Physics with Philosophy

Core Modules

Year 1

• Mathematics for Scientists 1

  In this module you will develop an understanding of how to solve problems involving one variable (either real or complex) and differentiate and integrate simple functions. You will learn how to use vector algebra and geometry and how to use the common probability distributions.

• Mathematics for Scientists 2

  In this module you will develop an understanding of how to solve problems involving more than one variable. You will learn how to use matrices and solves eigenvalue problems, and how to manipulate vector differential operators, including gradient, divergence and curl. You will also consider their physical significance and the theorems of Gauss and Stokes.

• Scientific Skills

  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.

• Classical Mechanics

  In this module you will develop an understanding of how to apply the techniques 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 rigid bodies. You will also examine the various techniques of physical analysis to solve problems, such as force diagrams and conservation principles.

• 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 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.

• Problems of Knowledge

  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 better knowers?; is there such a thing as collective knowledge?; do animals have knowledge?; is there such a thing as knowledge at all?

   

• Philosophical Methods

  On this module you’ll learn to reason critically: to distinguish between bad arguments and good ones, supporting evidence from mere distraction. Everybody has the basic ability to do this, but it is not always as developed we need it to be: and in this complex world being able to present your point forcefully and rationally is vitally important. The aim of this module is to help you develop the skills required to get the most out of your degree.

Year 2

• Mathematical Methods

  In this module you will develop an understanding of the mathematical representation of physical problems, and the physical interpretation of mathematical equations. You will study both ordinary and partial differential equations, and learn about their properties:  linear, order, homogeneous and inhomogeneous. You will learn to solve partial differential equations using the separation of variables method, and solve Laplace's equation in Cartesian, polar and spherical coordinates.  Solutions will involve application of sines and cosines, Legendre polynomials, Bessel's equation, and the Sturm–Liouville theorem. In addition, you will become familiar with the Dirac delta function,  the Gamma function, and Fourier transforms. 

• 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 photons. You will also consider the quantum theory of solids, including energy bands and the Bloch theorem, as well as exploring fermiology, intrinsic and extrinsic semiconductors, and magnetism.

• 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.

• 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.

• Classical and Statistical Thermodynamics

  In this module you will develop an understanding of thermal 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.

• Fields and Waves

  In this module you will develop an understanding of how electric and magnetic fields are generated from static charges and constant currents flowing through wires. You will derive the properties of capacitors and inductors from first principles, and you will learn how to analyse simple circuits. You will use complex numbers to describe damped harmonic oscillations, and the motion of transverse and longitudinal waves.

• Kant

  In this module you’ll look at key texts by Immanuel Kant, which are the foundation of Modern European Philosophy. These texts raise questions concerning the status of human knowledge and the nature and justification of human action that have concerned philosophers ever since. The module considers Kant's Critique of Pure Reason and the core theme is how philosophy responds to the situation in which it can no longer rely on theological support for its claims about truth and morality. The questions raised by the module recur in most of the main Philosophy courses studied from the second year onwards.

• Mind and World

  In this module 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 contemporary debates in philosophy, psychology and cognitive science.

Year 3

• Optics

  In this module you develop an understanding of the properties of light, starting from Maxwell’s equations. You will look at optical phenomena such as refraction, diffraction and interference, and how they are exploited in modern applications, from virtual reality headsets to the detection of gravitational waves. You will also examine masers and lasers, and their usage in optical imaging and image processing.

• Electromagnetism

  In this module you will develop an understanding of how James Clerk Maxwell unified all known electrical and magnetic effects with just four equations, providing Einstein’s motivation for developing the special theory of relativity, explaining light as an electromagnetic phenomenon, and predicting the electromagnetic spectrum. You examine these equations and their consequences, looking at how Maxwell’s work underpins all of modern physics and technology. You will also consider how electromagnetism provides the paradigm for the study of all other forces in nature.

• Advanced Skills in Physics

  This module builds on skills developed in the second year to prepare you for the final year project and beyond. You will plan and carry out three assignments: the first introduces advanced data analysis techniques, and the second is a group project.  Through the mini-project, you will be introduced to some of the research activities within the Department and to the methods of working within the groups. There are opportunities to practise important skills such as report writing and giving oral presentations. 

