In this module, students will build upon the foundations of algorithms and their complexity to develop a deeper understanding of algorithmic approaches to computational problem solving. They will explore computational complexity theory, which allows us to consider the very nature of computability – including non-deterministic polynomial (NP) complexity classes such as NP-hard, NP-complete and the classes of problems which cannot be solved. Students will be introduced to classical approaches to problem solving such as divide and conquer, recursion, and parallel approaches, emphasizing their relative benefits and weakness to different classes of problem. They will study advanced data structures in depth, such as tries, heaps, suffix arrays, k-d trees, and distributed hash tables, and explore the approaches for their efficient construction and use.

These theoretical aspects are grounded through practical work in the lab and placed in the context of case studies of extreme scale and embarrassingly parallel computing, derived from real-world problem domains introduced by invited speakers where possible. Finally, students explore key implications of algorithm performance including their impact on energy efficiency and sustainability to provide a coherent interface with other modules.

This module introduces the key ideas and fundamental principles of artificial intelligence (AI) and the types of problems that can be addressed by AI. Students will be introduced to the core concepts and philosophy of AI, including its history and definitions, classify the various approaches to AI, and discuss its presence in the modern world alongside its ethical considerations. They will unearth the underlying principles of search spaces, knowledge representation, and inference logic that form the core of rule-based systems.

Students will then go on to learn the principles of machine learning, emphasising clustering (e.g. k-means), classification (e.g. k-nearest neighbour) algorithms, linear regression, and neural networks. This deep dive provides the essential grounding necessary to progress to modules in topics such as Machine Learning, Computer Vision, and Natural Language Processing.

This module aims to teach and enhance skills, including both subject-related and transferable skills, appropriate to Part II students in Data Science. These skills include the preparation of mathematical documents and presentation materials, scientific writing, oral presentations and group work. As a part of this module, students will undertake both a group and individual project, both of which will involve the investigation of a topic relevant to Data Science. Students will also get the opportunity to utilise LaTex, becoming familiar with how to display formulae and mathematical symbols, as well as learning how to create sections, tables of contents, tables, and figures within the program.

Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.

They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

Probability provides the theoretical basis for statistics and is of interest in its own right.

Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.

Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.

The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.

Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.

This module provides broader exposure to alternative programming language paradigms beyond imperative and object-oriented programming. Particular emphasis is given to functional programming languages, and their unique constraints and features. More specifically, students will investigate how introducing the concept of absolute immutability into programming languages enables a suite of expressive mechanisms within programming languages including pure functions, lambdas, higher order functions, pattern matching, currying, map/reduce, and pattern matching.

As a part of this module, students will also explore why functional languages bring about increased reliability and scalability, and how they are now experiencing a resurgence within the software industry. Finally, through hands-on laboratory sessions, students see how functional programming concepts are being integrated in mainstream programming languages such as Java, Python and JavaScript, to create versatile multi-paradigm programming environments

The internet and the world wide web have now pervaded every aspect of our lives, from e-commerce and entertainment to logistics and social media. Increasingly, application software is no longer written for specific devices, but for internet web browsers. The internet has replaced operating systems as the de facto platform for application development, making an already global phenomenon truly ubiquitous.

This module studies the various approaches to internet applications development, investigating both the client side and server-side approaches, discussing the trade-off of performance, scalability, privacy, and trust associated with these approaches. Students will review the role of “cloud infrastructures” (federated distributed computation) in the provision and management of internet applications. Through interactive lectures and small group practical sessions, students study common frameworks for client-side application development and create and deploy an internet application from first principles.

The Third Year Project’s aim is to consolidate, integrate, and further develop the data scientific skills gained during the BSc Data Science programme. Projects will vary from student to student, but all will focus upon a substantive data scientific issue / research question (including but not limited to design, implementation, and/or evaluative projects).

The academic supervisor will provide structured guidance and support throughout the project to ensure the requisite level of academic content and rigour is being maintained. This module will consist of the capstone project for the BSc Data Science degree, and will provide students with the opportunity to produce a substantial piece of work which they can present to others as evidence of their academic achievement at Lancaster.

Bayesian statistics provides a mechanism for making decisions in the presence of uncertainty. Using Bayes’ theorem, knowledge or rational beliefs are updated as fresh observations are collected. The purpose of the data collection exercise is expressed through a utility function, which is specific to the client or user. It defines what is to be gained or lost through taking particular actions in the current environment. Actions are continually made or not made depending on the expectation of this utility function at any point in time.

Bayesians admit probability as the sole measure of uncertainty. Thus Bayesian reasoning is based on a firm axiomatic system. In addition, since most people have an intuitive notion about probability, Bayesian analysis is readily communicated.

Computer graphics is an interdisciplinary field which deals with visual and image aspects of computing. It underpins the development of video games, use of computer-generated imagery in movies and has helped advance machine learning, cryptography, and parallel computing.

In this module, students explore the fundamental concepts related to visual content generation through relevant theory, such as the essential mathematics, graphics data structures and algorithms, kinematics, collisions, colour, and light. In particular, students will investigate the practical aspects of graphical scenes and rendering including virtual cameras, materials, mesh manipulation, scene-graphs, animation and modelling. They will learn about hardware-specific concepts designed to improve the quality and performance of graphics applications, such as GPU programming, mobile and cloud render-pipelines, shaders, stereoscopic and volumetric rendering. Emerging technologies and trends in research are also introduced with an analytical lens to identify future challenges, opportunities, and solutions.

Computer vision is a branch of artificial intelligence, in which we aim to develop computer-based systems that can interpret and draw meaningful deductions from digital images.

