BSc (Hons) Mathematics with Integrated Foundation Year Bachelor's degree at Royal Holloway, University of London

The aims of this module are to develop fundamental practical skills in computer programming and computational thinking using a hands-on approach. This is an entry-level module and is suitable for those with no prior programming experience. This module will contain foundational programming topics, including basic data structures, conditionals and loops, functions, and classes.

This module aims to provide some key concepts in physical sciences that underpin all Physics and Engineering disciplines. The module will start with basic physics principles and will be gradually further developed in the Physical Sciences II module in the second term. Subjects explored on this module include Units and dimensions, Materials, Motion, Newton's laws, Connected particles, Static equilibrium, Fluids, Thermodynamics and Electricity.

This module aims to provide the mathematics required for a foundation in engineering and physical science, enabling students to progress to subsequent calculus-based courses. It is designed to help students develop comfort and skill in using mathematical concepts and applying these concepts to problems in Engineering, Computer Science, Maths, and Physics. Additionally, the module highlights the application of mathematical techniques to topics in engineering and physics. The main mathematical top

This module aims to provide some key concepts in physical sciences that underpin all Physics and Engineering discipline. This module will cover the topics that are not covered in the Physical Sciences I in the first term. Topics covered include Electric Fields, Magnetic fields, Electromagnetic induction, Capacitors, Waves and optics, Circular motion, Simple harmonic motion, and Quantum physics. A group project is a key element of assessment and provides an important focus on the development of l

This module is built around global issues. Each topic will embody issues of global importance and be based on authentic and topical world events. The module is intended to deliver an interdisciplinary, academically authentic introduction to global issues, which satisfies a wide range of interests appealing to students wanting to progress onto a range of subjects such as maths, physics, computer science and electronic engineering. Therefore, readings and lectures will approach the topics from an

The aim of the module is to provide the calculus and statistics required for a foundation in engineering and physical science. The module will provide a foundation so that a student can apply calculus to real world problems. The module also aims to aid students in developing familiarity and skills in differentiation and integration. The main mathematical topics and concepts in the module are differentiation, integration, first-order ordinary differential equations, Probability, and Statistics.

On completion of the module, students should be able to understand a range of topics in elementary geometry.

In this module, you will develop an understanding of how the techniques for solving differential equations can be applied to describe the real world. You will look at situations from balls flying through the air to planets orbiting the stars, including why the moon continues to orbit the Earth and not the Sun. You will consider the chaotic motion of a pendulum, and examine Einstein's theory of special relativity to describe the propagation of matter and light at high speeds.

In this module you will develop an understanding of the notion of probability and the basic theory and methods of statistics. You will look at random variables and their distributions, calculate probabilities of events that arise from standard distributions, estimate means and variances, and carry out t tests for means and differences of means. You will also consider the notions of types of error, power and significance levels, gaining experience in sorting a variety of data sets in a scientific

This module aims to develop the students' confidence and skill in dealing with mathematical expressions, to extend their understanding of calculus, and to introduce some topics which they may not have met at A-level. It also aims to ease the transition to university work and to encourage the student to develop good study skills.

In this module you will develop an understanding of the calculus functions of more than one variable and how it may be used in areas such as geometry and optimisation. You learn how to manipulate partial derivatives, construct and manipulate line integrals, represent curves and surfaces in higher dimensions, calculate areas under a curve and volumes between surfaces, and evaluate double integrals, including the use of change of order of integration and change of coordinates.

In this module you will develop an understanding of the fundamental algebraic structures, including familiar integers and polynomial rings. You will learn how to apply Euclid's algorithm to find the greatest common divisor of two integers, and use mathematical induction to prove simple results. You will examine the use of arithmetic operations on complex numbers, extract roots of complex numbers, prove De Morgan's laws, and determine whether a given mapping is bijective.

In this module you will develop an understanding of basic linear algebra, in particular the use of matrices and vectors. You will look at the basic theoretical and computational techniques of matrix theory, examining the power of vector methods and how they may be used to describe three-dimensional space. You will consider the notions of field, vector space and subspace, and learn how to calculate the determinant of an n x n matrix.

Real analysis studies the behaviour of the real numbers and real-valued functions. It provides the foundations of calculus, and is essential to both pure and applied mathematics. This module provides a user-friendly introduction to key ideas of real analysis, illustrated with copious examples. It examines topics such as the properties and axioms of the real numbers, and convergence of infinite sequences and infinite series.

In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to formulate and explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.

This course introduces you to the basics of Python programming for building solutions to mathematics-based tasks. This will encourage a deeper understanding of the mathematics that you will learn across your degree, developing general mathematical skills and group working. Additionally, the module will provide guidance through the process of applying for a summer internship or job, as well as reviewing the range of career options available to Mathematicians upon graduation.

In this module you will develop an understanding of vectors and matrices within the context of vector spaces, with a focus on deriving and using various decompositions of matrices, including eigenvalue decompositions and the so-called normal forms. You will learn how these abstract notions can be used to solve problems encountered in other fields of science and mathematics, such as optimisation theory.

In this module the vector calculus methods are applied to a variety of problems in the physical sciences, with a focus on electromagnetism and optics. On completion of the module, the student should be able to calculate relevant physical quantities such as field strengths, forces, and energy distributions in static as well as dynamical electromagnetic systems and be able to treat mathematically the interactions between moving electrical charges, magnets and optical fields.

In this module you will develop an understanding of statistical modelling, becoming familiar with the theory and the application of linear models. You will learn how to use the classic simple linear regression model and its generalisations for modelling dependence between variables. You will examine how to apply non-parametric methods, such as the Wilxocon and Kolmogorov-Smirnov goodness-of-fit tests, and learn to use the R open source software package.

The aim of this module is to enable you to plan and carry out longer assignments, which require significant preparation and/or advanced data analysis. This module will lay the groundwork for the comprehensive project work undertaken in your final year project whilst introducing you to some of the research activities within the Department. You will establish skills including report writing and oral presentations in the context of employment.