数学哲学博士

授予博士学位的不仅在于完成规定的学习课程，还在于清楚地证明其学术成就和数学方面的原始研究能力。博士生可以计划传统的数学学习计划（数学方向）或面向应用数学的学习计划（应用数学方向）。无论哪种情况，每个学生都必须修满36个学分的获批课程，平均成绩为B或更高。根据研究生委员会的决定，对于进入与我们的课程兼容的数学课程的硕士学位的学生，此要求减少到18个学时的认可课程。传统数学课程的学生必须证明自己对代数，分析（实际和复杂）和拓扑的基本概念和技术。这包括参加三个基本领域的所有课程，并成功完成代数和分析的资格考试。
Master the world’s universal language—and be prepared to teach it—with a PhD in Mathematics from Case Western Reserve University. In our program, you’ll expand your knowledge of core topics including measure theory and homological algebra—and you’ll come away prepared to work in fields directly related to your doctoral training. Many of our graduates enter careers in academia, while others go on to work in industry or government roles. A doctoral student in the mathematics track must take written examinations on abstract algebra and real analysis, as well as an oral examination in his or her chosen area of specialization. Subjects include complex analysis, control and calculus of variations, differential equations, dynamical systems, functional analysis, geometry, probability, and topology. 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.