This module covers the fundamentals to understanding image formation and information relating to the human visual system and some fundamental image interpretation methodologies, including convolution, edge detection and feature extraction and comparison. Students will tackle key problems in current research, including semantic segmentation, object detection, and three-dimensional image interpretation. They will cover a range of approaches, from low-level image processing to convolutional neural networks. At the end of the module, students will be equipped to construct software components that implement contemporary image processing and computer vision algorithms and recognise issues within computer vision in order to develop and evaluate solutions.

This module will explore machine learning, which sits within the field of artificial intelligence and enables a computer to learn how to perform a task from data rather than traditional programming.

Students will study the key ideas and techniques of machine learning, which will help students to develop practical skills in problem solving and to understand the implications and potential of machine learning in business and society. They will begin by looking at real-world machine learning problems, challenges, and fundamental techniques in current machine learning methodology. Building on this, the module will cover a variety of approaches to machine learning, from decision trees to a wide range of deep neural networks, including multilayer perceptrons, convolutional neural networks, long short-term memory, autoencoder and generative adversarial networks.

Digital Health concerns the utilisation of digital technologies for health and care. It has a key and ever-growing role to play in improving health systems and public health, as well as increasing and improving the equity of access to health services. It has the potential to transform health and care delivery and support individuals to improve their health.

In this module, students will discover the practical applications, implications, and enabling technologies of digital health. They will survey the sensor technologies that permit remote and automated patient monitoring, study the technologies and processes that enable patient-driven healthcare. This module also investigates the structure of health data in electronic health records, and methods for the evaluation of digital health solutions. Alongside these applied topics, students will also learn about data governance and the ethical issues surrounding digital health technologies, policy, and regulation.

All programming languages are based on theoretical principles of formal language theory. In this module, students take a deep dive into formal languages representation and grammars, and how relate to programming language compilers and interpreters.

Students will study formal language syntax and semantics, phrase structure grammars and the Chomsky Hierarchy. They will learn how to classify languages and explore the concepts of ambiguity in Context Free grammars and its implications. In particular, they will learn about the compilation process including lexical analysis and syntactic analysis, recursive descent parsers, and semantic analysis. Finally, students get to investigate the synthesis phase, where intermediate representations, target languages, and structures lead to code generation. In the School, we blend lectures with small group lab sessions where students gain hands-on experience of applying such theory.

Statistical inference is the theory of the extraction of information about the unknown parameters of an underlying probability distribution from observed data. Consequently, statistical inference underpins all practical statistical applications.

This module reinforces the likelihood approach taken in second year Statistics for single parameter statistical models, and extends this to problems where the probability for the data depends on more than one unknown parameter.

Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?

The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

Using the classical problem of data classification as a running example, this module covers mathematical representation and visualisation of multivariate data; dimensionality reduction; linear discriminant analysis; and Support Vector Machines. While studying these theoretical aspects, students will also gain experience of applying them using R.

An appreciation for multivariate statistical analysis will be developed during the module, as will an ability to represent and visualise high-dimensional data. Students will also gain the ability to evaluate larger statistical models, apply statistical computer packages to analyse large data sets, and extract and evaluate meaning from data.

This module formally introduces students to the discipline of financial mathematics, providing them with an understanding of some of the maths that is used in the financial and business sectors.

Students will begin to encounter financial terminology and will study both European and American option pricing. The module will cover these in relation to discrete and continuous financial models, which include binomial, finite market and Black-Scholes models.

Students will also explore mathematical topics, some of which may be familiar, specifically in relation to finance. These include:

• Conditional expectation
• Filtrations
• Martingales
• Stopping times
• Brownian motion
• Black-Scholes formula

Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated risk-neutral probability; performing calculations with the Black-Scholes formula; and proving various steps in the derivation of the Black-Scholes formula. They will also be able to describe basic concepts of investment strategy analysis, and perform price calculations for stocks with and without dividend payments.

In addition, to these subject specific skills and knowledge, students will gain an appreciation for how mathematics can be used to model the real-world; improve their written and oral communication skills; and develop their critical thinking.

The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.

Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.

They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

This module provides a broad introduction to Natural Language Processing (NLP), a branch of Artificial Intelligence where we develop computational methods to analyse and understand human languages.

Students will be exposed to the core concepts of the NLP pipeline covering methods and techniques for data collection, cleaning, tokenisation, and annotation using a hierarchy of linguistic levels (e.g. morphology, syntax, and semantics). They will experiment with and comparatively evaluate different methods and techniques, including rule based, probabilistic, machine learning and deep learning approaches. Students will also learn to apply and adapt NLP pipelines and tools to real world text mining scenarios and problems, including examples such as health and finance. Key issues such as ethical data collection, bias in language models, and employing sustainable computing methods are also emphasised throughout the learning and teaching in this module.

The rapid increase in consumption and innovation within Artificial Intelligence (AI) and Machine Learning (ML) has significant repercussions for cyber security. This encompasses both how AI and ML can be leveraged to augment and improve established cyber security techniques (from firewalls, risk analysis, and attack detection), as well as the emerging threat of attacks against AI itself (data poisoning, extraction, membership inference).

In this module, students will learn key concepts of secure AI, how it is being used to revolutionise the established cyber security field, as well as the emergent threats of attacks against ML models and data. By the end of the module, students will be able to compare and contrast the roles that Artificial intelligence and Machine Learning can play within the field of cyber security, analyse contemporary security threats against Artificial Intelligence and Machine Learning technologies, as well as evaluate the effectiveness of cyber security AI technologies.

The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).

Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.

As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).

The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Modern statistics is characterised by computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.

Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.

Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.

Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.