Set Theory Logic

AY2024/2025 Semester 1

This course aims to provide you with a basic understanding of formal mathematical logic and axiomatic set theory. Mathematical logic provides a foundational basis for the practice of mathematics, and axiomatic set theory provides a rigorous justification for the existence of mathematical objects and structures. This course will equip you with the awareness of foundational issues in mathematics. It will allow you to understand how proofs in mathematics are rigorously defined, and how the concepts of 'truth' and 'provability' interact. It will also enable you to judge which objects and processes in mathematics are well-defined, and which ones require further axiomatic justifications. It is aimed at increasing awareness among mathematics students for why the common practices in mathematics are rigorously grounded, and which ones are ill-defined and should be avoided. This course is aimed at 3rd and 4th year students interested in learning about the foundations upon which all of mathematics is built upon, particularly mathematics and computer science students who are interested in the theoretical aspects of mathematics. This course is also crucial for students intending to pursue further studies in theoretical mathematics.