Physics and Astrophysics MPhys

Core modules:

Fundamental Physics and Mathematics I: Mechanics, Oscillations, Waves and Thermal Physics

This core module will give you an understanding of the fundamental physical principles, mathematical tools, and laboratory skills you'll use throughout your degree. 

You'll learn about key physical principles, such as Newton's laws, linear and rotational equations of motion, the wave equation, the laws of thermodynamics, and heat transfer. 

You'll also learn about the linear algebra and calculus that underpins these principles, covering differentiation and integration, complex numbers, matrices and differential equations. 

You'll build a strong foundation in laboratory techniques through hands-on experience. You'll learn how to build and use DC circuits and set up experiments to test principles, including kinematic motion, standing and travelling waves, heat engines, and diffraction.

40 credits

Fundamental Physics and Mathematics II: Electricity, Magnetism and Quantum Physics

In this core module you'll further develop your knowledge of the fundamental physical principles, mathematical tools and laboratory skills needed for your degree.

You'll explore topics across electricity, magnetism and quantum physics, such as electric potentials and fields, electrical circuits, magnetic fields, the Lorentz force, the photo-electric effect, and the quantum wave function. You'll also learn to describe these phenomena through vector calculus and probability theory.

You'll gain hands-on experience of conducting laboratory work. You'll test various aspects of physical principles, including measuring and mapping electric and magnetic fields, and building and using AC circuits.

40 credits

Mapping the Night Sky: the Astronomer's Toolbox

In this core module you'll learn foundational skills and techniques that will support your studies as an astrophysicist,  covering essentials such as astronomical observation, positional astronomy, and computing.

You'll learn how to navigate the night sky, plan observations, and use our telescopes. You'll learn how to import and analyse astronomical data in Python, and present these results professionally. You'll also learn how to be effective at self study, conduct and report on research projects ethically, and integrate AI responsibly. 

You'll employ general problem-solving techniques that are routinely used in physics, including dimensional analysis, making approximations, and checking your calculations using order-of-magnitude estimations, limiting behaviour, and symmetry considerations.

Through employability workshops, you'll receive guidance on how to showcase your achievements effectively to help secure projects, placements, and graduate opportunities.

20 credits

Introduction to Astrophysics

This module will provide you with an understanding of important physical concepts and techniques involved in astrophysics, with an emphasis on how fundamental results can be derived from observations.

You'll apply basic physical principles to astrophysical problems, exploring topics such as solar systems, the properties and evolution of stars and galaxies, as well as the origins and fate of the Universe.

20 credits

Core modules:

Fundamental Physics and Mathematics III

This module further develops the foundations of physics and mathematics that you need in your degree. 

You'll learn special relativity and thermal physics, as well as the mathematical foundations and applications of Fourier analysis and ordinary and partial differential equations. 

Through lab sessions, you'll refine your practical skills, learning how to conduct structured physics experiments. 

If you are on our Theoretical Physics programmes, you'll model physical systems with symbolic computer maths (Mathematica), instead of doing experimental labs.

40 credits

Fundamental Physics and Mathematics IV

This module further develops the foundations of physics and mathematics that you need in your degree. 

You'll learn quantum mechanics and electromagnetism, and how to apply these in physical problems. You'll also be introduced to solids and subatomic physics.

Through lab sessions, you'll refine your practical skills, learning how to conduct open-ended physics experiments. 

If you are on our Theoretical Physics programmes, you'll explore more advanced problems and techniques in theoretical physics, instead of doing experimental labs.

40 credits

Observational Astronomy

This module builds upon observational astronomy content from your first year, equipping you with the skills and understanding to plan, obtain and analyse observational data of astronomical objects. 

You'll learn how astronomical observatories work and the technology that underpins them. You'll also learn how to use the data obtained to understand the physical properties of astronomical objects.

20 credits

Stars and Galaxies

This module explores the properties and underlying physics of stars and galaxies. 

You'll learn how observational data is used to explain astrophysical phenomena, and make physical models of these systems. 

We'll equip you with deeper knowledge of stellar and galactic astrophysics in preparation for research-level topics, and provide opportunities to enhance your skills in communication, physics modelling and problem solving.

20 credits

Core modules:

Mathematical and Physical Sciences Projects and Professional Skills

Through this module you'll hone the skills and knowledge required of a graduate-level professional.

You'll undertake extended project work, which will include relating project work to the literature, setting project aims and objectives, planning and carrying out the work, and reporting it using disciplinary conventions.

You'll investigate how your academic studies relate to either research, society, or industry. You'll develop an understanding of where your degree could lead you and reflect on your career ambitions.You'll also undertake activities to develop the professional skills needed to complete applications for employment or further study.

40 credits

Nebular Astrophysics and Stellar Atmospheres

This module will explore how the spectral lines of ionised nebulae arise from the underlying physics of hydrogen, helium and complex atoms, such as trace metals, and how they are affected by interstellar gas and dust.You'll discover how the interaction between radiation and matter shapes stellar atmospheres, and how you can use the width of spectral lines to study the structure of stellar atmospheres.

20 credits

Atomic and Particle Physics

This module explores the foundation of particle atomic and particle physics. 

You'll learn about the Schrödinger equation for the hydrogen atom and the atomic wave functions that emerge from it. You'll then explore the atomic selection rules, spectral fine structure and the effects of external fields. 

You'll gain an understanding of selected multi-electron atoms and the concept of stimulated emission, which is central to the operation of lasers. 

