Showing **91** courses for the subject **Mathematics**

#### Introduction to Data Science

##### DATA101

We live in an increasingly data-driven world with the volume of data generated annually following a roughly exponential trend. Data scientists find themselves in high demand because of their skills to derive valuable insights from data. But what exac...

An introduction to the range of mathematical techniques employed by engineers, including functions, calculus, linear algebra, vector geometry, set theory, logic and probability. This course emphasises engineering applications and modelling.

Further mathematical techniques employed by electrical and electronic engineers, with a focus on methods of calculus, differential equations, and linear algebra. There is an emphasis on engineering applications and use of software.

Mathematical techniques employed by cybersecurity and software engineers, including combinatorics, logic, probability distributions, model fitting and estimation. The course emphasises engineering applications.

This course provides an introduction to, or review of, fundamental skills and ideas in mathematics. The course is designed for students who require some mathematics in their degree, but who may not have a lot of mathematical experience. Topics includ...

#### Calculus 1A

##### MATH141

Determining the rate of change of a function as its dependent variable changes is a key question in many sciences. It is also the basis for differential calculus, which is the first part of mathematical analysis. This course provides a thorough devel...

#### Calculus 1B

##### MATH142

Integration looks at summing continuous variables, providing a way to define and compute areas and volumes, which are essential for many applications. This course develops integral calculus, including the view of integration as anti-differentiation, ...

#### Algebra

##### MATH151

Linear algebra is central to mathematics, and essential in science and engineering. This course introduces linear algebra, motivated by some of these applications, and maintaining a practical approach using fundamental mathematical objects such as ma...

#### Discrete Mathematics and Logic

##### MATH161

Logic underlies all of mathematics. This course introduces the basic notions of logic and discusses what makes some arguments good or valid, and others invalid. This leads to a definition of a mathematical proof, whereby the truth of mathematical sta...

Heads or tails? That's fair, right? Is the coin fair though - and how could you check? How might you choose in a more complicated situation? This course gives you an introduction to probability models in Statistics and their use in good decision maki...

#### Techniques of Data Science

##### DATA201

Discover the essential computational techniques at the heart of data science, encompassing the realms of data integration and encryption. Dive into the mathematical concepts and techniques that underpin the entire data lifecycle, from generation and ...

#### Data Management and Programming

##### DATA202

Explore the practical side of data management in this course designed for those working with data sources. You will get hands-on experience in programming and data management using a high-level language and SQL. You will build confidence in skills su...

#### Introduction to Real Analysis

##### MATH212

The theoretical underpinnings of calculus took many years to develop rigorously. This course provides insight into the basic techniques of real analysis in the familiar context of single-variable differential calculus. There is a focus on the proof t...

#### Multivariable Calculus

##### MATH243

In order to apply calculus to many physical systems, its concepts have to be extended to higher dimensions. The course introduces vector-valued functions of one variable (curves in the plane and in space), real-valued functions of several variables, ...

#### Ordinary Differential Equations

##### MATH244

Ordinary Differential Equations (ODEs) have motivated a lot of mathematics, both for themselves and for their applications, particularly in the wider sciences. This course introduces ODEs, covering their classification, and various solution methods f...

#### Computational Mathematics

##### MATH245

Combining mathematics with computational techniques allows us to study a wide variety of applications in science, for example, solving physics problems by approximating integrals and derivatives, and compressing digital images using singular-value de...

#### Linear Algebra

##### MATH251

Linear algebra is a fundamental part of mathematics. This is a second course in linear algebra, focusing on more abstract representations and giving an axiomatic treatment of vector spaces. The course introduces the underlying concepts of linear alge...

#### Groups and Graphs

##### MATH261

This course explores two fundamental mathematical structures: groups and graphs. Both have wide applications in mathematics, as well as in fields such as computer science, cryptography, physics, and chemistry. The course starts with basic group theor...

#### Mathematical Statistics

##### MATH277

Topics covered: a review of basic probability theory; discrete and continuous random variables; joint distributions of random variables; expectation, variance, covariance and moment generating functions; correlation and linear combinations of random ...

#### Data Science in Practice

##### DATA301

Take your data science skills to the next level with our capstone course. Dive into interactive displays, infographics, and dashboards equipped with mathematical modelling tools and coding skills. Sharpen your communication and reporting abilities th...

#### Partial Differential Equations

##### MATH301

This course is an introduction to Partial Differential Equations (PDEs), including those of importance for the natural sciences. The course covers solution methods for linear PDEs, including the use of boundary values and initial values. The course d...

This course introduces a range of machine learning techniques of importance in Data Science, and gives students experience in using modern software libraries for implementing machine learning pipelines. Topics will include machine learning techniques...

#### Statistics for Data Science

##### DATA303

In this course we uncover the role that Statistics plays in Data Science. With a focus on understanding relevant statistical methods and their practical applications, this course will help you consolidate key data science skills. Topics covered inclu...

#### Simulation and Stochastic Models

##### DATA304

Simulation and modelling of stochastic systems, covering examples from Operations Research and Computer Science, including queues, networks and computer systems. Design, analysis and validation of simulation experiments. Previous experience with comp...

