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

You will develop an understanding of the key concepts in Calculus, including differentiation and integration. You will learn how to factorise polynomials and separate rational functions into partial fractions, differentiate commonly occurring functions, and find definite and indefinite integrals of a variety of functions using substitution or integration by parts. You will also examine how to recognise the standard forms of first-order differential equations, and reduce other equations to these

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.

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.

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.

Knowledge is often thought to be the highest achievement of rational creatures, the thing that distinguishes us from other animals and is the basis of our ability to predict and control our environment. Beginning with the most Platonic of questions, 'what is knowledge?', this course introduces you to basic topics in contemporary epistemology. Among the questions it goes on to address are: why is knowledge valuable?; how do we acquire knowledge and how do we pass it on to others?; how do we become

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 set in a scientific way.

You will develop an understanding of the formal study of arguments through the two basic systems of modern logic - sentential or propositional logic and predicate logic. You will learn how to present and analyse arguments formally, and look at the implications and uses of logical analysis by considering Bertrand Russell's formalist solution to the problem of definite descriptions. You will also examine the broader significance of findings in logic to philosophical inquiry.

You will develop an understanding of the relationship between the mind and the brain. You will examine the key theories, from Descartes' dualist conception of the relationship between mind and body through to Chalmers's conception of consciousness as 'the hard problem' in the philosophy of mind. You will also consider some of the famous thought experiments in this area, including Descartes's and Laplace's demons, the Chinese Room and the China Brain, Mary and the black-and-white room, and the pr

You will develop an understanding of the central problems and debates within moral philosophy and aesthetics. You will look at questions relating to both metaphysical and ethical relativism, including the ways we view our moral commitments within the world, how the individual is related to society, and the value and nature of the work of art. You will also examine approaches from the history of philosophy, including the Anglo-American tradition and recent European philosophy.

You will develop an understanding of how mathematics has been used to describe space over the last 2,500 years. You will look at ruler and compass constructions from ancient Greece, the influence of algebra on geometry in the renaissance, and the intricate and beautiful fractal patterns developed by Benoît Mandelbrot in the 1970s. You will learn to sketch simple curves using polar coordinates, draw and classify conics, and use simple arguments to distinguish between countable and uncountable set

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.

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.

You will develop an understanding of the basic complex variable theory. You will look at the definitions of continuity and differentiability of a complex valued function at a point, and how Cauchy-Riemann equations can be applied. You will examine how to use a power series to define the complex expontential function, and how to obtain Taylor series of rational and other functions of standard type, determining zeros and poles of given functions. You will also consider how to use Cauchy's Residue

You will develop an understanding of the major debates in European and some Anglo-American philosophy. You will look at the key texts by eighteenth and nineteenth-century philosophers Immanuel Kant and Georg Wilhelm Friedrich Hegel, examining the continuing significance of their ideas. You will consider the major epistemological, ethical and aesthetical issues their ideas raise, and the problems associated with the notion of modernity. You will also analyse the importance of the role of history

You will develop an understanding of how the rationalist and empiricist traditions in philosophy influence contemporary thought in the philosophy of mind. You will look at the continuing relevance of the mind-body problem to the question of what it is to be a human being and consider the connections between the analytic and European traditions in philosophy with respect to language, subjectivity, and the phenomenology of experience. You will also examine the importance of consciousness to contem

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.

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.

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.

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

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.