The ability to apply logic, reason and mathematics in the solution of problems is a core skill. Mathematics gives physics its predictive power and ability to abstract and generalise the laws of nature often into a few, relatively simple, equations. This module seeks to develop core knowledge and skills required for degree level physics especially in terms of mathematical modelling.

Physics is completely dependent on rigorous, scientific experiments in both the discovery of new phenomena and in the testing of physical hypothesis. To be an experimental physicist requires the ability to make accurate measurements of physical properties, to gain insight from the observation of natural phenomena, and to design and construct experiments that can discriminate between different hypotheses. This module will provide an environment in which these skills can be gained and will, in addition to training in basic skills, have a strong emphasis of the creative aspect of designing experiments.

A part aim for this module is to enable students to become aware of and develop their academic, professional and personal skills through Personal Best. Personal Best is a development programme available to all students at Loughborough University.

As with all science and engineering disciplines, computing has become part of the core toolset of the professional physicist. Through problem solving, this module introduces its use for modelling and simulation of physical systems to students of all levels, regardless of computational background. It aims to introduce good programming practice and develop skills in scientific computation.

Good programming practice is emphasised throughout the module so that students should begin to appreciate the discipline of programming beyond that of developing simulations of simple physical systems. By the end of the module students should be equipped with the skills so that they can make meaningful progress on substantive problems that add real value to current technological problems.

The aim is to equip students with the necessary skills and knowledge to effectively utilise computational tools for solving complex problems in physics, while instilling ethical standards and best practices in coding to uphold integrity and reliability in scientific research.

The aims of this module are:

• to introduce the notion of convergence as this applies to sequences and series
• to introduce the notion of continuous function of one real variable
• to provide a firm basis for future modules in which the idea of convergence and continuity is used
• to help students recognize the necessity and power of rigorous argument

The two key aims of this module are:

• To introduce classical and analytical mechanics and some of the foundational principles of modern physics.
• To introduce physics thinking, the world view of the physicist and their problem solving approaches.

The students will gain knowledge in concepts in classical mechanics and experience in problem-solving. They will use foundational ideas and principles such as the principle of least action.

Skills range from using vectors to represent a system and applying Newton's laws, through to determining and analysing the equations of motion of a system using analytical mechanics and Noether's theorem.

The student should be able to use these ideas and principles to begin to be able to set up and solve models to better understand physical systems within the area of classical mechanics thus providing a strong foundation for the modules to be studied later in the programme.

The aims of this module are:

• to give a rigorous introduction to the analytical theory underpinning calculus for functions of one real variable
• to develop the basic ideas of real analysis in several variables

This module aims to provide a comprehensive introduction to electromagnetic theory, fields and special relativity, providing students a solid foundation in both conceptual understanding and analytical problem-solving skills. It emphasises core principles, such as the unification of electric and magnetic fields, enabling students to apply electromagnetic concepts to topics in modern physics and technology.

The aim of this module is to equip students with mathematical concepts and methods applicable to theoretical physics.

Quantum mechanics is foundational to modern physics and technology, underpinning advancements in fields like quantum computing and materials science. It challenges classical notions of reality with concepts like entanglement and superposition, offering deep insights into the nature of the universe. Studying quantum mechanics is crucial for innovation and research, equipping individuals with the mathematical and physical skills needed to understand nature and contribute and create emerging and future technologies.

Overall, the module aims to equip students with a solid foundation in quantum mechanics and its applications to a level where they are able to critically access recent advances in the subject. Our unique programme leverages students existing knowledge of Hamiltonian mechanics to provide deep insights into the similarities and differences between quantum and classical physics. We further provide a comprehensive introduction to the key contributions of quantum mechanics to science and problem solving in these areas. Topics include tunnelling, hydrogenic atoms as well as the chemical bond and molecular spectra.

Building on Physics Laboratory I, the central aim here is for the student to become a competent experimental physicist who not only understands good experimental technique but can also engineer laboratory equipment and instrumentation.

This module includes a mix of experimental practical sessions, computer workshops and seminars to develop the key skills of an experimental physicist and enhance our students' employability. Students will have the opportunity to design and build their own equipment, collect and analyse data, and link their experimental work to theories that they are investigating in other modules of their programme. Both semesters include a long form project spread over multiple weeks, and in Semester 2 this takes the form of a group project where students can choose their own area of interest.