#### Mathematical Logic

##### MATH309

This course examines symbolic languages, which are a foundational pillar of mathematics as well as the basis of computer science. Their semantics and proof theory are studied, explaining the role of logic in describing mathematical structures and for...

#### Algebra

##### MATH311

The abstraction of algebra to sets with extra structure has led to many important mathematical developments. The basic algebraic structures, groups, rings and fields, are the focus of this course, together with some of their applications, such as sol...

#### Metric Spaces

##### MATH317

This course is an introduction to spaces with a generalised length function called a metric. Metric spaces are fundamental objects in modern analysis, featuring notions of convergence of sequences and continuity of functions in a very general framewo...

#### Hilbert Spaces

##### MATH318

This course extends the techniques of linear algebra and real analysis so that problems of an intrinsically infinite-dimensional nature can be studied. A Hilbert space is an inner product space with the analytic structure suitable for studying such p...

#### Applied Mathematics I

##### MATH321

Two topics in applied mathematics, not including any taken by the same candidate in MATH 322 or MATH 323. Topics may include: Cartesian tensors and applications, seismology, classical mechanics, fluid mechanics, meteorology, fractals, quantum mechani...

#### Applied Mathematics II

##### MATH322

Two topics in applied mathematics, not including any taken by the same candidate in MATH 321 or MATH 323. Topics may include: Cartesian tensors and applications, seismology, classical mechanics, fluid mechanics, meteorology, fractals, quantum mechani...

#### Mathematics for Earth Sciences

##### MATH323

Two topics in applied mathematics, chosen from the following, and not including any taken by the same candidate in MATH 321 or MATH 322: fluid mechanics, Cartesian tensors and applications, differential equations for earth sciences, meteorology proje...

#### Coding and Cryptography

##### MATH324

Encoding messages so that they can be transmitted robustly and efficiently, while being safe from eavesdroppers, is an important part of modern communication. This course starts with modern coding theory, introducing linear codes, coding bounds, perf...

#### Computability and Complexity

##### MATH335

The basic theory of the algorithmic content of mathematics: models of computation and their equivalence, including register machines, Turing machines, and partial recursive functions; computably enumerable sets and the fixed point theorem; basic noti...

#### Special Topic: to be confirmed

##### DATA341

Topic yet to be confirmed.

#### Data Science Internship

##### DATA351

Students will complete an approved and supervised project in a public, private or non-profit organisation with established data science work stream. This project will enable students to gain professional work experience in the application of data sci...

#### Optimisation

##### MATH353

A course in the theory, algorithms and applications of optimisation. Topics include linear programming, integer programming, and non-linear optimisation.

#### Graph Theory

##### MATH361

Graphs provide an abstraction that enables many different systems to be modelled and analysed, from computer networks to disease spread. This course introduces graphs as mathematical objects and covers topics including: connectivity and Menger’s Theo...

#### Probability and Random Processes

##### MATH377

The course provides a firmer foundation in probability theory and an introduction to random processes. The topics include continuity of probability measures; Stieltjes integrals; almost sure convergence; conditional distributions and effects of condi...

#### Special Topic: Complex Analysis

##### MATH381

Complex analysis extends real analysis to functions of complex variables. This course covers the fundamentals of complex analysis, including the Cauchy-Riemann equations, holomorphic functions, harmonic functions, the Cauchy integral formula, power s...

#### Special Topic

##### MATH382

#### Discrete Mathematics

##### MATH432

Discrete mathematics deals with mathematical structures that can be counted. These structures can describe, for example, the pairwise relationships between a set of objects (forming graphs) or discrete symmetries of crystals (forming groups). Another...

#### Model Theory

##### MATH433

Model theory describes mathematical structures by investigating logical statements that are true of those structures. This course introduces the fundamental ideas and techniques of model theory, such as structures and formulas, the ultraproduct const...

#### Set Theory

##### MATH434

Set theory lies at the foundations of mathematics - all objects of mathematical interest can be construed as sets. Contemporary set theory explores some of the rich structure of the class of all sets, and the limitations of the theory. The course con...

#### Computability and Complexity

##### MATH435

The questions of the minimal computational effort required to find answers to certain problems, and whether there are limits to what can be computed, are at the heart of this course. Topics covered include the basics of computability theory, partial ...

#### Galois Theory and Number Theory

##### MATH436

Galois theory brings together several branches of mathematics and is a natural bridge between algebra and number theory. The course starts with the historical question of whether polynomial equations can be solved by radicals and rediscovers Galois' ...

#### Knots and Complexity

##### MATH438

This course introduces polynomial invariants of knots and graphs, including Jones polynomials of knots and Tutte polynomials of graphs. The focus is on complexity theoretic aspects associated with their evaluation. The course serves as further study ...

#### Category Theory

##### MATH439

#### Directed Individual Study

##### MATH440

A supervised programme of study approved by the Head of School.

#### Measure Theory

##### MATH441

Measure theory generalises mathematical notions such as length and volume, and has important applications in probability, physics, and mathematical analysis. Topics that are covered in this introductory course include measurable spaces and measures, ...

