Mathematics and Physics

The MSci Mathematics and Physics degree focuses on mathematical rigour and theoretical aspects of physics taught by discipline experts. Mathematics and Physics are closely interlinked subjects, with each providing many fascinating insights into the other. The course provides a parallel track of theoretical physics taught by the Physics Department and mathematical physics and applied mathematics options taught by the Mathematics Department which culminates in the opportunity to study particle theory, superstrings, modern theories of electronic structure, and vibrational properties of materials including superconductivity in Year 4.

The first year lays the foundation in physics theory, mathematical skills and laboratory skills that are needed to tackle more complex content later in the course. As the course through progresses the level of theoretical content increases, extending your knowledge in areas such as electromagnetism, quantum mechanics, particle theory, and advanced mathematical theory. The MSci has the same course structure as the BSc with an equal balance of Mathematics and Physics to provide an essential foundation. From the third year, the MSci introduces a wider range of modules that are more closely aligned to real-world issues and an advanced project in the final year. You can also apply for a one-year work placement, increasing the course from four years to five or the potential to substitute the existing Year 3 with a Year Abroad. The Institute of Physics recognize this degree.

Course structure

Year 1

Core modules:

Calculus builds on ideas of differentiation and integration in A-level mathematics, beginning with functions of a single variable and moving on to functions of several variables. Topics include methods of solving ordinary and partial differential equations, and an introduction to Fourier Series and Fourier transforms.

Linear Algebra presents mathematical ideas, techniques in linear algebra and develops the geometric intuition and familiarity with vector methods in preparation for more challenging material later in the course.

Analysis aims to provide an understanding of real and complex number systems, and to rigorously develop the calculus of functions of a single variable from basic principles.

Foundations of Physics introduces classical aspects of wave phenomena and electromagnetism, as well as basic concepts in Newtonian mechanics, quantum mechanics, special relativity and optical physics.

Discovery Skills in Physics provides a practical introduction to laboratory skills development with particular emphasis on measurement uncertainty, data analysis and written and oral communication skills. It also includes an introduction to programming.

Year 2

Core modules:

Complex Analysis introduces the theory of complex analysis through the study of complex differentiation; conformal mappings; metric spaces; series and uniform convergence; contour integrals and calculus of residues; and applications.

Analysis in Many Variables provides an understanding of calculus in more than one dimension, together with an understanding of, and facility with, the methods of vector calculus. It also explores the application of these ideas to a range of forms of integration and to solutions of a range of classical partial differential equations.

Foundations of Physics A develops your knowledge of quantum mechanics and electromagnetism. You will learn to apply the principles of physics to predictable and unpredictable problems and produce a well-structured solution, with clear reasoning and appropriate presentation.

Foundations of Physics B extends your knowledge of thermodynamics, condensed matter physics and optics.

EITHER

Mathematical Physics provides a mathematical appreciation of the conceptual framework of classical and quantum physics by following the development of mechanics after Newton's laws to the introduction of quantum mechanics.

OR

Theoretical Physics from a Physics perspective develops an appreciation of the Lagrangian and Hamiltonian formulations of classical mechanics; an ability to describe the rotational motion of a rigid body; describe elements of quantum mechanics in a rigorous mathematical way and to manipulate them at the operator level.

In recent years, optional modules have included:

• Algebra
• Numerical Analysis
• Stars and Galaxies
• Laboratory Skills and Electronics.

Year 3 (Year 4 if undertaking a placement)

Core modules:

Foundations of Physics A further develops your knowledge to include quantum mechanics and nuclear and particle physics. You will learn to apply the principles of physics to complex problems and produce a well-structured solution, with clear reasoning and appropriate presentation.

Theoretical Physics* introduces more advanced methods in electromagnetism that can be used to investigate more realistic problems and concepts. It also builds your quantum mechanics knowledge and addressing further applications and conceptual issues of measurement and interpretation.

* - required for students who took Theoretical Physics in Year 2

In recent years, optional modules have included:

• Analysis
• Differential Geometry
• Fluid Mechanics
• Solitons
• Topology
• Quantum Computing
• Geometry of Mathematical Physics
• Foundations of Physics B
• Computing Project
• Modern Atomic and Optical Physics
• Team Project
• Planets and Cosmology
• Science Enterprise.

Year 4

Core modules:

Either Project in Physics or a Mathematics Project is undertaken which provides experience of work in a research environment on a topic at the forefront of developments in a branch of either physics, mathematics, mathematical physics, theoretical physics or astronomy, and develops transferable skills for the oral and written presentation of research. The project can be carried out in one of the Mathematics or Physics research groups.

In recent years, optional modules have included:

• General Relativity
• Advanced Quantum Theory
• Superstrings
• Geophysical and Astrophysical Fluids
• Statistical Mechanics
• Advanced Theoretical Physics
• Atoms, Lasers and Qubits
• Particle Theory
• Theoretical Astrophysics.

Placement