University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 8

Semester: 1

Planned timetable: 11am Mondays (Odd) and Wednesdays and Fridays

This module provides an introduction to the study of combinatorics and finite sets and also the study of probability. It will describe the links between these two areas of study. It provides a foundation both for further study of combinatorics within pure mathematics and for the various statistics modules that are available. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass MT1002. If MT1002 has not been passed, A at Advanced Higher Mathematics or A at A-level Further Mathematics, or Co-requisite MT1010

Learning and teaching methods and delivery

Weekly contact: 2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 4 weeks), 1-hour examples class (x 5 weeks)

Scheduled learning hours: 34

Guided independent study hours: 116

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 70%, Coursework = 30%

As defined by QAA
Written examinations : 70%
Practical examinations : 0%
Coursework: 30%

Re-assessment: 2-hour Written Examination = 100%

Personnel

Module coordinator: Professor C M Roney-Dougal
Module teaching staff: Dr Michael Papathomas
Module coordinator email Colva.Roney-Dougal@st-andrews.ac.uk

Intended learning outcomes

• Identify, prove, and apply relevant formulae from lectures to solve problems involving counting sets, functions, permutations, tuples and multisets, and problems involving recursively-defined sequences
• State the axioms of probability. Calculate elementary probabilities, including conditional probabilities, appropriately use rules of probability, and be able to work with the concept of independence
• Define a random variable and associated distribution functions. Understand and work with discrete and continuous distributions to calculate probabilities, expectations and variances. State and apply the uniqueness theorem for probability and moment generating functions
• Demonstrate an understanding of multivariate distributions and associated distribution functions. Define and calculate expectations, variance, covariance and correlation for multiple random variables
• Demonstrate computational skills in Python through programming basic combinatorial procedures, and be able to apply these to a range of combinatorial and probabilistic problems