# MATH40840 Discrete Mathematics

Discrete mathematics is concerned with the study of mathematical structures that are in some sense finite or discrete. Examples of such objects include graphs, permutations, and finite geometries. As an area it has witnessed an explosive growth the last fifty years due to its strong ties to theoretical computer science. The aim of this module is to present several core topics and tools in discrete mathematics.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module the student should be able to demonstrate an adeptness with structures and concepts in discrete mathematics; solve enumeration problems related to these discrete structures; demonstrate a proficiency with the theory of partially ordered sets; state and prove results in discrete mathematics; solve a variety of problems in discrete mathematics such as characterisation theorems and recursive decompositions.

Indicative Module Content:

Principles and techniques of counting; discrete structures that include graphs, words, permutations, and lattice paths; recursion and generating functions; the theory of partially ordered sets; Young tableaux and the RSK Correspondence; permutation statistics and permutation patterns.

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

30

Autonomous Student Learning

50

Lectures

24

Tutorial

11

Total

115

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Requirements:

The student should already have a solid foundation university-level mathematics and have completed some level 1 or 2 modules related to algebra, analysis, or elementary discrete mathematics. In particular, the student should not be unfamiliar with producing and writing mathematics proofs.

Module Requisites and Incompatibles
Not applicable to this module.

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Two class tests, both worth 10%. Throughout the Trimester n/a Standard conversion grade scale 40% No

20

No
Examination: 2-hour written exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

80

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour