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MSciMathematics and Physics

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Overview

This intensive four-year programme allows you to explore the logical interplay between mathematics and physics and split your time equally between the two. It is accredited by the Institute of Physics. Mathematics has gone hand-in-glove with physics since the time of Newton. Physics is widely conceived as the most fundamental of sciences in that all other branches can be said to derive from its theories and principles, but it couldn’t be studied without a strong working knowledge and appreciation of mathematics. As well as covering all the core theories and principles of physics, you will delve deep into the world of abstract mathematical ideas and explore their wide range of applications in the world around us.

You will be welcomed into a vibrant, friendly learning environment and guided by world-class researchers and teachers who offer generous office hours. While the joint degree is arguably more challenging than a single honours degree, it will equip you with an enviable set of skills to set you apart in the world of work. By combining physics and mathematics you will have the opportunity to approach mathematics from a more rigorous point of view, giving you a deeper understanding of the theoretical aspects of core physics topics such as quantum theory and general relativity. Because the first year of our BSc and MSci programmes is the same, you will have the option of transferring onto the second year of the three-year BSc programme if you prefer.

Our MSci course covers all of the core topics of a physics degree, although some of the laboratory components from the physics degree will be reduced to make way for the mathematics teaching. In years 3 and 4, you will have the flexibility to specialise more in physics or mathematics based study and research, according to your own interests. In your final year you will also have the opportunity to take your chosen area to a higher level through a major project and research review.

Our Department of Mathematics is internationally renowned for its work in pure mathematics, information security, statistics and theoretical physics, while our Department of Physics is one of the most respected centres for physics teaching and research in the UK, boasting cutting-edge laboratories and research facilities and dedicated technical support. There is an astronomical dome on the roof of the department and thanks to our parkland location, away from the big city, our telescopes enjoy the best observational capacities of the University of London campuses.

Programme structure

Year 1

Mathematics: Calculus
In this module, 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 forms and solve them.

Mathematics: Functions of Several Variables
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.

Mathematics: Number Systems
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 comon 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.

Mathematics: Matrix Algebra
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.

Physics: Scientific Skills 1
In this module you will develop an understanding of good practices in the laboratory. You will keep a notebook, recording experimental work as you do it. You will set up an experiment from a script, and carry out and record measurements. You will learn how to analyse data and plot graphs using a computer package, and present results and conclusions including error estimations from your experiments.

Physics: Classical Mechanics
In this module you will develop an understanding of how to apply the techques and formulae of mathematical analysis, in particular the use of vectors and calculus, to solve problems in classical mechanics. You will look at statics, dynamics and kinematics as applied to linear and rigidy bodies. You will also examine the various techniques of physical analysis to solve problems, such as force diagrams and conservation principles.

Physics: Classical Matter
In this module you will develop an understanding of the macroscopic properties of the various states of matter, looking at elementary ideas such as ideal gases, internal energy and heat capacity. Using classical models of thermodynamics, you will examine gases, liquids, solids, and the transitions between these states, considering phase equilibrium, the van der Waals equation and the liquefaction of gases. You will also examine other states of matter, including polymers, colloids, liquid crystals and plasmas.

Physics: Physics of the Universe
In this module you will develop an understanding of the building blocks of fundamental physics. You will look at Einstein’s special theory of relativity, considering time-dilation and length contraction, the basics of quantum mechanics, for example wave-particle duality, and the Schrödinger equation. You will also examine concepts in astrophysics such as the Big Bang theory and how the Universe came to be the way we observe it today.

Year 2

Mathematics: Vector Analysis and Fluids
In this module you will develop an understanding of the concepts of scalar and vector fields. You examine how vector calculus is used to define general coordinate systems and in differential geometry. You will learn how to solve simple partial differential equations by separating variables, and become familiar with how these concepts can be appield in the field of dynamics of inviscid fluids.

Mathematics: Ordinary Differential Equations and Fourier Analysis
In this module you will develop an understanding of the concepts arising when the boundary conditions of a differential equation involve two points. You will look at eingenvalues and eingenfunctions in trigonometric differenital equations, and determine the Fourier series for a periodic function. You will learn how to manipulate the Dirac delta-function and apply the Fourier transform. You will also examine how to solve differential equations where the coefficients are variable.

Physics: Scientific Computing Skills
In this module you will develop an understanding of how computers are used in modern science for data analysis and visualisation. You will be introduced to the intuitive programming language, Python, and looking at the basics of numerical calculation. You will examine the usage of arrays and matrices, how to plot and visualise data, how to evaluate simple and complex expressions, how to sample using the Monte Carlo methods, and how to solve linear equations.

Physics: Quantum Mechanics
In this module you will develop an understanding of quantum mechanics and its role in and atomic, nuclear, particle and condensed matter physics. You will look at the wave nature of matter and the probabilistic nature of microscopic phenomena. You will learn how to use the key equation of quantum mechanics to describe fundamental phenomena, such as energy quantisation and quantum tunnelling. You will examine the principles of quantum mechanics, their physical consequences, and applications, considering the nature of harmonic oscillator systems and hydrogen atoms.

Physics: Classical and Statistical Thermodynamics
In this module you will develop an understanding of themal physics and elementary quantum mechanics. You will look at the thermodynamic properties of an ideal gas, examining the solutions of Schrödinger’s equation for particles in a box, and phenomena such as negative temperature, superfluidity and superconductivity. You will also consider the thermodynamic equilibrium process, entropy in thermo-dynamics, and black-body radiation.

Physics: The Solid State
In this module you will develop an understanding of the physical properties of solids. You will look at their structure and symmetry, concepts of dislocation and plastic deformation, and the electrical characteristics of metals, alloys and semiconductors. You will examine methods of probing solids and x-ray diffraction, and the thermal properties of phonons. You will also consider the quantum theory of solids, including energy bands and the Bloch thorem, as well as exploring fermiology, intrinsic and extrinsic semiconductors, and magnetism.

Year 3

Physics: Optics
Physics: Atomic and Nuclear Physics
Physics: Experimental or Theoretical Project
Physics: Electromagnetic Theory
Mathematics: Non-Linear Phenomena and Chaos

Year 4

Physics: Research Review

Optional modules

In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.

Career opportunities

With a masters-level qualification in Mathematics and Physics you will be in strong demand for your advanced understanding of the theoretical and practical aspects of both disciplines, as well as for your wide range of transferrable skills, such as data handling and analysis, numeracy, logical thinking, technical skills and creative problem solving abilities. You will be particularly well placed to work at a high level in research or industry and take advantage of a strong and lucrative jobs market.

Graduate employment levels for physicists are amongst the highest of any subject and more than 90% of our mathematics and physics graduates are in full-time employment or further study within six months of graduation. Our Department of Mathematics is also part of the School of Mathematics and Information Security and enjoys particularly strong ties with the information security sector as well as with industry at large. In physics we benefit from strong collaborative ties with international projects and laboratories such as CERN, the National Physical Laboratory (NPL) and SNOLAB. We also offer an array of exciting postgraduate opportunities in mathematics or physics, or a combination of the two.

Recent mathematics and physics graduates have gone on to enjoy successful careers in a wide range of careers, including: aeronautics and other fields of engineering, scientific technical support, sales, finance and investments, management consultancy, software design, computer analysis and programming, accountancy, the civil service, teaching, actuarial science, risk analysis and scientific research. We have graduates working for organisations such as Lockheed Martin, St James’s Place, Qinetiq, the Bank of New York, Deutsche Bank, KPMG, Ernst & Young, the Ministry of Defence, the Department of Health, Logica, McLaren and TowersWatson, to name just a few.

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States