The principal aim of this course is to practice mathematical problem interpretation, proof techniques, and question formulation. The course is intended not only for beginning students in the mathematical sciences, but also for all students interested in mathematical art and rigor. Students in the course will be expected to explain, justify, defend, disprove, conjecture and verify mathematical statements, both orally and in writing, in order to develop proof-writing skills. (These skills should prove useful in more advanced mathematics courses). Topics covered include basic logic; basic set theory; definitions and properties of functions; definitions and properties of binary relations; fundamental proof techniques, including proof by induction. Depending on student background and instructor preferences, the course objectives may be conveyed through a selection of problems from various mathematical sub-disciplines, through discussions of current events in the mathematical sciences, including recently solved problems and open challenges facing todays scientists, or through discussions of applications of mathematics.
At least two courses in Mathematical Sciences at WPI, or equivalent.