MTH1110 · Foundations of mathematics

Overview

This unit develops foundational concepts and techniques in discrete mathematics, with an emphasis on mathematical structures, proof and abstraction. Topics include logic and proof, sets, relations and functions, combinatorics, recurrence relations, graph theory and elementary probability. These topics provide the language and methods for reasoning about discrete structures that arise throughout modern mathematics and its applications, including computation, algorithms, data science, network analysis and discrete modelling. The unit provides a foundation for further study in mathematics and related quantitative disciplines.

Areas of study: Mathematics Pure Mathematics Applied and Computational Mathematics Probability and Statistics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Construct, analyse and critique rigorous mathematical arguments, including direct proofs, proofs by contradiction and proofs by induction;
2. Use sets, relations and functions as foundational mathematical structures, and apply them to formulate and solve abstract problems;
3. Develop, solve and interpret recurrence relations as models for discrete and recursively defined processes;
4. Apply graph-theoretic concepts, including trees and graphs, to model discrete structures and prove structural properties;
5. Use combinatorial reasoning to solve enumeration problems, including problems that require constructing and justifying appropriate counting methods.

Workload

• One 3-hour seminar; • One 2-hour applied class (in weeks 2–12) and • Seven hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.