#### Functional Analysis

##### MATH442

An introductory course in Functional Analysis covering the major theorems including the fixed point, Hahn-Banach, closed graph and open mapping theorems, and their applications.

#### Operator Algebra

##### MATH443

Operator algebras have a rich algebraic and analytic structure modelled on the properties of bounded linear operators on a Hilbert space. This course introduces the basic theory of Banach and C*-algebras with an emphasis on how it is used.

#### Topology

##### MATH452

Topology is a fundamental subject that interacts with most other areas of mathematics. This course covers basic point set topology, providing a foundation used throughout mathematics. Abstractions of analytic notions such as continuity, compactness, ...

#### Lie Groups and Lie Algebras

##### MATH453

#### Directed Individual Study

##### MATH460

A supervised programme of study approved by the Head of School.

#### Differential Equations

##### MATH461

#### Chaotic Dynamics

##### MATH462

Dynamical systems, which are time-varying, underlie much of mathematical physics. This course covers the fundamental concepts of qualitative theory of dynamical systems, including limit sets and periodic orbits, stable manifolds and crises, and bifur...

#### Differential Geometry

##### MATH464

#### General Relativity and Cosmology

##### MATH465

#### Topics in Applied Mathematics

##### MATH466

Two topics of a more advanced nature in applied mathematics or mathematical physics from a selection that may include: classical mechanics, fluid mechanics, quantum mechanics, special relativity. Topics may not include any already or concurrently tak...

#### Topics in Applied Mathematics

##### MATH467

Two topics of a more advanced nature in applied mathematics or mathematical physics from a selection that may include: classical mechanics, fluid mechanics, quantum mechanics, special relativity. Topics may not include any already or concurrently tak...

#### Practical Data Science

##### DATA471

A course in practical data science. The course will introduce interactive displays, infographics and dashboards, focussing on communication, reporting and visualisation. It will bring together techniques in statistical and mathematical modelling with...

#### Data Management and Programming

##### DATA472

A course in the practical aspects of data management for those who work with data sources. Students will apply programming and data management techniques using a high-level language and SQL. Web scraping, data transformation, data cleaning, summary a...

In this course we uncover the role that Statistics plays in Data Science. With a focus on understanding relevant statistical methods and their practical applications, this course will help you consolidate key data science skills. Topics covered inclu...

#### Simulation & Stochastic Models

##### DATA474

Simulation and modelling of stochastic systems, covering examples from Operations Research and Computer Science, including queues, networks and computer systems. Design, analysis and validation of simulation systems. Design, analysis and validation o...

#### Probability

##### MATH477

The course starts with weak and almost sure convergence, then covers limit theorems and semi-groups of distributions, infinitely divisible and stable distributions and Levy processes, with emphasis on compound Poisson processes, random walks and Brow...

This course provides students with an opportunity to develop their research skills in Data Science, including use of library resources, constructing literature reviews, developing research questions, writing research proposals and developing skills i...

#### Special Topic

##### MATH480

#### Special Topic:

##### DATA481

#### Special Topic

##### MATH481

#### Special Topic:

##### DATA482

This course will focus on the application of infinitary methods (logic, topology, dynamical systems) in Ramsey theory and the combinatorial study of finite discrete structures.

#### Special Topic:

##### DATA483

This course will focus on the theory of rings and modules, with an eye to applications to algebraic number theory.

#### Research Project

##### DATA487

Supervised research project in Data Science.

#### Research Project 1

##### MATH487

Supervised research project in Mathematics.

#### Research Project 2

##### MATH488

Supervised research project in Mathematics.

#### Research Project

##### DATA489

Supervised research project in Data Science.

#### Research Project

##### MATH489

Supervised research project in Mathematics.

#### Mathematics for Data Science

##### DATA491

This course covers key mathematical methods used in the construction and maximisation of likelihoods, analyses of experimental data and general linear models, and exploration of probability distributions. Topics will include differentiation and optim...

#### Data Science Algorithms

##### DATA492

This course will derive the fundamental algorithms of data science from mathematical and statistical principles. Algorithms for regression, clustering, dimensionality reduction and stochastic optimisation will be derived, together with methods to gen...

A course in the application of Data Science techniques to a problem. Each student will develop a distributable software package to process, investigate, analyse, manipulate, summarise and visualise data from a data source. The package will be develop...

#### Data Science Practicum

##### DATA581

This course enables students to gain professional work experience in the application of Data Science. Each student is supervised by a host organisation involved in Data Science applications in the public or private sectors. The placement allows stude...

#### Research Project

##### DATA588

Supervised research project in Data Science.

#### Thesis in Data Science

##### DATA591

MSc thesis in Data Science.

#### Thesis

##### MATH591

MSc or MA thesis in Mathematics.

#### Data Science for PhD

##### DATA690

Data Science for PhD.

#### Mathematics for PhD

##### MATH690

#### Mathematics for PhD (Science)

##### MATH691

Showing results 1 - 91 of 91 results

Showing **1 - 91** of **91 ** results for **Mathematics**