Mathematics and Statistics BSc (Hons)

Program Overview

The Mathematics and Statistics BSc (Hons) program at the University of Liverpool provides a comprehensive foundation in mathematics, statistics, and probability, preparing students for careers in various fields. Students can customize their education with a wide range of optional modules and enhance their global perspective through a year abroad or summer abroad placements. The program is accredited by the Institute of Mathematics and its Applications and the Royal Statistical Society, ensuring the highest academic standards. Graduates possess highly sought-after problem-solving skills and career opportunities in diverse sectors, including finance, data science, and engineering.

Program Outline

Mathematics and Statistics BSc (Hons) - University of Liverpool

Degree Overview:

This program is designed for students interested in the fascinating and diverse field of mathematics, which underpins a wide range of disciplines. The program aims to provide a solid foundation for students to pursue careers in various fields, including physical sciences, social sciences, biology, business, and finance. The University of Liverpool boasts a large department with highly qualified staff, a first-class reputation in teaching and research, and a great city in which to live and work. The program offers the option to take a year abroad in year three, providing students with an incredible opportunity to expand their academic and cultural horizons. During the year abroad, students will take a variety of modules related to the culture, history, and society of their host country, as well as discipline-related modules. This allows students to gain in-depth knowledge about their host country while also learning new and exciting knowledge that complements their degree studies back in Liverpool.

Outline:

The Mathematics and Statistics BSc (Hons) program is a three-year full-time program. The program is structured into three years, with compulsory and optional modules in each year.

Year One:

• Compulsory Modules:
• Calculus I (MATH101)
• Calculus II (MATH102)
• Introduction to Linear Algebra (MATH103)
• Introduction to Statistics using R (MATH163)
• Mathematical IT skills (MATH111)
• Introduction to Study and Research in Mathematics (MATH107)
• Newtonian Mechanics (MATH122)
• Numbers, Groups and Codes (MATH142)
• Module Descriptions:
It covers the basics of real numbers, sequences, limits, real functions, and continuity, and provides a rigorous treatment of derivatives and integrals for real functions of one real variable.
• Calculus II (MATH102): This module builds upon the knowledge gained in Calculus I and covers power series, functions of several variables, partial differentiation, double integrals, and their applications.
• Introduction to Linear Algebra (MATH103): This module introduces students to vector spaces and linear mappings, covering topics such as lines, planes, subspaces, and intersections.
It also includes a study of complex numbers. Students will learn how to use R to some degree of proficiency in certain contexts and become aware of possible career paths using statistics.
• Mathematical IT skills (MATH111): This module introduces students to powerful mathematical software packages such as Maple and Matlab, which can be used for numerical computations, symbolic computations, and creating visual representations of curves and surfaces.
• Introduction to Study and Research in Mathematics (MATH107): This module explores what it means to be a mathematician as an undergraduate and beyond, covering topics such as research mathematics, careers for mathematicians, and core elements of mathematical language and writing.
• Newtonian Mechanics (MATH122): This module introduces classical (Newtonian) mechanics, covering basic principles like conservation of momentum and energy, and leading to the quantitative description of motions of bodies under simple force systems.
It includes angular momentum, rigid body dynamics, and moments of inertia.
• Numbers, Groups and Codes (MATH142): This module introduces group theory, motivated by examples in number theory, combinatorics, and geometry, as well as applications in data encryption and data retrieval.

Year Two:

