Mathematical Reasoning and Discrete Structures

• Credit value: 30 credits at Level 5
• Convenor: Professor Maura Paterson
• Assessment: two short-problem sets (10% and 15%), a one-hour test (25%) and a two-hour examination (50%)

In this module we provide you with a rigorous foundation in mathematical thinking and fundamental discrete mathematics. You will develop skills in constructing and analysing mathematical proofs, explore different number systems, and learn concepts from counting, probability and graph theory.

Indicative syllabus

• The language of mathematics: statements, theorems, definitions and logical connectives, quantifiers and negating statements, elementary proof techniques, proof by induction
• Integers, rationals, real and complex numbers: the division algorithm and the Euclidean algorithm, congruence and modular arithmetic, boundedness and the least upper bound property, arithmetic involving complex numbers and the Argand diagram, binary operations
• Counting and probability: product rule, counting strings and subsets, probability triples, conditional probabilities
• Graphs: definitions of graphs and classes of graphs, trees, applications

By the end of this module you will be able to:

• construct rigorous mathematical proofs using various techniques
• apply number theoretic concepts, including the division algorithm and modular arithmetic to solve problems
• formulate and solve combinatorial problems using systematic counting techniques, and apply fundamental probability concepts including conditional probability in discrete scenarios
• analyse graph structures and their properties.