Mathematics BSc

Program Overview

The Mathematics BSc program at the University of Leeds equips students with core mathematical skills, problem-solving abilities, and logical thinking coveted by employers. The diverse curriculum includes topics ranging from fluid dynamics to risk management, allowing students to specialize or explore multiple areas. Taught by expert academics, the program offers extensive tutorial support, work placement opportunities, and Leeds for Life career development initiatives, preparing students for careers in various fields where mathematical skills are highly valued.

Program Outline

Degree Overview:

Mathematics is a key subject in the sciences and business disciplines. The degree program at the University of Leeds aims to equip students with core mathematical skills, logical thinking, problem-solving, and decision-making abilities, all highly valued by employers. The program offers a diverse range of topics, including fluid dynamics, mathematical biology, number theory, risk management, stochastic calculus, and topology. Students can specialize in a particular area or explore multiple areas. The program is shaped by the University's renowned mathematics research department, one of the largest in the UK.

Outline:

The Mathematics BSc program is structured across three years, with each year consisting of 120 credits. The program includes both compulsory and optional modules.

Year 1:

• Compulsory Modules:
• Core Mathematics (40 credits):
Covers foundational concepts of function, number, and proof, building upon basic calculus and extending it to advanced techniques.
• Real Analysis (20 credits): Develops the theory of differential and integral calculus of real-valued functions in a rigorous manner.
• Computational Mathematics and Modelling (20 credits): Introduces computational techniques, algorithms, numerical solutions, and the mathematics of discrete systems.
Includes basic programming in Python.
• Introduction to Group Theory (10 credits): Introduces group theory, a fundamental branch of mathematics, with applications to permutations and symmetries.
• Dynamics and Motion (10 credits): Focuses on Newtonian mechanics, exploring forces, accelerations, and the dynamics of objects.
• Probability and Statistics (20 credits): Introduces key ideas in probability and statistics, with probability forming the theoretical basis for statistical tests and inference.

Year 2:

• Compulsory Modules:
• Investigations in Mathematics (20 credits):
Introduces ideas and methods of mathematical research, drawing examples from pure mathematics, applied mathematics, and statistics. Students conduct independent research and produce a report.
• Further Linear Algebra and Discrete Mathematics (20 credits): Explores abstract ideas of vector spaces and linear transformations, introducing the area of discrete mathematics.
• Vector Calculus and Partial Differential Equations (20 credits): Extends calculus to higher dimensions, providing the mathematical framework for studying physical systems like fluid mechanics and electromagnetism.
• Optional Modules:
• Pure and Applied Mathematics Pathway:
• Calculus, Curves and Complex Analysis (20 credits):
Introduces differential geometry and complex analysis, with applications to theoretical physics.
• Mathematical Modelling (20 credits): Covers analytical and computational techniques for solving ordinary and partial differential equations.
• Optional Modules:
• Introduction to Logic (10 credits):
Introduces mathematical logic and formal languages.
• Optimisation (10 credits): Develops the theory and practice of maximizing or minimizing functions.
• Rings and Polynomials (10 credits): Introduces rings and their properties.
• Calculus of Variations (10 credits): Studies variational problems and the Euler-Lagrange equations.
• Pure Mathematics and Statistics Pathway:
• Calculus, Curves and Complex Analysis (20 credits):
Introduces differential geometry and complex analysis, with applications to theoretical physics.
• Statistical Methods (20 credits): Lays the foundations for the analysis of statistical models.
• Optional Modules:
• Introduction to Logic (10 credits):
Introduces mathematical logic and formal languages.
• Stochastic Processes (10 credits): Explores key features of stochastic processes, including the Markov property.
• Rings and Polynomials (10 credits): Introduces rings and their properties.
• Time Series (10 credits): Focuses on techniques for model identification, parameter estimation, and forecasting in time series analysis.
• Applied Mathematics and Statistics Pathway:
• Statistical Methods (20 credits):
Lays the foundations for the analysis of statistical models.
• Mathematical Modelling (20 credits): Covers analytical and computational techniques for solving ordinary and partial differential equations.
• Optional Modules:
• Stochastic Processes (10 credits):
Explores key features of stochastic processes, including the Markov property.
• Optimisation (10 credits): Develops the theory and practice of maximizing or minimizing functions.
• Time Series (10 credits): Focuses on techniques for model identification, parameter estimation, and forecasting in time series analysis.
• Calculus of Variations (10 credits): Studies variational problems and the Euler-Lagrange equations.

