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Masters

Mathematics MMath

University of Liverpool
Suzhou , China
Easy Apply
Students
Tuition Fee
GBP 24,800
Start Date
Medium of studying
Duration
48 months
Program Facts
About Program
About University
Admission Requirements
Ambassadors
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Easy Apply
Program Facts
Program Details
Degree
Masters
Major
Mathematics | Pure Mathematics
Area of study
Mathematics and Statistics
Course Language
English
Tuition Fee
Average International Tuition Fee
GBP 24,800
About Program

Program Overview

This four-year MMath program provides ambitious students with a comprehensive understanding of mathematics, probability, and statistics. Graduates earn a master's degree, enhancing their job prospects and opening doors to research careers. The program emphasizes teamwork, digital fluency, problem-solving skills, and effective communication of mathematical ideas.

Program Outline

Degree Overview:

This four-year MMath program is designed for ambitious students who want to delve deeply into mathematics. Graduates earn a master's degree, which provides a competitive edge in the job market and opens doors to research careers.

Objectives:

  • Gain a comprehensive understanding of pure and applied mathematics, probability, and statistics.
  • Develop advanced knowledge in specific areas of mathematics that align with individual interests.
  • Enhance teamwork, digital fluency, and sophisticated problem-solving skills.
  • Master the art of communicating complex mathematical ideas effectively.

Outline:

Year One:

  • Compulsory Modules:
  • Calculus I (MATH101): Covers the fundamentals of limits, derivatives, and integrals for real functions of one real variable.
  • Introduction to Linear Algebra (MATH103): Explores vector spaces, linear mappings, and the solution of systems of linear equations.
  • Introduction to Statistics using R (MATH163): Introduces fundamental statistical concepts and probability using the R programming language.
  • Mathematical IT skills (MATH111): Familiarizes students with mathematical software packages like Maple and Matlab for numerical and symbolic computations.
  • Introduction to Study and Research in Mathematics (MATH107): Explores the nature of mathematics at university level, research mathematics, and careers for mathematicians.
  • Newtonian Mechanics (MATH122): Introduces classical mechanics, covering principles like conservation of momentum and energy, and the description of body motion under force systems.
  • Numbers, Groups and Codes (MATH142): Provides an introduction to group theory, exploring its applications in number theory, combinatorics, geometry, and data encryption.

Year Two:

  • Compulsory Modules:
  • Differential Equations (MATH221): Covers the theory and applications of ordinary and partial differential equations, emphasizing problem-solving and examples.
  • VECTOR CALCULUS WITH APPLICATIONS IN FLUID MECHANICS (MATH225): Introduces fluid mechanics, electromagnetism, vector integrals, and applications of vector calculus to physical situations.
  • Linear Algebra and Geometry (MATH244): Extends the concepts of linear algebra, introducing abstract vector spaces and their applications in geometry, algebra, and differential equations.
  • Statistics and Probability I (MATH253): Introduces statistical methods with a focus on applying and interpreting standard techniques, utilizing a statistical software package.
  • COMPLEX FUNCTIONS (MATH243): Introduces the theory of complex functions, highlighting its connections to other areas of mathematics and physical sciences.
  • Optional Modules:
  • CLASSICAL MECHANICS (MATH228): Delves deeper into classical mechanics, exploring concepts like energy, force, momentum, and angular momentum.
  • METRIC SPACES AND CALCULUS (MATH242): Introduces metric spaces and their applications in real analysis, multivariable analysis, and functional analysis.
  • Commutative Algebra (MATH247): Covers the theory and methods of modern commutative algebra, with applications to number theory, algebraic geometry, and linear algebra.
  • STATISTICS AND PROBABILITY II (MATH254): Explores probabilistic methods used in actuarial science, financial mathematics, and statistics.
  • Financial Mathematics (MATH260): Introduces mathematical finance, focusing on derivative pricing and hedging.
  • Operational Research (MATH269): Explores mathematical methods for achieving goals with limited resources, using optimization techniques.
  • STEM Education and Communication (MATH291): Provides experience in communicating mathematical concepts in various media and contexts.
  • Numerical Methods for Applied Mathematics (MATH226): Introduces numerical methods for solving mathematical problems, including finding roots, approximating integrals, and interpolating data.

