Logic: The Propositional Calculus
In many college mathematics curricula students are challenged to bridge the mental gap between heavily computational courses such as multivariable calculus and proof-based courses such as linear algebra and real analysis. While a number of institutions offer semester-long classes on set theory and logic, most mathematics departments consign the pedagogy of such topics to a few lectures in their intermediate curricular offerings, where they receive only perfunctory and incomplete treatment at best.
This minicourse remedies this lacuna in the university mathematics curriculum by offering to students a concise yet thorough description of mathematical reasoning and logic. With exercises, self-correcting problem sets and a host of examples, the syllabus provides an ideal platform for self-guided study that students can tackle at any point during the academic year.
The estimated completion time is 20 hours. With a clear understanding of deduction and rules of inference, students in intermediate-level mathematics courses are better prepared to follow and to create arguments based on these logical principles.