is required prior to enrollment at UCSB. Applicants whose native language is not English are required to take the Test of English as a Foreign Language (TOEFL), the International English Language Testing System (IELTS), or the Duolingo English Test (DET). TOEFL paper-based test (PBT) 550, TOEFL internet-based test (iBT) and TOEFL iBT Home Edition 80, IELTS Academic and IELTS Indicator - Overall Band Score of 7.

Tuition USD 29,118

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