Though content of each of our courses is different, there are a number of common pedagogical themes that run throughout our curriculum. In our courses, students learn to
- Perform mathematical calculations, implement numerical algorithms, and use computational software or programming language to produce viable solutions; gain facility in selecting the appropriate tool.
- Draw from existing knowledge and extend it, applying concepts to solve novel problems in new contexts.
- Use mathematical and statistical structures to represent real world phenomena, gain insight, and answer questions.
- Identify, describe, and explain patterns. Connect ideas across disparate contexts, within one course as well as through sequential courses.
- Write and present logical arguments clearly and concisely to a variety of audiences. This includes not only the formal writing that is typical for mathematical scholarship, but also the informal mathematical conversations one holds with peers when discussing course content or collaborating on problems.
- Appreciate the intellectual development of mathematics. Majors understand mathematics as a powerful tool and a dynamic, growing body of knowledge. Students recognize the progression to mastery often starts with experimenting to identify patterns, and that sometimes valid solutions are uncovered only after learning from unsuccessful attempts. Students see the role of creativity and appreciate the beauty of deep mathematical ideas and connections.