The aim of this module is for students to become capable in the use of computers in the solution of physics-based problems and experience in a variety of software and language solutions. This involves developing an understanding of the application of computers not just for but also beyond numerical simulation for modelling and simulation related to real-world quantum physics, condensed matter and semiconductor device physics.

The aims of this module are:

• To give students some real understanding of mathematical concepts involved in higher dimensional calculus.
• To prove theorems involving functions in more than one dimension.

The aims of this module are to:

• Further develop aptitude in physics in areas pertinent to Loughborough research strengths. The focus here is on condensed matter and solid state physics.
• To apply notions of electromagnetism, quantum mechanics and statistical mechanics to explain the stability of matter and basic physical properties of metals, insulators and semiconductors starting from microscopic principles.
• To understand the principles of modern characterisation techniques of materials.
• To relate microscopic parameters to properties of solids, often based on the powerful method of dimensional analysis.
• To estimate numerical values of material quantities.
• To retrieve and make use of scientific resources, experimental data from papers and online databases.

The aim of this module is to give a grounding in the central ideas of topology, sufficient for the main applications in geometry, analysis and mathematical physics.

The aims of this module are to provide students with a comprehensive understanding of the fundamental principles of thermodynamics and statistical physics. This will include: developing a solid understanding of the laws of thermodynamics and their applications; exploring the microscopic origins of macroscopic thermodynamic properties through kinetic theory; analysing phase transitions and critical phenomena; introducing the principles of statistical physics and their role in describing thermal systems at the microscopic level.

In this module, students will dive into collaborative learning, partnering with industry experts to attempt to find solutions to real-world problems. In addition to advanced physics thinking and problem-solving methods, students will apply a variety of industry-standard systems engineering methodologies and practices used to accelerate productivity in complex tasks.

Tailored to each specialization, whether it's Mathematics and Physics, Physics with Theoretical Physics, or Engineering Physics, students will apply their unique skills to deliver a technical project equivalent to approximately 1500 hours of individual work (team size may vary).

This module aims to refine your research capabilities by engaging you in the application of scientific methods and advanced physics concepts to address complex and challenging open-ended problems. Through this rigorous process, you will have the opportunity to deeply explore a particular topic that interests you, showcasing your ability to innovate and think critically as expected of a skilled physicist.

The project encourages you to integrate and apply your specialized knowledge in any branch of physics to develop solutions that are both creative and scientifically viable. By doing so, you will practice and demonstrate a broad range of key competencies, from planning and executing a comprehensive research strategy to critically analysing and presenting your findings.

This module not only aims to bolster your understanding of how physics can be practically applied to produce insightful and impactful work, but also enhances other essential skills such as scientific writing, project management, and critical evaluation. These skills are vital for your future career in academia or industry, preparing you to tackle future challenges with confidence and expertise.

The aim of this module is to introduce the basic ideas and methods of the classical differential geometry of curves and surfaces in three-dimensional Euclidean space.

The aim of this module is to provide students with fundamental methods of classical number theory and some of its diverse applications.

The aim of this module is to introduce students to the notions and methods of the theory of dynamical systems with an emphasis on its applications.

The aims of this module are to introduce students to modern concepts and methods of combinatorics and graph theory.

Statistical mechanics main purpose is to study properties of assemblies of systems in terms of physical laws. Its applications include many problems in the fields of physics, biology, chemistry, economics, neuroscience.

In Advanced Statistical Mechanics we will develop the fundamental formalisms of equilibrium statistical mechanics from microscopic properties of systems (which include electrons, atoms, molecules and magnetic moments on the sites of lattices). Then we will relate them to the thermodynamic quantities such as internal energy, free energy, entropy, specific heat and related properties of both classical and quantum-mechanical systems. We will discuss real systems from classical and quantum world. The last part of the module will be devoted to phase transitions and their description.

The aims of this module are to introduce a variety of physical phenomena that occur in condensed matter physics and show how they can be understood in terms of microscopic processes.

