Proof and Structure (EMMS095S)

This year I am teaching Proof and Structure.

Module description:

This module introduces the essential logical and theoretical concepts necessary for the degree-level study of mathematics. At the end of the module you will have obtained a thorough grounding in the basic mathematical concepts which will be used throughout the degree programme. What makes mathematics different from the sciences is the emphasis placed on proof. In this module you will be introduced to various common methods of proof, such as proof by contradiction and proof by induction, as well as the basic components of propositional logic: connectives, quantifiers and truth tables. The main number sets (natural numbers, integers, rational, real and complex numbers) will be defined and their properties studied. Binary relations and binary operations and the concept of a group will be introduced and some elementary results established.

Course content: