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You can complete your PhD in just five years, taking classes on topics such as algebraic topology, differential geometry, convexity and optimization, and high-dimensional probability. 365betÌåÓýÔÚÏßÊÀ½ç±­ Case Western Reserve, one of the top research universities in the U.S., you’ll work alongside our renowned faculty who conduct research on algebraic and differential geometry, analysis, category theory, convexity, probability and many other areas.

As a part of your program, you’ll take written examinations on abstract algebra and real analysis, as well as an oral examination in your chosen area of specialization. Possible subject areas include complex analysis, control and calculus variations, differential equations, dynamical systems, functional analysis, geometry (algebraic, differential, or tropical), and persistent homology.

Our program thrives when we have students with diverse perspectives and a range of educational, professional and life experiences. We look forward to learning more about you!
The application process requires:

• , including a statement of purpose and personal statement
• $50 application fee
• Bachelor’s from an accredited institution (either already complete, or will be complete before you enroll)
• Unofficial transcripts
• Current resume/CV
• Three letters of recommendation
• Test scores for GRE (general) and GRE (math) are optional but preferred
• International applicants: Results of TOEFL, IELTS or PTE