• Compulsory Modules:
• VECTOR CALCULUS WITH APPLICATIONS IN FLUID MECHANICS (MATH225)
• COMPLEX FUNCTIONS (MATH243)
• Linear Algebra and Geometry (MATH244)
• Differential Equations (MATH221)
• STATISTICS AND PROBABILITY II (MATH254)
• Statistics and Probability I (MATH253)
• Optional Modules:
• CLASSICAL MECHANICS (MATH228)
• METRIC SPACES AND CALCULUS (MATH242)
• Commutative Algebra (MATH247)
• Financial Mathematics (MATH260)
• Operational Research (MATH269)
• STEM Education and Communication (MATH291)
• Numerical Methods for Applied Mathematics (MATH226)
• Becoming Entrepreneurial (ULMS254)
• Module Descriptions:
• VECTOR CALCULUS WITH APPLICATIONS IN FLUID MECHANICS (MATH225):
This module introduces fluid mechanics and electromagnetism, vector integrals, the operators div, grad, and curl, and their applications to physical situations.
• COMPLEX FUNCTIONS (MATH243): This module introduces students to the theory of complex functions, which has connections to other areas of mathematics and physical sciences.
• Linear Algebra and Geometry (MATH244): This module builds upon the concepts introduced in Introduction to Linear Algebra and explores applications of linear algebra in geometry, algebra, differential equations, physics, biology, and statistics.
• STATISTICS AND PROBABILITY II (MATH254): This module introduces probabilistic methods used in actuarial science, financial mathematics, statistics, and physical sciences.
It focuses on discrete and continuous random variables, properties of distributions, transformations, moment and probability generating functions, and limit theorems. It uses a statistical software package throughout.
• CLASSICAL MECHANICS (MATH228): This module covers the motion of physical bodies in everyday situations and in the solar system, introducing concepts such as energy, force, momentum, and angular momentum.
• METRIC SPACES AND CALCULUS (MATH242): This module introduces the basic concepts and techniques of modern real analysis, covering topics such as convergence, continuity, and the Picard Theorem.
• Commutative Algebra (MATH247): This module introduces the theory and methods of modern commutative algebra, with applications to number theory, algebraic geometry, and linear algebra.
• Financial Mathematics (MATH260): This module introduces the basic concepts in Financial Mathematics and uses models for the dynamic of stock price to solve problems of pricing and hedging derivatives.
• STEM Education and Communication (MATH291): This module provides students with experience of communicating in a variety of media and contexts, introducing them to contemporary issues in education and educational practice.
• Numerical Methods for Applied Mathematics (MATH226): This module introduces numerical methods for finding roots, approximating integrals, and interpolating data, examining the advantages and disadvantages of different approaches in terms of accuracy and efficiency.
• Becoming Entrepreneurial (ULMS254): This module focuses on identifying, exploring, and implementing entrepreneurial opportunities that create and capture value, providing students with a foundation in entrepreneurial thinking and developing the skills and attributes needed to build their own start-up or add value within existing companies.

Year Three:

• Compulsory Modules:
• APPLIED PROBABILITY (MATH362)
• Linear Statistical Models (MATH363)
• APPLIED STOCHASTIC MODELS (MATH360)
• Optional Modules:
• MEASURE THEORY AND PROBABILITY (MATH365)
• THEORY OF STATISTICAL INFERENCE (MATH361)
• MEDICAL STATISTICS (MATH364)
• MATHEMATICAL RISK THEORY (MATH366)
• Stochastic Theory and Methods in Data Science (MATH368)
• FURTHER METHODS OF APPLIED MATHEMATICS (MATH323)
• CARTESIAN TENSORS AND MATHEMATICAL MODELS OF SOLIDS AND VISCOUS FLUIDS (MATH324)
• QUANTUM MECHANICS (MATH325)
• Relativity (MATH326)
• GROUP THEORY (MATH343)
• NETWORKS IN THEORY AND PRACTICE (MATH367)
• Professional Projects and Employability in Mathematics (MATH390)
• More Is Different: Statistical Mechanics, Thermodynamics, and All That (MATH327)
• Game Theory (MATH331)
• Numerical Methods for Ordinary and Partial Differential Equations (MATH336)
• NUMBER THEORY (MATH342)
• TOPOLOGY (MATH346)
• DIFFERENTIAL GEOMETRY (MATH349)
• Mathematical Biology (MATH335)
• Mathematics of Networks and Epidemics (MATH338)
• Maths Summer Industrial Research Project (MATH391)
• Module Descriptions:
• APPLIED PROBABILITY (MATH362):
This module studies discrete-time Markov chains and introduces the most basic continuous-time processes, covering topics such as the Chapman Kolmogorov equation, communication of states, periodicity, recurrence and transience properties, asymptotic behavior, limiting and stationary distributions, and an introduction to Poisson processes.
• Linear Statistical Models (MATH363): This module extends earlier work on linear regression and analysis of variance, and then goes beyond these to generalized linear models.
It emphasizes applications of statistical methods and uses statistical software throughout.
• APPLIED STOCHASTIC MODELS (MATH360): This module introduces continuous-time stochastic processes, covering topics such as standard concepts and methods of stochastic modeling, the diversity of applications of stochastic processes in science, and exercises in the applications of simple stochastic analysis to appropriate problems.
• MEASURE THEORY AND PROBABILITY (MATH365): This module covers the abstract theory of integrating and the deep theoretical background of probability theory, providing a foundation for postgraduate studies in probability, including financial applications.
• THEORY OF STATISTICAL INFERENCE (MATH361): This module introduces fundamental topics in mathematical statistics, including the theory of point estimation and hypothesis testing.
It covers key concepts such as sufficiency, completeness, and others.
• MEDICAL STATISTICS (MATH364): This module covers the design of studies, methods of analysis, and interpretation of results in medical statistics, covering topics such as epidemiology, survival analysis, clinical trials, and meta-analysis.
• MATHEMATICAL RISK THEORY (MATH366): This module covers the mathematical risk theory used in practice in non-life actuarial departments of insurance firms, providing an introduction to mathematical methods for managing risk in insurance and finance.
• Stochastic Theory and Methods in Data Science (MATH368): This module explores how mathematical methods from stochastics can be used to deal with problems arising in various areas, including quantifying uncertainty, problems in physics, optimization, and decision making.
• FURTHER METHODS OF APPLIED MATHEMATICS (MATH323): This module covers methods for solving ordinary and partial differential equations, including inhomogeneous linear second-order ODEs, optimization of functionals, systems of two linear first-order PDEs, and second-order PDEs.
• CARTESIAN TENSORS AND MATHEMATICAL MODELS OF SOLIDS AND VISCOUS FLUIDS (MATH324): This module introduces basic concepts and principles of continuum mechanics, using Cartesian tensors to analyze problems in solid and fluid mechanics.
• QUANTUM MECHANICS (MATH325): This module introduces the development of Quantum Mechanics, covering topics such as the nature of reality, the mathematical foundations of quantum mechanics, and its applications to the microscopic world.
• GROUP THEORY (MATH343): This module introduces the modern theory of finite non-commutative groups, covering topics such as basic definitions, examples, constructions, and the Sylow theory.
• NETWORKS IN THEORY AND PRACTICE (MATH367): This module explores optimization methods for real-world problems using fundamental tools from network theory, covering topics such as network flow, shortest path problem, transport problem, assignment problem, and routing problem.
• Professional Projects and Employability in Mathematics (MATH390): This module provides students with the opportunity to further develop their mathematical problem-solving skills and apply mathematical results to real-world scenarios through group activities.
It aims to develop skills needed for employment or research, such as working in-depth on a problem, writing reports, communicating mathematical results, and working collaboratively.
• More Is Different: Statistical Mechanics, Thermodynamics, and All That (MATH327): This module introduces the foundations of Statistical Physics, developing an understanding of the stochastic roots of thermodynamics and the properties of matter.
It covers topics such as statistical ensembles, entropy, temperature, classical and quantum gases, the laws of thermodynamics, and phase transitions.
• Game Theory (MATH331): This module explores game-theoretic models used to understand phenomena involving conflict and cooperation, covering topics such as human relationships, economic bargaining, threats, coalition formation, and war.
• NUMBER THEORY (MATH342): This module covers number theory, focusing on the study of integers and covering results due to Euclid, Euler, Gauss, Riemann, and others.
• TOPOLOGY (MATH346): This module introduces the basic notions of topological space and continuous map, illustrating them with examples from different areas of mathematics.
It also introduces homotopy theory.
• DIFFERENTIAL GEOMETRY (MATH349): This module introduces the methods of differential geometry on curves and surfaces in 3-dimensional Euclidean space, building upon the methods of differential geometry on plane curves.
• Mathematics of Networks and Epidemics (MATH338): This module explores different classes of networks and how to quantify and describe them, including their structures and nodes.
It focuses on real-world biological applications of network theory, particularly epidemics.
• Maths Summer Industrial Research Project (MATH391): This module provides students with the experience of working in a research environment or setting different from any project work undertaken in the Department of Mathematics.
It aims to provide insight into how students may apply skills and experiences later in their career.

