2025/6 – MTHT5003B Financial Accounting for Actuaries
Autumn Semester, Level 6 module, Credits: UCU 20
Organiser: Dr Lorna Gregory
Assessment Type: Examination with Coursework or Project
The subject of mathematical logic takes a closer look at the interplay between mathematics and logical reasoning. It gives different insights into many branches of mathematics from calculus and analysis, where it explains how we can work with infinitesimals, to algebra where it gives new tools to work with groups and fields. Historically, mathematical logic led to the idea of computer programming, and recent developments include using computers to help mathematicians in new ways: not just in doing calculations but also in doing proofs. In this module, we first formalize the language we use to do mathematics, making it precise enough to prove things about. We then give the basic notions of Proof Theory and Model Theory. Proof Theory studies mathematical reasoning. You will see a Natural Deduction proof system, which gives us insight into how mathematical proofs work. A highlight is Gödel’s Completeness Theorem, which says that, for a suitably restricted (but still very large) part of mathematics, every true statement can be proved. Model Theory studies how mathematical theories and structures are characterised by axioms. We will see how some classes of structures can be described by axioms in our formal language, and others cannot. A highlight is the Compactness Theorem, which gives a way to build exotic mathematical objects such as an ordered field with infinitesimals.
Before taking this module you must take MTHA5003Y or take MTHA5008Y or take MTHA5003B