BSc (Hons) Mathematics Bachelor's degree at the University of Sheffield

This core module is designed to consolidate A-level material and explore topics in mathematics that you'll use throughout your degree. You'll also be introduced to core skills, such as mathematical literacy, communication and problem-solving. Throughout this module you'll develop a strong foundation in core mathematics. You'll consider techniques for solving equations, special functions, calculus, vectors, complex numbers, and finite and infinite series.

This core module is designed to further develop your knowledge of the core mathematics you'll use across your degree. You'll learn about two-dimensional coordinate geometry, discussing the theory of matrices geometrically and algebraically. You'll also define and evaluate derivatives and integrals for functions that depend on more than one variable, with an emphasis on functions of two variables. Throughout this module you'll continue to develop your employability skills, exploring the career op

The module aims to give an overview of basic constructions in pure mathematics; starting from the integers, we develop some theory of the integers, introducing theorems, proofs, and abstraction. This leads to the idea of axioms and general algebraic structures, with groups treated as a principal example. The process of constructing the real numbers from the rationals is also considered, as a preparation for "analysis", the branch of mathematics where the properties of sequences of real numbers a

Probability theory is branch of mathematics concerned with the study of chance phenomena. Data science involves the handling and analysis of data using a variety of tools: statistical inference, machine learning, and graphical methods. The first part of the module introduces probability theory, providing a foundation for further probability and statistics modules, and for the statistical inference methods taught here. Examples are presented from diverse areas, and case studies involving a variet

This module introduces topics which will be useful throughout students' time as undergraduates and in employment. These skills fall into two categories: computer literacy and presentation skills. One aim of this module is to develop programming skills within Python to perform mathematical investigations. Students will also meet the typesetting package LaTeX, the web design language HTML, and Excel for spreadsheets. These will be used for making investigations, and preparing reports and presentat

Mathematics is the language of science. By framing a scientific question in mathematical language, it is possible to gain deep insight into the empirical world. This module aims to give students an appreciation of this astonishing phenomenon. It will introduce them to the concept of mathematical modelling via examples from throughout science, which may include biology, physics, environmental sciences, and more. Along the way, a range of mathematical techniques will be learned that tend to appear

Linear algebra and calculus are fundamental to most advanced work in pure and applied mathematics and to much of statistics. This module will provide you with basic tools and techniques from linear algebra and calculus. You'll also develop an understanding of the theory underpinning these, enabling you to use these methods in a variety of situations beyond the module. Building on your first year, you'll also continue to develop employability skills throughout this module.

This module will develop your understanding of theory covered in first year modules. You'll explore analysis, which underpins core concepts across the mathematical sciences. You'll examine why familiar tools, like differentiation and integration, actually work, allowing us to prove their formal properties. This rigorous foundation in analysis will enable you to tackle more complex problems in the future. You'll extend your understanding of ideas from calculus to higher dimensions, considering di

Statistical inference and modelling are at the heart of data science, a field of rapidly-growing importance in the modern word. This module develops methods for analysing data, and provides a foundation for further study of probability and statistics at higher Levels. You will learn about a range of standard probability distributions beyond those met at Level 1, including multivariate distributions. You will learn about sampling theory and summary statistics, and their relation to data analysis.

Differential equations are perhaps the most important tool in applied mathematics. They are foundational for modelling all kinds of physical and natural phenomena, including fluids and plasmas, populations of animals or cells, cosmological objects (via relativity), subatomic particles (via quantum mechanics), epidemics, even political and social opinions have been modelled using differential equations. This module will build on the tools learned at Level 1 for analysing differential equations, e

This module will further develop your understanding of abstract algebra. The theory of groups, met at Level 1, will be developed in more generality, with further theory as well as applications to combinatorial problems. You'll also meet the abstract concepts of rings and fields. A ring is similar to a group, but where we have two operations, of addition and multiplication, like the integers, while a field also has a division operation. You'll see concrete examples of both, realising that a numbe

This module examines stochastic processes. These are models of natural and physical processes that incorporate randomness, to reflect the way that life can change unpredictably over time. You'll explore a number of general models for processes where the state of a system is fluctuating randomly. This might include the length of a queue, the size of a reproducing population, or the amount of payouts on insurance policies. You'll learn various techniques for the analysis of these models, preparing

This module builds on first-year mathematical modelling. You'll develop sophisticated models of the universe, grow your skills with vectors and calculus for two or more variables, and learn to translate physical phenomena into solvable mathematical equations. You'll explore the motion of point particles in two dimensions and rigid body rotation. Using Newton's laws, you'll study the power of vectors, and explore the consequences of the conservation of energy and angular momentum in orbital dynam

This module further develops practical programming and data analysis using Python. You'll learn to select and apply suitable Python functions and libraries, develop efficient programming workflows, and perform statistical analysis on data sets of varying sizes. We'll focus on fitting complex models, interpreting results, and evaluating analytical reliability. You'll also gain experience assessing and integrating external Python code, and build the skills to adapt, reuse, and document code respon

Through this module you'll hone the skills and knowledge required of a graduate-level professional. You'll undertake extended project work, which will include relating project work to the literature, setting project aims and objectives, planning and carrying out the work, and reporting it using disciplinary conventions. You'll investigate how your academic studies relate to either research, society, or industry. You'll develop an understanding of where your degree could lead you and reflect on y