Year Three:

  • Optional Modules:
  • FURTHER METHODS OF APPLIED MATHEMATICS (MATH323): Covers advanced methods for solving ordinary and partial differential equations.
  • CARTESIAN TENSORS AND MATHEMATICAL MODELS OF SOLIDS AND VISCOUS FLUIDS (MATH324): Introduces continuum mechanics, focusing on conservation laws and their role in modeling physical phenomena.
  • Relativity (MATH326): Introduces Einstein's theories of special and general relativity, covering their mathematical foundations and applications.
  • NUMBER THEORY (MATH342): Delves deeper into number theory, studying results from Euclid, Euler, Gauss, Riemann, and other mathematicians.
  • GROUP THEORY (MATH343): Covers the modern theory of finite non-commutative groups, exploring its applications in various fields.
  • DIFFERENTIAL GEOMETRY (MATH349): Introduces the methods of differential geometry on curves and surfaces in 3-dimensional Euclidean space.
  • APPLIED PROBABILITY (MATH362): Studies discrete-time Markov chains and introduces continuous-time processes.
  • Linear Statistical Models (MATH363): Extends linear regression and analysis of variance, introducing generalized linear models.
  • Game Theory (MATH331): Explores game-theoretic models for understanding phenomena involving conflict and cooperation.
  • Numerical Methods for Ordinary and Partial Differential Equations (MATH336): Covers numerical methods for solving ordinary and partial differential equations on a computer.
  • TOPOLOGY (MATH346): Introduces the basic notions of topological space and continuous map, exploring their applications in various fields.
  • THEORY OF STATISTICAL INFERENCE (MATH361): Covers fundamental topics in mathematical statistics, including point estimation and hypothesis testing.
  • MEDICAL STATISTICS (MATH364): Introduces medical statistics, covering the design of studies, methods of analysis, and interpretation of results.
  • MEASURE THEORY AND PROBABILITY (MATH365): Explores the abstract theory of integration and the theoretical background of probability theory.
  • MATHEMATICAL RISK THEORY (MATH366): Covers mathematical risk theory used in insurance and finance.
  • NETWORKS IN THEORY AND PRACTICE (MATH367): Explores optimization methods for real-world problems using network theory.
  • Stochastic Theory and Methods in Data Science (MATH368): Introduces stochastic methods for dealing with problems in data science.
  • More Is Different: Statistical Mechanics, Thermodynamics, and All That (MATH327): Introduces statistical physics, thermodynamics, and the properties of matter.
  • Professional Projects and Employability in Mathematics (MATH390): Develops skills for mathematical problem-solving and applying mathematical results to real-world scenarios.
  • Maths Summer Industrial Research Project (MATH391): Provides experience working in a research environment outside the Department of Mathematics.
  • APPLIED STOCHASTIC MODELS (MATH360): Introduces continuous-time stochastic processes and their applications in various fields.
  • LINEAR DIFFERENTIAL OPERATORS IN MATHEMATICAL PHYSICS (MATH421): Covers advanced methods for solving linear partial differential equations that arise in mathematical physics.
  • QUANTUM FIELD THEORY (MATH425): Introduces quantum field theory, its mathematical language, and its applications in particle and condensed matter physics.
  • MATH499 - Project for M.Math.
    • (MATH499): Involves research in an advanced topic in a specific area of mathematics under the supervision of a member of staff.
  • Advanced topics in mathematical biology (MATH426): Explores mathematical applications in biological problems, including developmental biology, epidemic dynamics, and biological fluid dynamics.
  • WAVES, MATHEMATICAL MODELLING (MATH427): Introduces the analysis of waves in physical systems, covering both linear and nonlinear models.
  • Mathematical Biology (MATH335): Covers the construction and analysis of models for biological systems.
  • Mathematics of Networks and Epidemics (MATH338): Explores network theory and its applications to real-world systems, particularly epidemics.
  • MANIFOLDS, HOMOLOGY AND MORSE THEORY (MATH410): Introduces the topology of manifolds, emphasizing homology and Morse theory.
  • REPRESENTATION THEORY OF FINITE GROUPS (MATH442): Studies the representation theory of finite groups and its applications.
  • Riemann Surfaces (MATH445): Introduces the theory of Riemann surfaces and its applications.
  • Singularity Theory of Differentiable Mappings (MATH455): Introduces singularity theory and its applications in mathematics, natural sciences, and technology.
  • INTRODUCTION TO STRING THEORY (MATH423): Covers bosonic string theory and its applications in particle physics and string theory.
  • INTRODUCTION TO MODERN PARTICLE THEORY (MATH431): Introduces modern particle theory, covering its concepts and applications.
  • HIGHER ARITHMETIC (MATH441): Covers topics in analytic number theory, including the behavior of arithmetic functions, the Riemann zeta function, and the distribution of prime numbers.
  • Elliptic curves (MATH444): Introduces the theory of elliptic curves and its applications.
  • Geometry of Continued Fractions (MATH447): Introduces a geometric vision of continued fractions and its applications.
  • Algebraic Geometry (MATH448): Covers the basics of algebraic geometry, focusing on examples illustrating fundamental concepts and phenomena.
  • Galois Theory (MATH449): Introduces Galois theory and its applications to polynomial equations and geometric constructions.

