Selected faculty opinions.

The PhD at Illinois represents a strong mathematical education and an ability to apply mathematical ideas to solve new problems. Students must master a broad range of mathematical topics in reasonable depth. A strong faculty maintains standards for the quality of research represented by the thesis. The large size of the department facilitates both the breadth of topics available and the opportunity for research and teaching n a variety of modes. Thus graduating students are thoroughly prepared or their career.

The purpose of the PhD program at UIUC is to train our students to be productive members of the mathematics enterprise. All students must write a PhD thesis that is a sizable and original investigation into mathematics. Many of our students go on to be successful research mathematicians, others become college teachers, and some work in industry. In all cases our program trains them by insisting on a high intellectual standard. The size and diversity of our programs provide students many opportunities for development in mathematics and in the teaching of mathematics.

Confirmation of a PhD degree certifies that the recipient has demonstrated sufficient level of achievement in scholarship and research so as to be considered "a professional" and "colleague" by the community of research scientists. The phrase "sufficient level of achievement" in this contex carries with it the "promise" that professional activity is likely to continue over the duration of a career.

The purpose of the PhD in Mathematics at UIUC is to learn something deep and difficult--how to conduct research in mathematics. The construction of a good mathematics research paper, with its careful and intricate web of interconnecting statements and ideas, results in a work of art that can match that of any artist.

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