A crystal interacts with the environment through its surface. Since surface atoms have fewer chemical bonds than atoms inside the crystal, surfaces may differ from bulk crystals in terms of crystallographic order, chemical composition, electronic and ionic conductivity, lattice vibrations, mechanical properties etc. Surfaces need to be studied and understood in order to work with catalysis, metal oxidation, corrosion, adhesion, crystal and thin film growth. Further, both the thin film growth technology and experimental surface science use high vacuum equipment. Thin films are used to manufacture semiconductor electronics, optoelectronics, magnetic data storage, nanostructures, optical, conductive and hard coatings.

You will study interactions of vapour molecules with surfaces, physics and technology of high vacuum, electron spectroscopy, physics of surface structures and diffraction of electrons, preparation of thin solid films and a range of further techniques that are available for the investigation of surfaces and thin films, for example scanning probe microscopy.

This module introduces the physics of the nucleus and nuclear radiations, with a view to understanding its applications and implications.

Over 99.9% of the visible mass in the universe arises from protons and neutrons - their interactions explain everything from why the stars shine to how we are able to mine helium on Earth.

Nuclear radiation is hazardous to humanity but was also a major driver of our evolution and finds applications in medical treatments and diagnostics. Fission reactors could spare mankind from the consequences of fossil fuel driven climate change, but these are underutilised. Meanwhile, we have been within 20 years of a working fusion reactor for the last 40 years. Alongside discussing the relevant physics, this module explores how historical choices and public perception shapes our use of nuclear energy.

The aims of the module are:

• To develop a range of skills within students and provide an early introduction to teaching for those interested in pursuing it, or a related field, as a career.
• To develop confidence and competence in communicating their subject.
• To provide opportunities to devise and develop science and mathematics projects and teaching methods appropriate to the age and ability of those the student is working with.

The aims of this module are:

• that students gain familiarity with linear ODEs with non-constant coefficients
• to introduce linear PDEs with constant and non-constant coefficients

The aims of this module are:

• To introduce rigorous mathematical tools which are useful in economics analysis.
• To give students a solid mathematical background in game theoretic models.

Photonics is the science of light. The Photonics module aims to equip students with a robust understanding of the fundamental physics underpinning the development and advancement of photonic technologies. It has keen focus on the physical principles at the base of the development that underpin sectors as diverse as healthcare, telecommunications, and defense and the links with classical and quantum background related to light. The vision is to provide the background of key aspects of technologies relevant for impactful careers in a sector that mirrors the innovation and resilience of the UK's £15.2 billion photonics economy.

The module is rooted in the exploration of electromagnetic energy and intensity, monochromatic fields, and complex formalism, and delves into the intricacies of field-matter interaction within both linear and nonlinear optics. Students will engage with core concepts such as, the complex refractive index, and the mechanisms of radiation-matter interaction, the principles underlying absorption and emission of light. By the end of this module, students will have acquired the essential background to understand the physics of photonic technology, the analytical tools to assess photonic systems, and the design skills to develop cutting-edge photonic devices and systems.

The aim of this module is to give students an overview of the uses of physics in medicine and allow them to gain an appreciation of how physics contributes to society. With a thorough grounding in the basics, students will be able to independently investigate more advanced techniques and draw informed conclusions about published health-related research. They will also be more prepared to go into healthcare or healthcare-adjacent careers.

The module aims to give a broad introduction to the theories and experiments of modern elementary particle physics, and to acquaint the student with the latest developments in the subject.

Particle phenomenology is introduced, followed by an exploration of the basic concepts of relativistic quantum mechanics, which predicts and explains anti-particles.

The fundamental interactions are described using Feynman diagrams, and Feynman's rules are used to convert these diagrams into amplitudes for scattering calculations to explain results from the big particle physics experiments.

The ideas of quantum field theory, which treats the field as the fundamental entity and all the particles and antiparticles as excitations of their respective fields, and which constitute the standard model of particle physics, are developed.

Qualitative concepts around symmetries and symmetry breaking are introduced to explain the pattern of particles that exist and the origin of the nucleons' mass, of which only 1% is explained by the explicit quark masses.

The module aims to provide students with a comprehensive understanding of the physics of semiconducting and magnetic nanodevices, with a particular emphasis on their applications in modern data storage and information processing technologies.