Santa Barbara,
CA,
United States
Type
Public
Degrees offered
Bachelor's Degree
PhD in Mathematics - Number Theory in Santa Barbara United States | University of California, Santa Barbara
University of California, Santa Barbara
|
Santa Barbara United States
Visit institution website
for more information
Qualification
Doctor of Philosophy
Languages
English
Delivery Mode
On-Campus
Tuition (2025)
USD
29,118
Attendance
Full-time
Full-time Duration
48 months
Number theory is filled with problems that are simple to formulate but notoriously hard to crack. Take Fermat's Last Theorem, proposed by Pierre de Fermat roughly 350 years ago. Proving this theorem stumped generations of mathematicians, who nevertheless advanced number theory through innovations like elliptic curve theory over finite fields. It wasn't until 1995 that Andrew Wiles published his groundbreaking proof in the Annals of Mathematics.
Another celebrated number theory puzzle is the Riemann hypothesis, which explores characteristics of the Riemann zeta function—a key player in understanding prime number distribution. Despite being over a century old, this problem remains unsolved, with the Clay Mathematics Institute even offering a $1 million reward for its resolution.
The Goldbach conjecture represents yet another enduring mystery, asserting that every even whole number can be expressed as the sum of two primes. While its statement requires only basic mathematical knowledge, this conjecture has withstood attempts by numerous mathematicians to prove it.
Destination of Study
Subjects of Study
Language Requirements
English
IELTS 7.0
Qualification Requirements
To be considered for admission to UCSB, applicants must have received a bachelor's degree or its equivalent (with a cumulative grade point average of 3.0 or better) from an accredited university prior to the quarter for which admission is sought.
completed an undergraduate or graduate degree at an institution whose primary language of instruction is English. The minimum score for consideration is 550 when taking the paper-based TOEFL, or 80 when taking the internet-based test, some departments require a higher score. Applicants must make arrangements to take the TOEFL directly with ETS (www.ets.org). Scores should be reported to UCSB using institution code 4835. TOEFL scores must be no more than two years old at the time of application submission. UCSB also considers a minimal score of 7 on the IELTS as an alternative to the TOEFL. IELTS scores must be no more than two years old at the time of application submission.
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.
completed an undergraduate or graduate degree at an institution whose primary language of instruction is English. The minimum score for consideration is 550 when taking the paper-based TOEFL, or 80 when taking the internet-based test, some departments require a higher score. Applicants must make arrangements to take the TOEFL directly with ETS (www.ets.org). Scores should be reported to UCSB using institution code 4835. TOEFL scores must be no more than two years old at the time of application submission. UCSB also considers a minimal score of 7 on the IELTS as an alternative to the TOEFL. IELTS scores must be no more than two years old at the time of application submission.
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