MT2504 Combinatorics and Probability

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11am Mondays (Odd) and Wednesdays and Fridays

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr M Papathomas

Dr M Papathomas
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Finn Smith

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

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-requisites

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

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

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

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

116

The number of hours that students are expected to invest in independent study over the period of the module.

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

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at https://www.st-andrews.ac.uk/mathematics-statistics/students/ug/module-choices-2000/