Students will understand core graduate mathematics material and students must demonstrate substantial comprehension of Linear Algebra and Analysis, the common core subjects required of all students in the program.Competence in written and oral communication is essential for most mathematical careers. Such communication skills are also important in many other aspects of life, therefore students will be able to deliver written and oral presentations demonstrating comprehension of complex mathematical content and the ability to communicate that complex mathematical content to a broad audience (general department faculty and graduate students).Students should have the opportunity to hear research talks in seminars and colloquia, and participate in research projects (this might come through on campus employment, independent study, or thesis work). Students are strongly encouraged to attend our biweekly colloquium.