Year 3:

• Compulsory Modules:
• Project in Mathematics (40 credits):
Students conduct independent research on a topic in mathematics, developing research skills and producing a report.
• Optional Modules:
• Pure and Applied Mathematics Pathway:
• Optional Modules:
• Groups and Symmetry (20 credits):
Explores group theory and its applications to symmetry.
• Methods of Applied Mathematics (20 credits): Develops techniques for solving ordinary and partial differential equations.
• Metric Spaces and Measure Theory (20 credits): Studies metric spaces and measure theory, proving fundamental results.
• Computational Applied Mathematics (20 credits): Introduces techniques of finite differences, numerical linear algebra, and stochastic simulation.
• Numbers and Codes (20 credits): Explores number theory and error-correcting codes.
• Proof and Computation (20 credits): Proves Gödel's First Incompleteness Theorem.
• Entropy and Quantum Mechanics (20 credits): Studies calculations involving entropy and quantum mechanics.
• Fluid Dynamics (20 credits): Sets out the fundamental concepts of fluid dynamics.
• Mathematics in Social Context C (20 credits): Explores the relationship between mathematics and society.
• Graph Theory and Combinatorics (20 credits): Provides a foundation in graph theory and combinatorics.
• Differential Geometry (20 credits): Develops the geometry of curves and surfaces.
• Mathematical Biology (20 credits): Introduces areas of mathematical biology and medicine.
• Nonlinear Dynamical Systems and Chaos (20 credits): Provides tools for analyzing nonlinear dynamical systems.
• Pure Mathematics and Statistics Pathway:
• Optional Modules:
• Groups and Symmetry (20 credits):
Explores group theory and its applications to symmetry.
• Statistical Modelling (20 credits): Studies extensions to the linear statistical model.
• Metric Spaces and Measure Theory (20 credits): Studies metric spaces and measure theory, proving fundamental results.
• Actuarial Mathematics 1 (20 credits): Introduces the theory of interest rates and life insurance.
• Numbers and Codes (20 credits): Explores number theory and error-correcting codes.
• Proof and Computation (20 credits): Proves Gödel's First Incompleteness Theorem.
• Stochastic Calculus and Derivative Pricing (20 credits): Provides a rigorous introduction to stochastic calculus.
• Mathematics in Social Context C (20 credits): Explores the relationship between mathematics and society.
• Graph Theory and Combinatorics (20 credits): Provides a foundation in graph theory and combinatorics.
• Differential Geometry (20 credits): Develops the geometry of curves and surfaces.
• Multivariate Analysis and Classification (20 credits): Extends univariate statistical techniques to a multivariate setting.
• Actuarial Mathematics 2 (20 credits): Expands on the theory of life insurance.
• Applied Mathematics and Statistics Pathway:
• Optional Modules:
• Methods of Applied Mathematics (20 credits):
Develops techniques for solving ordinary and partial differential equations.
• Statistical Modelling (20 credits): Studies extensions to the linear statistical model.
• Computational Applied Mathematics (20 credits): Introduces techniques of finite differences, numerical linear algebra, and stochastic simulation.
• Actuarial Mathematics 1 (20 credits): Introduces the theory of interest rates and life insurance.
• Stochastic Calculus and Derivative Pricing (20 credits): Provides a rigorous introduction to stochastic calculus.
• Entropy and Quantum Mechanics (20 credits): Studies calculations involving entropy and quantum mechanics.
• Fluid Dynamics (20 credits): Sets out the fundamental concepts of fluid dynamics.
• Mathematics in Social Context C (20 credits): Explores the relationship between mathematics and society.
• Multivariate Analysis and Classification (20 credits): Extends univariate statistical techniques to a multivariate setting.
• Mathematical Biology (20 credits): Introduces areas of mathematical biology and medicine.
• Nonlinear Dynamical Systems and Chaos (20 credits): Provides tools for analyzing nonlinear dynamical systems.
• Actuarial Mathematics 2 (20 credits): Expands on the theory of life insurance.

Assessment:

Students are assessed through a variety of methods, including formal exams and in-course assessments.

Teaching:

Students are taught through lectures, tutorials, workshops, and practical classes. The program offers extensive tutorial support and flexibility in workload and options. The University provides welcoming spaces for study and socialization, including social and group study areas, a library with a café, a seminar room, a Research Visitors Centre, and a Mathematics Active Learning Lab. Teaching is delivered by expert academics, including lecturers, professors, industry professionals, and trained postgraduate researchers.

Careers:

Mathematical skills are highly valued in various fields, leading to diverse employment opportunities for graduates. The program prepares students for careers in accountancy, insurance, banking and finance, asset management and investment, engineering, teaching, data analysis, law, and consultancy. The program develops transferable skills sought by employers, including numerical, analytical, and problem-solving abilities, as well as logical thinking.

Other:

The program offers optional work placement and study abroad opportunities. Students can choose to spend a year working in a company or studying at a partner university worldwide. These opportunities enhance employability and career prospects. The University's Leeds for Life initiative supports students in developing skills and experience for their future careers. The Employability Team provides specialist support and advice, including help with finding work experience, internships, industrial placements, and graduate positions. Students have access to the University's Careers Centre, one of the largest in the country.