Year Four:

  • Compulsory Modules:
  • MATH499 - Project for M.Math.
    • (MATH499): Involves research in an advanced topic in a specific area of mathematics under the supervision of a member of staff.
  • MATH490 - Project for M.Math.
    • (MATH490): Involves research in an advanced topic in a specific area of mathematics under the supervision of a member of staff.
  • Optional Modules:
  • LINEAR DIFFERENTIAL OPERATORS IN MATHEMATICAL PHYSICS (MATH421): Covers advanced methods for solving linear partial differential equations that arise in mathematical physics.
  • QUANTUM FIELD THEORY (MATH425): Introduces quantum field theory, its mathematical language, and its applications in particle and condensed matter physics.
  • Advanced topics in mathematical biology (MATH426): Explores mathematical applications in biological problems, including developmental biology, epidemic dynamics, and biological fluid dynamics.
  • WAVES, MATHEMATICAL MODELLING (MATH427): Introduces the analysis of waves in physical systems, covering both linear and nonlinear models.
  • FURTHER METHODS OF APPLIED MATHEMATICS (MATH323): Covers advanced methods for solving ordinary and partial differential equations.
  • CARTESIAN TENSORS AND MATHEMATICAL MODELS OF SOLIDS AND VISCOUS FLUIDS (MATH324): Introduces continuum mechanics, focusing on conservation laws and their role in modeling physical phenomena.
  • Relativity (MATH326): Introduces Einstein's theories of special and general relativity, covering their mathematical foundations and applications.
  • NUMBER THEORY (MATH342): Delves deeper into number theory, studying results from Euclid, Euler, Gauss, Riemann, and other mathematicians.
  • GROUP THEORY (MATH343): Covers the modern theory of finite non-commutative groups, exploring its applications in various fields.
  • DIFFERENTIAL GEOMETRY (MATH349): Introduces the methods of differential geometry on curves and surfaces in 3-dimensional Euclidean space.
  • APPLIED STOCHASTIC MODELS (MATH360): Introduces continuous-time stochastic processes and their applications in various fields.
  • APPLIED PROBABILITY (MATH362): Studies discrete-time Markov chains and introduces continuous-time processes.
  • Linear Statistical Models (MATH363): Extends linear regression and analysis of variance, introducing generalized linear models.
  • Game Theory (MATH331): Explores game-theoretic models for understanding phenomena involving conflict and cooperation.
  • Numerical Methods for Ordinary and Partial Differential Equations (MATH336): Covers numerical methods for solving ordinary and partial differential equations on a computer.
  • TOPOLOGY (MATH346): Introduces the basic notions of topological space and continuous map, exploring their applications in various fields.
  • THEORY OF STATISTICAL INFERENCE (MATH361): Covers fundamental topics in mathematical statistics, including point estimation and hypothesis testing.
  • MEDICAL STATISTICS (MATH364): Introduces medical statistics, covering the design of studies, methods of analysis, and interpretation of results.
  • MEASURE THEORY AND PROBABILITY (MATH365): Explores the abstract theory of integration and the theoretical background of probability theory.
  • MATHEMATICAL RISK THEORY (MATH366): Covers mathematical risk theory used in insurance and finance.
  • NETWORKS IN THEORY AND PRACTICE (MATH367): Explores optimization methods for real-world problems using network theory.
  • Stochastic Theory and Methods in Data Science (MATH368): Introduces stochastic methods for dealing with problems in data science.
  • More Is Different: Statistical Mechanics, Thermodynamics, and All That (MATH327): Introduces statistical physics, thermodynamics, and the properties of matter.
  • Professional Projects and Employability in Mathematics (MATH390): Develops skills for mathematical problem-solving and applying mathematical results to real-world scenarios.
  • Maths Summer Industrial Research Project (MATH391): Provides experience working in a research environment outside the Department of Mathematics.
  • Mathematical Biology (MATH335): Covers the construction and analysis of models for biological systems.
  • Mathematics of Networks and Epidemics (MATH338): Explores network theory and its applications to real-world systems, particularly epidemics.
  • MANIFOLDS, HOMOLOGY AND MORSE THEORY (MATH410): Introduces the topology of manifolds, emphasizing homology and Morse theory.
  • REPRESENTATION THEORY OF FINITE GROUPS (MATH442): Studies the representation theory of finite groups and its applications.
  • Riemann Surfaces (MATH445): Introduces the theory of Riemann surfaces and its applications.
  • Singularity Theory of Differentiable Mappings (MATH455): Introduces singularity theory and its applications in mathematics, natural sciences, and technology.
  • INTRODUCTION TO STRING THEORY (MATH423): Covers bosonic string theory and its applications in particle physics and string theory.
  • INTRODUCTION TO MODERN PARTICLE THEORY (MATH431): Introduces modern particle theory, covering its concepts and applications.
  • HIGHER ARITHMETIC (MATH441): Covers topics in analytic number theory, including the behavior of arithmetic functions, the Riemann zeta function, and the distribution of prime numbers.
  • Elliptic curves (MATH444): Introduces the theory of elliptic curves and its applications.
  • Geometry of Continued Fractions (MATH447): Introduces a geometric vision of continued fractions and its applications.
  • Algebraic Geometry (MATH448): Covers the basics of algebraic geometry, focusing on examples illustrating fundamental concepts and phenomena.
  • Galois Theory (MATH449): Introduces Galois theory and its applications to polynomial equations and geometric constructions.

