# Applied Mathematics and Physics (BSC HONS)

Program start date | Application deadline |

2024-09-01 | - |

## Program Overview

The BSc in Applied Mathematics and Physics combines the power of mathematics and the wonder of physics, providing students with a deep understanding of both fields. The program equips graduates with the skills to solve complex problems, foster critical thinking, and pursue careers in diverse fields such as science, technology, finance, and education. Through a blend of theoretical and practical learning, students develop a strong foundation in mathematics and physics, preparing them for success in a wide range of industries and research institutions.

## Program Outline

### Degree Overview

### Overview:

The BSc in Applied Mathematics and Physics is a unique, challenging, and intellectually stimulating program that combines the power of mathematics and the wonder of physics. This interdisciplinary degree provides students with a strong foundation in both fields, allowing them to explore the intriguing interaction between mathematics, physics, and the world around us.

### Objectives:

- To develop a deep understanding of the core principles of mathematics and physics.
- To equip students with the mathematical and computational skills to solve complex problems.
- To foster critical thinking, problem-solving, and analytical skills.
- To provide students with the knowledge and skills to pursue further study or embark on careers in diverse fields.

### Program Description:

The BSc in Applied Mathematics and Physics offers a balanced curriculum covering both theoretical and practical aspects of both disciplines. Students will delve into areas such as mechanics, electromagnetism, quantum theory, thermodynamics, statistical mechanics, linear algebra, calculus, and differential equations. The program features a blend of lectures, tutorials, practical sessions, and project work to ensure a well-rounded learning experience.

### Outline

### Program Content:

The BSc in Applied Mathematics and Physics covers a broad range of topics, including:

- Classical Mechanics: Newton's Laws, elasticity, simple harmonic motion, damped/forced/coupled oscillations, two-body dynamics, center of mass, reduced mass, collisions, rotational motion, torque, angular momentum, moment of inertia, central forces, gravitation, Kepler's Laws.
- Special Relativity: Lorentz transformations, length contraction/time dilation, paradoxes, velocity transformations, relativistic energy/momentum.
- Waves: wave equation, travelling waves, superposition, interference, beats, standing waves, dispersive waves, group velocity, Doppler effect.
- Electricity and Magnetism: static electric and magnetic fields, time-varying magnetic fields, motional emf, electrical circuit analysis (dc/ac theory, circuit transients).
- Light and Optics: electromagnetic waves, dispersion by prisms and diffraction gratings, interference, diffraction, polarization, X-rays.
- Quantum Theory: wave-particle duality, photoelectric effect, Bohr model, spectra of simple atoms, radioactive decay, fission/fusion, fundamental forces, Standard Model.
- Thermodynamics: kinetic theory of gases, Van der Waal's equation, first/second laws of thermodynamics, internal energy, heat capacity, entropy, thermodynamic engines, Carnot cycle, changes of state.
- Solid State: solids, crystal structure, bonding/potentials, thermal expansion, band structure of metals, insulators/semiconductors, electric/magnetic dipoles.
- Mathematical Methods: calculus, complex numbers, differential equations, linear algebra, vectors, matrices, eigenvalues/eigenvectors, Newtonian mechanics, curves in 3D, partial derivatives, Taylor expansions, vector calculus, line/surface/volume integrals, Green's theorem, Gauss's theorem, Stokes' theorem.
- Analysis: sequences/series, convergence, completeness, Bolzano-Weierstrass theorem, limits, continuity, differentiability, Rolle's theorem, Mean Value Theorem, L'Hopital's rule, inverse/implicit differentiation, applications of derivatives.

### Program Structure:

The BSc in Applied Mathematics and Physics is a 4-year program. The first two years provide a foundation in core mathematics and physics concepts. In the latter years, students can specialize in specific areas of interest by selecting elective modules.

### Course Schedule:

- Stage 1: Focuses on foundational mathematics and physics courses: Foundations of Physics, Scientific Skills, Mathematical Methods 1, Introduction to Algebra and Analysis.
- Stage 2: Students delve deeper into core concepts and encounter topics like Quantum and Statistical Physics, Electricity, Magnetism and Optics, Linear Algebra, Mathematical Methods 2.
- Stage 3: Students choose elective modules based on their interests and career aspirations. Examples include Astrophysics I, Classical Mechanics, Physics of the Solid State, Employability for Mathematics and Physics, Metric Spaces, Group Theory, Atomic and Nuclear Physics, Analysis, Functional Analysis, Statistical Mechanics, Advanced Electromagnetism and Optics, Quantum Mechanics and Relativity, Geometry of Optimisation, Advanced Solid State Physics, Topological Data Analysis, Fourier Analysis and Applications to PDEs, Measure and Integration, Nuclear and Particle Physics, Physics in Medicine.
- Throughout the program, students also complete two compulsory modules: Functional Analysis and a one-year Physics Single Project.

### Module Descriptions:

- Foundations of Physics: Introduction to classical mechanics, special relativity, waves, electricity, magnetism, light and optics, quantum theory, thermodynamics, and solid state.
- Scientific Skills: Experimental methods, statistics, safety, using standard instruments, experimental investigation, writing skills, oral communication, computer skills.
- Mathematical Methods 1: Review of A-level calculus, complex numbers, differential equations, vectors in 3D, rotations, linear transformations, eigenvalues/eigenvectors, Newton's laws, solving problems in kinematics and dynamics, conic sections, curves in 3D, partial derivatives, Taylor series, functions of several variables, vector operators, line integrals, double/triple integrals, surface and volume integrals, change of coordinates, surface integrals for shapes like cube/sphere/cylinder, Green's theorem, Gauss's divergence theorem, Stokes' theorem.
- Introduction to Algebra and Analysis: Elementary logic, set theory, number systems, bounds, supremums/infimums, basic combinatorics, functions, sequences of real numbers, limits, convergence, divergence, completeness, Bolzano-Weierstrass theorem, series of non-negative reals, convergence tests, limits of functions, continuous functions, differentiability, L'Hopital's rule, Rolle's theorem, Mean Value Theorem, rules of differentiation, matrix representation of linear maps, eigenvalues/eigenvectors, matrix inversion, determinant, relation to area/volume, change of basis, diagonalization, similarity transformations, inner product spaces, orthogonality, Cauchy-Schwarz inequality, special matrices, basic computer applications of linear algebra techniques.

