Graduate Study in the Department of Mathematics at Case Western Reserve University
Doctoral Program Review
The Department of Mathematics at Case Western Reserve University seeks to broaden and deepen the graduate studentsí understanding of mathematics and its applications and to promote research in its foundations or its applications. The need to master the subtleties of the mathematical formalism is tantamount to learning the grammar and vocabulary of a language: however tedious and demanding this task might be, it is absolutely necessary to advance to more creative and innovative ventures. The core courses of our graduate program ensure that the student is knowledgeable of the mathematical techniques that will be needed to pursue advanced research. In the Department of Mathematics at CWRU there are two strong nuclei of research, in pure and in applied mathematics. The two tracks of the graduate program, which offer separate degrees in Mathematics and in Applied Mathematics, reflect the strength of the research of the Faculty. The cores of the two programs have been designed so that graduate students master the foundations which are most appropriate for the line of research that they intend to pursue. The blend of pure and applied mathematics in the research of the faculty is reflected in the soft boundaries in the graduate programs, which allow students in pure mathematics to take classes in applied mathematics and vice versa.†
Although the relatively small size of the Department does not support cutting edge research in all areas of pure and applied mathematics, the breadth of the graduate courses provides students with a good foundation. The research areas where faculty are most active are reflected in a higher density of advanced courses and active seminars and colloquia. Throughout their graduate career, students interact with faculty and students in all disciplines within the Department, as well as outside the Department.† Since teaching is an important part of the graduate education of doctoral students who might consider looking for an academic position, all students in the Ph.D. program must take a course on teaching and gain some classroom experience, under the supervision of faculty.
Active research areas in pure mathematics include analysis, dynamical systems, geometry and probability.† The research direction with the highest concentration of faculty straddles the border between analysis and probability. It includes the study of high dimensional phenomena with links to computer science, mathematical physics and other mathematical sciences. Faculty in this area attract considerable external funding, in particular an NSF funded Focused Research Group initiative (engaging five other institutions), which provides educational, research and travel opportunities for graduate students. Another active area is geometry. It is expected that pending and planned hires will add further breadth to the faculty.
The research in applied mathematics is concerned with biological and biomedical systems, Brownian motion, epidemiology, imaging, electromagnetism, and scientific computing. The approaches used and the techniques applied to these studies are rather varied, including analytical expansions, orthogonal polynomials, integration of deterministic systems into probabilistic frameworks, numerical analysis, dynamical systems, differential equations and computational Markov chain Monte Carlo.† Most graduate students currently working towards a doctoral degree in applied mathematics are conducting research related in some way to life science applications. Some of the graduate students in applied mathematics have been or are currently supported by NSF and NIH grants.
The description of the active areas of research in the department, are identified in the Research portion of the department web page (url: http://www.case.edu/artsci/math/ResearchAreas.htm).
The holder of a bachelor's degree from any accredited college or university is eligible for consideration for admission to our Graduate Program. It is normally expected that entering graduate students will possess basic competence in advanced calculus and linear algebra. In addition to completing the application form for admission and sending in official transcripts of all previous undergraduate and graduate study, applicants are also required to take the General (Aptitude) Section of the Graduate Record Examination in time to have their scores on file at CWRU when their applications are being considered. Three letters of recommendation are required from individuals who are able to assess the applicant's mathematical ability. Foreign students for whom English is not the native language and who have not completed a baccalaureate or master's degree program from an English-speaking university must submit TOEFL scores. The University requires a TOEFL written exam score to be above 550 or a computer based exam score to above 213 and a minimum iBT score of 79. For GRE scores, the Department requires the quantitative portion to be well above 600 and the analytical writing should be at least 3.0. The IELTS minimum acceptable score is 6.5. If an applicant has a B.A./B.S. degree or other qualifying degree from a certified English speaking university this requirement may be waived.
The manner in which the program addresses the needs of the state or region
The doctoral program in mathematics provides graduates with a solid, broadly based education in pure mathematics which enables them to teach in any of more than 130 institutions of higher education in the state of Ohio. Some of our graduates have followed that route.
The research in applied mathematics carried out in the Department covers a number of areas relevant to the state and region, with an ongoing stress on engineering applications and a new emphasis in mathematics of importance to biology, biomedical engineering, medicine, and in the mathematics of imaging. The addition of faculty with expertise in the mathematics of electromagnetism strengthens the connection with the biotechnological enterprises active in northern Ohio.
Placement objectives for graduates
Graduate students have usually secured a job offer by the time they complete the requirements for their graduation. The great majority of our graduates since 2000 have pursued academic careers, with the exception of one who is working in the private sector. Among the current Ph.D. candidates, one third are considering seeking employment outside academia.
Date of last review: Spring, 2009
Date of next scheduled web update: Spring, 2011
Date of next scheduled complete review: Spring, 2016