• Experimental or Theoretical Project

  This module aims to provide the high point of the three-year physics degree, which enables you to use your scientific knowledge, your abilities to plan and execute an extended experimental or theoretical investigation, and use all your communication skills to describe the results of your project. You will understand some of the techniques of research, including the presentation of results. You may choose your project in consultation with a member of staff, and the subject of the project may be in physics, electronics or astrophysics, and may be experimental or theoretical in emphasis.

Optional Modules

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

Year 1

• Introduction to Logic

  In this module 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 the broader significance of findings in logic to philosophical inquiry.

• Mind and Consciousness

  In this module 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 problem of zombie and bat consciousness.

• Introduction to Aesthetics and Morals

  In this module 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.

Year 2

• All modules are core

Year 3

• Energy and Climate Science

  This module aims to give students an overall view of the generation, transmission, storage and usage of energy (conventional and renewables). This course also examines the relationship between energy production, politics, economics and environmental pollution, particularly as regards to global warming.
  Course Content:
  Generation, transmission, storage and supply of energy. Conventional energy sources: fossil fuels and nuclear fission. Renewable sources of energy: fusion, hydroelectric, solar-thermal and solar-electric, wind, wave and tidal. Physics of the climate: energy and radiation, greenhouse effect, climate models, global warming. Experimental methods for measuring global temperatures and greenhouse gas emissions. Choice of an energy source for the UK taking into account technical, economic, political and environmental considerations.

• Advanced Classical Physics

  This module introduces you to advanced topics and methods in classical physics (including mechanics, electromagnetism and relativity). You will cover the Calculus of Variations including the Euler-Lagrange equation, constraints and the method of Lagrange multipliers; non-relativistic classical physics through the principle of stationary action and Lagrangian mechanics, integration of the equation of motion in one dimension, motion in a non-inertial reference frame, Hamiltonian mechanics, symmetries, constants of motion and conservation laws, canonical transformations and Liouville's theorem; the module will end with a dive into relativitstic physics covering the principle of relativity and relativistic formalism, Lagrangian of a charged particle in an electromagnetic field, equations of motion of a charged paritcle in an EM field and gauge invariance, electromagnetic field tensor, relativistic invariants of the field, covariant formulation of the Lorentz force and Maxwell's equations.

• Further Mathematical Methods

  This module introduces you to the mathematical areas of complex analysis, matrix theory and linear transformations, and group theory, and enables you to apply related advanced mathematical formalisms and methods to formulate and solve physics problems. In the complex analysis section, you will cover holomorphic functions, power series, logarithms, isolated singular points, complex integration, Cauchy’s theorem and integral formula, Laurent series, Cauchy’s residue theorem, and applications of contour integration. For the matrix theory and linear transformations topic, you will cover the fundamentals of matrix theory, unitary diagonalisation, vector spaces and linear transformations, matrix representations, equivalence and similarity, inner product, norm, orthonormal bases, dual space and bra–ket notation. For the final chapter, you will cover the fundamentals of group theory, crystal lattice symmetries, Lie groups and Lie algebra, reducible and irreducible group representations.

• Nonlinear Dynamical Systems

  This module introduces you to the fundamentals of the analysis of non-linear dynamical systems and, in particular, investigates whether the behaviour of a non-linear system can be predicted from the corresponding linear system. You will cover systems of first-order linear differential equations, similarity types for matrices and their connection with linear systems, the classification of two-dimensional linear phase portraits with extension to three dimensions, non-linear differential equations through Liapunov’s stability analysis, periodic solutions and limit cycles, and the Poincaré–Bendixson theorem, as well as applications to problems from physics, biology and economics. You will also cover non-linear difference equations, Poincaré surface of section, stability of critical points, and routes to chaos.

• Signal Recovery and Handling
• Quantum Theory

  This module introduces a more advanced level of quantum theory than experienced in earlier years. Here you will understand and use the bra–ket (Dirac) notation for quantum states, understand and use the vector space and matrix representation of operator formalism, expansion of any states in terms of some complete set, the ladder operator approach to the harmonic oscillator, and generalise the definition of angular momentum to include spin and solve the generalised angular momentum eigenvalue problem employing raising and lowering operator techniques. You will cover the properties of spin-1/2 systems and use the Pauli matrices to solve simple problems, understand the concept and consequences of identical particles for fermions and bosons, and state the rules for the addition of angular momenta and outline the underlying general mathematical arguments, applying them in particular to two spin-1/2 particles. Finally, you will formulate first-order and second-order time-independent perturbation theory and apply it to some simple examples; formulate the variational and WKB methods and apply them to some simple systems; and formulate first-order and second-order time-dependent perturbation theory. From this, you will show, as an example, how it can lead to Fermi's Golden Rule.

