Mathematical Sciences MSc

Program Overview

The MSc in Mathematical Sciences at the University of Liverpool offers advanced studies in mathematics and theoretical physics. Students can delve into a wide range of topics and develop mathematical programming and typesetting skills. Taught by world-leading experts, the program provides personalized supervision, exceptional support, and access to cutting-edge research. Graduates are well-equipped for careers in teaching, finance, software development, and research-oriented professions.

Program Outline

Degree Overview:

This program offers specialization in a wide range of areas across pure and applied mathematics and theoretical physics. It is suitable for mathematics graduates seeking to specialize and develop in these areas. The program is available for both full-time and part-time students.

Objectives:

The program aims to provide students with:

• Advanced mathematical methods
• Specialization in a broad range of areas across pure and applied mathematics and theoretical physics
• Development of skills in mathematical programming and typesetting

Description:

Mathematical Sciences at Liverpool is a center for world-class research and teaching, with a strong record of teaching quality. The department provides high-quality supervision, teaching, and IT support, and fosters a friendly and supportive atmosphere.

Outline:

Structure:

The program is delivered over 12 months full-time or 24 months part-time. It consists of taught modules in semesters one and two, followed by a final dissertation or project.

Course Schedule:

• Semester One: Students choose modules to make up 60 credits.
• Semester Two: Students choose modules to make up 60 credits.
• Final Project: Students complete a dissertation or project worth 60 credits.

Modules:

Semester One:

• Compulsory Modules:
• LATEX AND MATHEMATICAL PROGRAMMING PROJECT (MATH549): This module teaches students to use LaTeX and a mathematical software package.
Students undertake a project where they learn a new topic in mathematics and use their programming and typesetting skills to investigate it.
• Optional Modules:
• MANIFOLDS, HOMOLOGY AND MORSE THEORY (MATH410): This module introduces the topology of manifolds, emphasizing homology and Morse theory.
• LINEAR DIFFERENTIAL OPERATORS IN MATHEMATICAL PHYSICS (MATH421): This module focuses on linear partial differential equations (PDEs) that arise in mathematical physics and advanced methods for solving them.
• QUANTUM FIELD THEORY (MATH425): This module covers Quantum Field Theory, the mathematical language of modern theoretical particle and condensed matter physics.
• Singularity Theory of Differentiable Mappings (MATH455): This module introduces the calculus side of Singularity Theory.
• Riemann Surfaces (MATH445): This module introduces students to the theory of Riemann surfaces.
• FURTHER METHODS OF APPLIED MATHEMATICS (MATH323): This module addresses methods for solving ordinary and partial differential equations.
• CARTESIAN TENSORS AND MATHEMATICAL MODELS OF SOLIDS AND VISCOUS FLUIDS (MATH324): This module introduces basic concepts and principles of continuum mechanics.
• QUANTUM MECHANICS (MATH325): This module covers the development of Quantum Mechanics.
• GROUP THEORY (MATH343): This module provides an introduction to the modern theory of finite non-commutative groups.
• APPLIED PROBABILITY (MATH362): This module studies discrete-time Markov chains and introduces continuous-time processes.
• Linear Statistical Models (MATH363): This module extends earlier work on linear regression and analysis of variance.
• NUMBER THEORY (MATH342): This module studies results in number theory due to Euclid, Euler, Gauss, Riemann, and others.
• DIFFERENTIAL GEOMETRY (MATH349): This module introduces the methods of differential geometry on curves and surfaces in 3-dimensional Euclidean space.
• APPLIED STOCHASTIC MODELS (MATH360): This module introduces continuous-time stochastic processes.
• Advanced topics in mathematical biology (MATH426): This module presents a selection of mathematical applications in developmental biology, epidemic dynamics, and biological fluid dynamics.
• REPRESENTATION THEORY OF FINITE GROUPS (MATH442): This module studies the representation theory of finite groups.

Semester Two:

• Optional Modules:
• HIGHER ARITHMETIC (MATH441): This module provides an introduction to topics in Analytic Number Theory.
• WAVES, MATHEMATICAL MODELLING (MATH427): This module introduces the analysis of waves in physical systems.
• Elliptic curves (MATH444): This module introduces the theory of elliptic curves.
• Geometry of Continued Fractions (MATH447): This module introduces a geometric vision of continued fractions.
• Algebraic Geometry (MATH448): This module introduces the basics of algebraic geometry.
• MEASURE THEORY AND PROBABILITY (MATH365): This module covers the abstract theory of integrating and the theoretical background of probability theory.
• NETWORKS IN THEORY AND PRACTICE (MATH367): This module develops an appreciation of optimization methods for real-world problems using network theory.
• More Is Different: Statistical Mechanics, Thermodynamics, and All That (MATH327): This module introduces the foundations of Statistical Physics.
• Game Theory (MATH331): This module explores models used to understand phenomena involving conflict and cooperation.
• TOPOLOGY (MATH346): This module introduces the basic notions of topological space and continuous map.
• THEORY OF STATISTICAL INFERENCE (MATH361): This module introduces fundamental topics in mathematical statistics.
• MEDICAL STATISTICS (MATH364): This module provides knowledge of medical statistics.
• Stochastic Theory and Methods in Data Science (MATH368): This module raises awareness of how mathematical methods from stochastics can be used in data science.
• MATHEMATICAL RISK THEORY (MATH366): This module provides an understanding of mathematical risk theory used in insurance.
• Mathematics of Networks and Epidemics (MATH338): This module explores different classes of networks and their dynamics.
• Galois Theory (MATH449): This module introduces Galois Theory.
• MATH552 - Preliminary Dissertation (MATH552): This module provides an introduction to mathematical research.

Final Project:

• Compulsory Modules:
• MAIN DISSERTATION (MATH554): This module allows students to study a mathematical topic in depth and produce a written report.

Assessment:

• Continuous Assessment: Modules have a continuous assessment component, which may include class tests, coursework, or project-based tasks.
• Final Assessment: Modules have a final assessment component, taken in January and May exam periods.
• Dissertation: The final dissertation is assessed based on the quality of research, analysis, and presentation.

Teaching:

• Methods: The program is delivered through a combination of lectures and tutorials, typically totaling four hours per module per week.
Some modules may adopt a hybrid approach with online activity and interactive face-to-face classes.

Careers:

• Potential Career Paths:
• Teacher training programs
• Finance (actuarial, banking, insurance)
• Software development
• Drugs testing
• Defence work
• Opportunities: The MSc program is a natural route into doctoral study in mathematics and related fields.
• Outcomes: Graduates have gone on to postdoctoral positions, academic teaching jobs, and roles in research institutes.

Other:

• Liverpool Hallmarks: The program aligns with the Liverpool Curriculum Framework, which focuses on research-connected teaching, active learning, and authentic assessment.

UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland) Full-time place, per year: £12,400 Part-time place, per year: £6,200 International fees Full-time place, per year: £26,400 Part-time place, per year: £13,200 Fees stated are for the 2024-25 academic year. Tuition fees cover the cost of your teaching and assessment, operating facilities such as libraries, IT equipment, and access to academic and personal support. You can pay your tuition fees in instalments. All or part of your tuition fees can be funded by external sponsorship. International applicants who accept an offer of a place will need to pay a tuition fee deposit.