### Additional elective modules:

- Astrophysics I: Units of measurement, telescopes, photons, solar system, stellar luminosities/colours, Hertzsprung-Russell diagram, stellar classification, stellar properties, stellar structure, stellar formation, stellar evolution, binary-star evolution, stellar death, compact objects.
- Classical Mechanics: Calculus of variations, Newtonian mechanics, generalised coordinates, Lagrangian, least action principle, conservation laws, symmetries, Noether's theorem, integrable systems, D'Alembert's principle, motion in a central field, scattering, small oscillations, normal modes, rigid body motion, Legendre transformation, canonical momentum, Hamiltonian, Hamilton's equations, Liouville's theorem, canonical transformations, Poisson brackets.
- Physics of the Solid State: Periodicity and symmetry, basic crystallographic definitions, packing of atomic planes, crystal structures, reciprocal lattice, diffraction from crystals, Bragg condition and Ewald sphere, lattice waves, dispersion relations, phonons, Brillouin zones, heat capacity, density of vibrational states, Einstein and Debye models of heat capacity, thermal conductivity, thermal expansion, anharmonicity, free energy, enthalpy, entropy, order parameter, classification of phase transitions, Landau theory, electronic band structure, failures of classical model for metals/semiconductors, free electron gas description of metals, density of states, Fermi Dirac statistics, electronic heat capacity, development of band structure, prediction of intrinsic semiconducting behaviour, doping.

## Assessment:

The BSc in Applied Mathematics and Physics employs diverse assessment methods to evaluate student learning and progress. These include:

- Coursework: Assignments, problem sheets, practical reports, computer-based tasks, essays, tutorials, project work.
- Examinations: Written exams testing understanding of theoretical concepts and problem-solving abilities.
- Presentations: Oral presentations of project work or research findings.
- Laboratory Reports: Written reports documenting experimental procedures, results, and analysis.
- Project Work: Independent research project on a chosen topic, culminating in a written report and presentation. The specific assessment mix varies depending on the module but typically involves a combination of examinations, coursework, and project work.

### Teaching

### Teaching Methods:

The BSc in Applied Mathematics and Physics utilizes a variety of engaging teaching methods to maximize student learning and foster critical thinking. These methods include:

- Interactive lectures: Lectures are used to introduce key concepts and provide a framework for student understanding. However, interactive elements like question-and-answer sessions, problem-solving exercises, and group discussions are integrated into lectures to promote active learning.
- Small group tutorials: Smaller tutorial groups provide a platform for students to clarify concepts, discuss problem-solving approaches, and receive personalized feedback from tutors.
- Practical sessions: Hands-on laboratory sessions in well-equipped laboratories allow students to apply theoretical knowledge to real-world experiments and develop practical skills.
- Project work: Project work enables students to engage in independent research, deepen their understanding of a specific topic, and develop essential research and presentation skills.
- Computer-based learning: Computational tools and software are integrated into the program to enhance students' understanding of complex concepts and provide opportunities to practice their problem-solving skills.

### Faculty:

The BSc in Applied Mathematics and Physics is taught by a team of experienced and dedicated faculty with expertise in various areas of mathematics and physics. The faculty comprises both teaching and research-active staff. They bring their research experience to the classroom, ensuring that students are exposed to the latest developments in their fields.

### Careers

### Career Paths:

Graduates of the BSc in Applied Mathematics and Physics are highly sought-after in a wide range of industries and research institutions. The program equips students with a skillset that is invaluable in many fields, including:

- Science and technology: Physics, chemistry, engineering, materials science, astronomy, data science, artificial intelligence, machine learning, computational physics, biophysics, medical physics, theoretical physics, experimental physics, space science.
- Finance and business: Quantitative analysis, financial modelling, risk management, investment banking, data analytics, actuarial science, business consulting.
- Education and research: Teaching mathematics and physics at various levels, pursuing postgraduate research, contributing to academic journals and conferences.
- Other fields: Defence, aerospace, energy, healthcare, communications, environmental science, government agencies, policy analysis.

### Career Opportunities:

Specific career opportunities for graduates include:

- Physicist
- Researcher
- Data Scientist
- Financial Analyst
- Quantitative Analyst
- Actuary
- Teacher
- Lecturer
- Engineer
- Consultant
- Software Developer
- Policy Analyst

### Career Outcomes:

The BSc in Applied Mathematics and Physics equips graduates with a strong foundation in mathematics and physics, fostering critical thinking, problem-solving, and analytical skills. This prepares them well for a range of careers in diverse fields. Graduates frequently find employment in research-intensive industries, academia, and positions requiring advanced analytical and problem-solving skills.

### Tuition Fees and Payment Information:

- Northern Ireland (NI) 1 £4,750
- Republic of Ireland (ROI) 2 £4,750
- England, Scotland or Wales (GB) 1 £9,250
- EU Other 3 £25,300
- International £25,300