纯粹数学系是数学系五个独立的系之一。该系提供研究生课程，可授予数学硕士学位（MMath）和哲学博士学位（PhD）。博士学位课程包括课程工作
The Department offers exciting and challenging programs leading to MMath and PhD degrees. A broad range of courses are offered, covering the spectrum of pure mathematics. As well, students are welcome to take relevant courses in other departments in the University. All students work one-on-one with their supervisor to prepare a research paper or thesis for their master's degree, and to be guided through the process of doing original research for their PhD. Graduate students are provided with excellent financial support through a combination of teaching assistantships, research assistantships, and internal scholarships and awards. The cost of living in Waterloo is quite reasonable. Each program is tailored to the needs and interests of the individual students. Many of our graduates become university mathematics professors. Some study advanced mathematics as a foundation for more applied studies. Other common careers for our graduates are in the computer industry, teaching at the high school or college level, or in business, particularly the financial industry. There is no shortage of intellectually rewarding jobs for Pure Mathematics graduates.<br><br>Analysis is that branch of mathematics which evolved from the notions of approximations, limits and continuity of real- and complex-valued functions. While the fundamental theorem of calculus remains to this day one of the central pillars of mathematics, modern analysis deals with the above concepts in broader and more abstract settings such as those of topological groups and algebras.