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Thank you for taking the time to explore our web site. We hope that you will consider joining us here in the Department of Mathematical Sciences for your undergraduate studies.
It is strange that Mathematics is difficult to define, since some of its key ingredients are definitions, theorems and proofs. One reasonable approach to defining mathematics is to divide it into topics and subtopics. A prospective undergraduate could examine Programs of Study and the courses required for each Program. These methods won't explain *how* these elements became foundations of mathematics.
In the final analysis, mathematics is done by people. People who actively engage in learning and creating mathematics define it as a subject. The faculty (about 40 full-time) and students (about 50 primary math graduates each year) pursuing mathematics at Carnegie Mellon are outstanding.
I encourage you to visit the web pages of faculty members and to schedule a visit to campus in order to meet with undergraduate math majors and me. I am confident that you will find Carnegie Mellon to be an unusual place, with a critical mass of people dedicated to exploring and defining mathematics.