• Particle Physics

  In this module you will develop an understanding of the physics of elementary particles and their interactions, as well as experimental techniques to study these.  Topics include the simple quark model, leptons and lepton numbers, strange particles, heavy quarks,  quantum numbers, electroweak unification, W and Z bosons, the Higgs mechanism, and QCD.  Energy loss processes, particle detectors, accelerators, and spin-off applications will also be studied. Extended topics explore deep inelastic scattering, supersymmetry, beyond the Standard Model, dark matter, neutrino oscillations, and applications to industry and medicine. 

• Metals and Semiconductors

  This module covers the theory of electrons in metals and semiconductors, focusing on electronic structure, transport, and collective excitations. Topics include electrons in periodic potentials, nearly free and tight-binding models, bandwidth, effective mass, holes, and band structures of materials such as Si, Ge and GaAs. It also examines intrinsic and extrinsic semiconductors, charge transport via the Drude and semiclassical models, and electron response to electric and magnetic fields. Finally, it explores optical properties, particle–hole excitations, plasma oscillations, and screening in metals.

• Superconductivity and Magnetism
• Frontiers of Metrology
• General Relativity and Cosmology

  In this module you will develop an understanding of the core principles and mathematics of general relativity. You will learn how gravity arises from the curvature of spacetime, and explore the equivalence principle and tensor analysis in flat and curved spaces. You will study Einstein’s field equations in both vacuum and matter-filled spacetimes, and apply them to phenomena such as gravitational redshift, light bending, black holes, cosmology and gravitational waves. You will also gain practical experience in manipulating tensors and solving equations of motion in simple gravitational systems.

• Particle Astrophysics

  In this module you will develop an understanding of the connection between particle physics and cosmology. You will review the Standard Model and learn how to use Feynman diagrams to estimate cross-sections and decay rates. You will study the early universe through the Friedmann equations, exploring topics such as primordial nucleosynthesis, the cosmic microwave background, and the matter–antimatter imbalance. You will also examine the role of dark matter and inflation in cosmic evolution. Additional topics include the origin and detection of cosmic rays and the behaviour of neutrinos in astrophysical environments. You will gain experience in making order-of-magnitude estimates and solving problems related to processes in the early universe.

• Philosophy Dissertation

  You will demonstrate your skills as an independent learner by embarking upon a substantial piece of written work of between 8,000 and 10,000 words in length. You will be guided by a dissertation supervisor, but will choose your own topic, approach, and philosophical sources.

• Modern European Philosophy 1: Husserl to Heidegger
• Modern European Philosophy 2: Critical Theory and Hermeneutics
• Philosophy and the Arts
• The Varieties of Scepticism
• The Philosophy of Religion
• Philosophy and Literature
• The Good Life in Ancient Philosophy
• Atomic Physics

  On this module you'll learn to apply the principles of quantum mechanics (developing on from courses PH2210, PH3210) to many electron atomic systems; To build quantitative models to understand and predict the behaviour of multi-electron atoms, which were introduced qualitatively in PH1920; To understand experimental spectroscopy techniques and compare with model predictions.
  Course Content: Atomic transitions and selection rules. Transitions rates. Natural broadening of transition lines. Coupling to a continuum. Fermi golden rule. Doppler and collisional broadening.Magnetic properties of the atom. Magnetic dipole associated to orbital motion and to spin. Zeeman and Stark effects. Relativistic corrections and fine structure, in particular spin orbit interaction. Effect of the nucleus spin: hyperfine structure. Atomic clocks. Metrology of the hydrogen atom. Multi electron atoms. Effect of exchange interaction. Example of He.Effect of Coulomb interactions, mean field approximation (Hartree), self-consistent potential. Applications to the ground state of the multi-electron atom. Applications to the excited states of the multi-electron atom: optical transitions and Xray transitions.Spectroscopic notation. Multiplets. Landé interval rule.Introduction of the quantum model of the interaction between light and matter. Coupling to a quantized mode. Applications to quantum optics.Extension of atomic physics concepts to nuclear and molecular physics