Applied Mathematics, Ph.D. (Ithaca)
Field of Study
The graduate program in applied mathematics is based on a solid foundation in pure mathematics, which includes the fundamentals of algebra and analysis. It involves a grounding in the methods of applied mathematics and studies of scientific areas in which significant applications of mathematics are made. The field has a broadly based interdepartmental faculty that can direct student programs in a large number of areas of the mathematical sciences.
Many specialized or interdisciplinary programs can be designed for individual students, including, for example, a variety of possibilities in biomathematics.
The dissertation is normally a mathematical contribution toward the solution of a problem arising outside mathematics.
Students who are interested in this field may also want to investigate the related fields listed under Mathematical Sciences in "Opportunities for Study," pages 7-8.
Concentrations by Subject
- applied mathematics
Application Requirements and Deadlines
Fall, Jan. 15; no spring admission
Applicants must have an undergraduate background that contains a substantial mathematical component. Applicants are required to submit GRE general test scores, and are advised to submit GRE mathematics subject test scores.
- all Graduate School Requirements, including the TOEFL Exam for Non-Native English Applicants
- three recommendations
- GRE general test (GRE subject test in mathematics advised)
I. Learning Goals
Graduate Program in Applied Mathematics is one of the most broad and interdisciplinary programs at Cornell, with 95 members of the graduate fields representing 13 different departments. The research interests of the members of the Center of Applied Mathematics (CAM) range over mathematical biology, probability theory, nonlinear dynamics, numerical analysis, network theory, optimization, mathematical finance, signal processing, mathematical physics, game theory, and the list goes on and on. The uniting theme is deep mathematical analysis of applied problems, including development of new mathematical tools of attacking these problems.
The very flexible and interdisciplinary nature of the graduate program in Applied Mathematics determines the learning goals for a PhD student. The student is expected to acquire both excellent general mathematical background and background in the specific area of application the student is working in. The student is expected to learn to think as a mathematician. This means taking nothing for granted, until proved to be true. This means searching for new routes for solutions of problems, for bringing together ideas from different branches of mathematics. This means thinking originally, and using the work of others as a stepping stone, instead of following in their
footsteps. Finally, the student is expected to develop deep interest in applied problems and ability to translate the acquired mathematical knowledge into a framework for solving an applied problem.
A student in the graduate program in Applied Mathematics is expected to learn to communicate effectively technical ideas to his/her peers, students and lay audiences by developing written and presentation skills. These skills may be developed through coursework, writing papers and proposals, and by giving technical talks in both informal and formal setups. Finally, a student in the graduate program in Applied Mathematics is expected to learn to adhere to highest ethical standards in conducting and communicating research, teaching and professional community service.
A graduate student in Applied Mathematics is expected to demonstrate both mastery of knowledge in mathematics and its applications, and ability to create new mathematical knowledge and innovative ways to apply mathematical tools to important problems in science, industry and society. Each student is expected to demonstrate the following proficiencies.
- Make substantial original contributions to applied mathematics. This includes ability to identify new important and promising research problems; ability to think independently, critically and creatively;ability to complete research work by bringing it to the stage where it can be published and be used by the others.
- Maintain ability to acquire new knowledge by keeping up with the new developments in the field through professional publications and professional meetings.
- Ability to communicate effectively research findings and plans. This includes ability to present results in the format of technical papers and have them published in professional journals and conference proceedings; ability to explain complex ideas to peers in technical presentations; being aware of funding opportunities and ability to write effective research proposals and obtain research funding.
- Dedication to advancing science through effective teaching, advising, mentoring and service to professional community.
- Awareness of the ethical standards in the field, and ability to maintain and advance these standards.
III. Assessment of Learning Outcomes
There are several components to assessment of how graduate students in Applied Mathematics reach the learning outcomes of the program. The first component is the coursework and exams associated with this coursework. This component allows the Special Committee members and the
Director of CAM to assess the specific outcome of learning in the classroom environment.
The second component is the Admission to Candidacy Examination (the A exam). This exam is administered by student’s Special Committee. Due to the highly interdisciplinary nature of the Graduate Field for Applied Mathematics, the exact nature of the A exam depends somewhat on the specific field in which the student is planning to conduct research. Invariably, this oral exam allows the members of the Special Committee to assess the general knowledge of the student in mathematics and the selected applied field, as well as to assess the appropriateness and feasibility of the PhD research the student is planning to conduct. It also allows the committee members to make an assessment of the oral presentation skills of the student.
The third, and final, component is the B exam (thesis defense). This exam allows the members of the Special Committee to assess the completed PhD work of the student and to evaluate the resulting thesis. The B exam has a public part, that allows the faculty members and the graduate students to listen a presentation by the candidate and ask him/her questions. This allows another assessment of the presentation skills of the student.