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Doctor of Philosophy in Mathematics- Combinatorics
在史丹佛大學
關於課程
Combinatorics concerns the study of discrete objects. It has applications to diverse areas of mathematics and science, and has played a particularly important role in the development of computer science. While it is arguably as old as counting, combinatorics has grown remarkably in the past half century alongside the rise of computers. It borrows tools from diverse areas of mathematics. Examples include the probabilistic method, which was pioneered by Paul Erdös and uses probability to prove the existence of combinatorial structures with interesting properties, algebraic methods such as in the use of algebraic geometry to solve problems in discrete geometry and extremal graph theory, and topological methods beginning with Lovász’ proof of the Kneser conjecture. A notable application in number theory is in the proof of the Green-Tao theorem that there are arbitrarily long arithmetic progressions of primes. The Stanford Mathematics department is a leader in combinatorics, with particular strengths in probabilistic combinatorics, extremal combinatorics, algebraic combinatorics, additive combinatorics, combinatorial geometry, and applications to computer science.
開始日期及學費
如何申請
Entry requirements for 史丹佛大學
Minimum TOEFL Requirements ibt/pbt: 100/600.
Applicants from institutions outside the U.S. must hold the equivalent of a U.S. bachelor?s degree from a college or university of recognized standing.
GRE General Test Scores (No longer required or accepted as part of the application)
GRE Mathematics Subject Test Score (Not required or accepted for applicants to Autumn 2022)
Official transcripts (If you are offered admission to Stanford and accept the offer, you will be required to submit official transcripts at that time.)
Statement of Purpose (document uploaded to online application)
Soft copy of transcripts/academic records (document(s) uploaded to online application)
Names and contact information of your recommenders, minimum of 3, maximum of 6 (Your recommenders will receive an email with instructions for submitting their letters online.) Ask your recommenders to submit their letters by the application deadline.
4.) Arrange for your official transcripts/academic records from each institution listed in your online application to be sent by the institution(s) to the Department of Mathematics.
English language requirements
托福(TOEFL iBT)總分: 100.0
最後申請期限:
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