Logic Proof The Foundations Of Calculus

This course will provide a rigorous introduction to logic and mathematical proof, with applications to the foundations of calculus also given as a concrete testbed for the students' understanding. The course will start at the very beginning bottom of the classical 'stack' of mathematics, namely propositional and predicate logic. We will then introduce the axioms of set theory, and then apply these concretely to foundational topics in real analysis to see how these tools translate into practical mathematical results.

Students will gain the following:

• An understanding of logic and proof theory, which are fundamental topics in computer science in their own right
• A grounded ability to construct rigorous mathematical arguments, which will in turn provide a strong foundation for students who wish to pursue any further technical subjects involving mathematics (e.g. machine learning)
• Sharpened critical thinking and abstract reasoning abilities, providing transferable skills to a much broader range of engagements in research and industry alike

This course will also provide a taste for type theory and proof assistants, which constitute more advanced research topics in modern computer science.