Assessment:

  • Each module has a tailored assessment scheme, which may include:
  • Traditional written exams
  • Class tests
  • Assignments
  • Projects
  • Group work
  • Online exercises with automatic marking and immediate feedback

Teaching:

  • The program utilizes a variety of teaching methods, including:
  • Traditional lectures
  • Tutorials
  • Video content
  • Interactive learning sessions
  • One-to-one project supervision
  • The program aligns with the Liverpool Curriculum Framework, emphasizing research-connected teaching, active learning, and authentic assessment.

Careers:

  • A mathematics degree opens doors to a wide range of career opportunities, including some of the most lucrative professions.
  • Employers value mathematicians' high level of numeracy and problem-solving skills.
  • Typical career paths include:
  • Actuarial trainee analyst
  • Graduate management trainee
  • Risk analyst
  • Trainee chartered accountant
  • Recent employers of graduates include:
  • Aston University
  • Deloitte
  • EuroMoney Training
  • Norwich Union
  • Venture Marketing Group
  • Wolsley Group

Other:

  • The program offers a year abroad option, allowing students to spend an academic year at one of the university's partner universities.
  • Students can choose to go abroad either between years two and three or between years three and four.
  • The MMath degree is accredited by the Institute of Mathematics and its Applications (IMA) and the Royal Statistical Society (RSS).
  • The university has a large Mathematical Sciences department with highly qualified staff, a first-class reputation in teaching and research, and a friendly, supportive environment.
  • The program is designed with the needs of employers in mind, providing a solid foundation for a variety of career paths.
  • Graduates have experience in mathematics research and independent working skills, which are highly valued by employers.
  • The university provides careers and employability support, including help with career planning, understanding the job market, and strengthening networking skills.
  • The university has a dedicated student services team that provides assistance with studies, health and wellbeing, and financial advice.
  • The university offers confidential counselling and support for students facing personal problems affecting their studies and general wellbeing.
  • UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland)
    • Full-time place, per year £9,250 Year in industry fee £1,850 Year abroad fee £1,385
  • International fees
    • Full-time place, per year £24,800 Year abroad fee £12,400 Fees shown are for the academic year 2024/25. Please note that the Year Abroad fee also applies to the Year in China.
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