Bachelor of Science (BSc)

BSc Mathematics with Placement Year

Strengthen your employability by taking our Placement Year programme.
  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: G101 / Institution code: M20
  • Key features:
  • Industrial experience
  • Accredited course

Full entry requirementsHow to apply

Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £34,500 per annum. For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Course unit details:
Multivariate Statistics and Machine Learning

Course unit fact file
Unit code MATH38161
Credit rating 10
Unit level Level 3
Teaching period(s) Semester 1
Available as a free choice unit? No

Overview

Multivariate statistical models and methods are essential for analysing complex-structured and possibly high-dimensional data from any areas of science and industry, ranging from biology and medicine, and genetics to finance and sociology. Multivariate statistics also provides the foundation of many machine learning algorithms.

In the first part of this module covers the foundations of multivariate data analysis, e.g., multivariate random variables, covariance and correlation, and multivariate regression. In addition, related approaches such dimension reduction and latent variable models are discussed.

The second part of the course is concerned with multivariate approaches for statistical learning in supervised and unsupervised settings, including techniques from machine learning, and their application in pattern recognition, classification, and high-dimensional data analysis.

Pre/co-requisites

Unit title Unit code Requirement type Description
Probability and Statistics 2 MATH27720 Pre-Requisite Compulsory
Please note

Desirable

Good working knowledge in the R statistical programming language.

Students are not permitted to take more than one of MATH38161 or MATH48061 for credit in the same undergraduate year.  Students are not permitted to take MATH48061 and MATH68061 for credit in an undergraduate programme and then a postgraduate programme.

Aims

To familiarise students with the fundamental concepts and ideas underlying multivariate statistical data analysis methods and related supervised and unsupervised machine learning approaches for pattern recognition and classification, as well as with their practical implementation and application using the R statistical programming language.

Learning outcomes

On successful completion of the course students will be able to:

  • use the programming language R for multivariate data analysis and graphical presentation
  • apply dimension reduction techniques such as PCA and CCA
  • perform clustering and classification using tools from both statistics and machine learning
  • make good choices among available parametric and nonparametric approaches
  • analyse high-dimensional data sets with suitable regularisation techniques

Syllabus

  • Multivariate normal model: distributional properties, estimation of covariance and correlation matrix both in large and small sample settings (using likelihood and regularised/shrinkage estimation), connection with multivariate regression. [4]
  • Dimension reduction and latent variable models: whitening transformations, Principle Components Analysis (PCA), Canonical Correlation Analysis (CCA), Factor Analysis (FA). [4]
  • Unsupervised learning / clustering: model-based clustering (finite normal mixture models), algorithmic approaches (e.g. K-means, hierarchical clustering). [4]
  • Supervised learning / classification: Diagonal, Linear, and Quadratic Discriminant Analysis (DDA, LDA, QDA) and regularised versions for high-dimensional data analysis.  Further approches to classification (eg support vector machines). [4]
  • Nonlinear and Nonparametric models: splines, decision trees, random forest. [4]

Assessment methods

Method Weight
Other 30%
Written exam 70%
  • Coursework: weighting 30%
  • End of semester examination: weighting 70%

Feedback methods

Computer labs will provide an opportunity for students to try out the methods on real data and to get feedback from the instructor. Coursework projects also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour or after class.

Recommended reading

Study hours

Scheduled activity hours
Lectures 11
Tutorials 11
Independent study hours
Independent study 78

Teaching staff

Staff member Role
Nilabja Guha Unit coordinator

Additional notes

The independent study hours will normally comprise the following. During each week of the taught part of the semester:
 
•         You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently
•         You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week
•         There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises
•         In some weeks you may be preparing coursework or revising for mid-semester tests
 
Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.
The remaining independent study time comprises revision for and taking the end-of-semester assessment.
 
The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.

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