The PhD program in the Mathematics Department has four main components: coursework, qualifying exams, a comprehensive exam, and the writing and oral defense of a PhD thesis.<br><br>The goal of this program is to develop your abilities to the point where you can contribute original research in mathematics. To this end, we offer a wide range of basic graduate courses as well as advanced topics courses, and the faculty usually run a few seminars every semester. During your time here, youll work towards a broad understanding of graduate mathematics, develop your mathematical abilities and creativity, and reach the cutting edge of research in one of the many fields our faculty studies, all culminating in the writing and oral defense of your PhD thesis. Along the way, youll have a few milestones to reach: taking at least 10 courses (with some breadth requirements), passing two qualifying exams (out of four: algebra, analysis, applied mathematics, and topology), and completing a comprehensive exam with a faculty advisor.