Assessment:

Most modules are assessed by a two and a half hour examination in January or May, but many have an element of coursework assessment. This might be through homework, class tests, mini-project work, or key skills exercises.

Teaching:

The program is delivered by the Department of Mathematical Sciences. Learning activities consist of lectures, tutorials, practical classes, problem classes, private study, and supervised project work. In year one, lectures are supplemented by a thorough system of group tutorials, and computing work is carried out in supervised practical classes. Key study skills, presentation skills, and group work start in first-year tutorials and are developed later in the program. The emphasis in most modules is on the development of problem-solving skills, which are highly valued by employers. Project supervision is on a one-to-one basis, apart from group projects in year two.

Careers:

A mathematically-based degree opens up a wide range of career opportunities, including some of the most lucrative professions. Recent employers of graduates include Barclays Bank plc, Deloitte, Forrest Recruitment, Marks and Spencer, Mercer Human Resource Consulting Ltd., Venture Marketing Group, BAE Systems, BT, Guardian Media Group, Royal Bank of Scotland, Siemens, and Unilever. 5% of mathematical sciences graduates go on to work or further study within 15 months of graduation (Discover Uni, 2018-19).

Other:

The program is accredited by the Institute of Mathematics and its Applications (IMA) and the Royal Statistical Society. The IMA is the professional learned institute for mathematicians, supporting the advancement of mathematical knowledge and its applications. The RSS is a professional body for all statisticians and data analysts. The program also offers global opportunities, including a year abroad at a partner university, a year in China at Xi'an Jiaotong Liverpool University, and summer abroad placements. Students can also study a language as part of or alongside their degree.

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. Tuition fees cover the cost of your teaching and assessment, operating facilities such as libraries, IT equipment, and access to academic and personal support.