Instruction is one of the most essential functions of our department. We take our teaching very seriously, constantly working on innovations in curriculum and teaching methods, and on training our less experienced colleagues to be better teachers. Our faculty and graduate students are regularly selected for campus-wide teaching awards. We also devote a significant amount of time working with interested undergraduates on research projects because nothing prepares a student better for graduate school and a career in science than a taste of research, work on a problem where the answer is not in the back of the textbook. Training graduate students and postdocs is a key mission of the department as well. Many of our trainees move on to leadership jobs in academia and industry, strengthening the Wisconsin Mathematics brand and impacting the future of education as well as the broader economy.