You'll explore the fundamental interactions between particles and how to do relativistic scattering calculations and using Feynman diagrams. 

You'll also learn about weak interactions and beta decay, as well as high energy electroweak unification, strong interactions and binding quarks into hadrons.

20 credits

Dark Matter and Cosmology

This module will develop your understanding of the Universe as its own entity, and focus on the evidence for and nature of Dark Matter.

You'll learn about key epochs during the history of the Universe. You'll also explore how the contents of the Universe affect its dynamic evolution, and how precision observational cosmology has enabled us to constrain the main components of the Universe.

One of the most important of these main components is Dark Matter, which we'll explore in detail. You'll encounter the overwhelming observational evidence for the existence of Dark Matter, explore what scientists believe it most likely to be, and learn what is happening in the world-wide search for Dark Matter particles, in which Sheffield is closely involved.

20 credits

Optional modules:

You'll take 20 credits (one module) from this group.

Solid State and Statistical Physics

This module explores the behaviour of many-body systems in physics such as quantum gases, metals, and organic and inorganic semiconductors. You'll learn how their physical properties, like conductivity and magnetisation, depend on temperature and on their underlying structure. 

You'll discover how electrons and holes in semiconductors lead to material properties that are fundamental to modern electronics and computing. 

You'll also develop an understanding of how the arrow of time arises from entropy and how phase transitions work.

20 credits

Planets and Astrobiology

This module investigates the huge question of whether there is life elsewhere, and what that life might be like.

You'll discover what we know about planets and planetary systems as homes for life, with a focus on our own Solar System, as it is the one we know most about. 

Together, we'll explore what we know about the origin and evolution of life on Earth as our only (current) example of life. We'll critically examine ideas about the frequency of life, advanced life, and technological civilisations in the universe.

20 credits

Biological and Soft Matter Physics

This module will develop your understanding of the materials with properties between those of solids and liquids, known as 'soft matter'. These include plastics, gels, soaps, foods, biological cells and tissues.

You'll learn which physical principles govern the behaviour of these complex materials. You'll also explore molecules essential to life, such as proteins and DNA, and materials key to technology, such as polymers.

We'll cover the experimental measurements and imaging techniques that are used to investigate soft matter and biological systems.

20 credits

Machine Learning

This module provides a practical toolkit for modelling and understanding complex datasets by integrating modern AI tools. 

Bridging computer science, statistics, and physics, you'll learn to implement industry-standard algorithms, from linear models to deep neural networks, using Python and modern libraries like Keras and scikit-learn.

You'll not only learn to code, but also effectively co-pilot with AI agents for debugging and code generation, preparing you for the future of technical work.

We'll focus on intuition and implementation. You'll learn to understand when to use a method, how to implement it, and why it works, enabling you to solve real-world problems in science, finance, and business.

20 credits

Mathematical Physics and Analytical Dynamics

This module will provide a deep dive into the core mathematical tools that we use in physics.

You'll learn how to set up a mathematical model of a physics problem using the variational principle and Lagrangian dynamics, and solve some of the resulting differential equations. 

You'll discover how linear finite and infinite dimensional spaces of functions and operators are used in physics, particularly in quantum mechanics but also in other areas of mathematical physics.

You'll also explore how to work with complex functions, which are indispensable for classical and quantum field theories.

20 credits

Quantum Theory and Electrodynamics

This module develops your understanding of quantum theory from the five postulates to operator algebras, uncertainty relations and entanglement theory.

You'll explore the structure of electrodynamics as a relativistic theory, uncovering a special symmetry called gauge invariance and exploring the behaviour of electromagnetic fields at boundaries and in different materials.

20 credits

Core modules:

- Research Project (60 credits)
- Star Formation and Evolution (15 credits)
- Galaxy Formation and Evolution (15 credits)

Optional modules:

You'll take 30 credits (two modules) from this group.

Fundamental Physics from Symmetries

In this module you will learn how symmetries under rotations, translations, and Lorentz boosts lead to the mathematical structure of the fundamental physical theories of Nature. We will develop the formalism of Lagrangian densities and prove Noether's theorem that links symmetries to physical conservation laws. We introduce Lie theory, which provides an elegant framework for capturing the consequences of symmetries for our physical theories. You will apply this framework to examples that include scalar fields such as the Higgs field, vector fields such as Yang-Mills fields with additional gauge symmetries, and classical Dirac spinor fields. Finally, you will explore the role of symmetry breaking.

15 credits

General Relativity

Einstein's theory of General Relativity is one of the most accurate and successful theories in physics, and stands as one of the foundational pillars of modern physics. In this module you will learn how General Relativity is built up, starting with the Equivalence Principle and how it leads to the fundamental laws of General Relativity, namely the Einstein equations. You will study the solutions to these equations, including Schwartzschild black holes, the Robertson-Walker expanding universe and gravitational waves. You will study aspects of differential geometry, which is the mathematical framework of General Relativity, and encounter objects such as the metric tensor and the Riemann curvature tensor. Finally, you will learn about the two predictions of General Relativity that convinced the world that the theory is, in essence, correct: the bending of light around stars and the anomalous precession of Mercury's orbit.

15 credits

- The Standard Model of Particle Physics (15 credits)
- Scientific Computing (15 credits)
- Nuclear Astrophysics (15 credits)
- Quantum Computing (15 credits)
- Enterprise and Innovation (15 credits)