Mathematics with Placement Year MMath

Program Overview

The Mathematics with Placement Year MMath program at Sheffield University equips students with advanced theoretical knowledge and practical experience in mathematics through a 5-year course structure that includes an industry placement year. Designed to develop problem-solving skills, the program offers a wide range of optional modules for specialization and prepares graduates for successful careers in fields such as finance, data science, and software development.

Program Outline

Degree Overview:

This program, Mathematics with Placement Year MMath, is a 5-year full-time program designed to provide students with a comprehensive understanding of mathematics and its applications in the real world. The program aims to equip students with advanced theoretical knowledge and practical experience through an industry placement year.

Objectives:

• Develop problem-solving skills: Students will learn to apply their mathematical skills to real-world problems.
• Gain industry experience: The placement year provides students with hands-on experience in applying mathematics in a business setting.
• Specialize in areas of interest: Students can tailor their degree by choosing from a wide range of optional modules.
• Enhance career prospects: The program incorporates career development skills and prepares students for successful careers in various fields.

Outline:

Year 1:

• Core Modules:
• Mathematics Core:
Covers foundational topics like calculus and linear algebra.
• Foundations of Pure Mathematics: Introduces basic constructions in pure mathematics, including axioms, proofs, and algebraic structures.
• Mathematical Modelling: Explores the application of mathematics in various scientific fields.
• Probability and Data Science: Introduces probability theory and data science tools using the R programming language.
• Mathematical Investigation Skills: Develops computer literacy and presentation skills using Python, LaTeX, HTML, and Excel.

Year 2:

• Core Modules:
• Mathematics Core II:
Builds upon Year 1's core modules, focusing on foundational skills for higher mathematics and employability.
• Differential Equations: Explores the application of differential equations in modeling various physical and natural phenomena.
• Analysis and Algebra: Delves deeper into analysis and algebra, providing a rigorous foundation for advanced mathematical concepts.
• Statistical Inference and Modelling: Develops methods for analyzing data and statistical modeling using the R programming language.
• Optional Modules:
• Stochastic Modelling:
Introduces models for processes with random fluctuations over time.
• Vector Calculus and Dynamics: Applies vector calculus and differential equations to understand the dynamics of physical systems.
• Group Theory: Explores the properties of groups, a fundamental object in mathematics.
• Mathematics and Statistics in Action: Investigates case studies of using mathematics and statistics to solve real-world problems.
• Scientific Computing: Develops programming skills in Python for mathematical investigations.
• Religion and the Good Life: Examines the relationship between religion and a well-lived life.
• Logic in Computer Science: Introduces the foundations of logic in computer science.
• Children and Digital Cultures: Examines the impact of digital technology on children's lives.
• Dimensions of Education Policy: Explores key issues in education policy.
• Unlocking Past Environmental Changes: Investigates methods for studying past environmental changes.
• Digital Storytelling: Introduces digital storytelling techniques and technologies.
• Political Philosophy Today: Investigates contemporary topics and issues in political philosophy.
• Theory of Knowledge: Examines philosophical issues surrounding knowledge.
• Automata, Computation and Complexity: Introduces the theoretical foundations of computing systems.

Year 3:

• Industry Placement: Students spend a year gaining practical experience in a relevant industry.

Year 4:

• Optional Modules:
• Topics in Mathematical Biology:
Focuses on mathematical modeling of biological phenomena.
• Introduction to Relativity: Introduces Einstein's theory of relativity and its physical consequences.
• Topics in Number Theory: Studies integers, primes, and equations.
• Metric Spaces: Explores convergence of iterative processes in metric spaces.
• Complex Analysis: Introduces the study of complex-valued functions of a complex variable.
• Combinatorics: Investigates the mathematics of selections and combinations.
• Game Theory: Applies mathematical skills to the study of game theory and its applications in economics.
• Medical Statistics: Covers clinical trials and survival data analysis.
• Financial Mathematics: Explores the mathematical ideas behind modern finance.
• Bayesian Statistics: Develops the Bayesian approach to statistical inference.
• Machine Learning: Introduces the theory and application of machine learning.
• Generalised Linear Models: Introduces the theory and application of generalised linear models.
• Probability with Measure: Introduces the modern basis for probability theory.
• Mathematical Modelling of Natural Systems: Provides a practical introduction to techniques for modeling natural systems.
• Operations Research: Introduces mathematical programming algorithms for constrained optimization problems.
• Quantum Theory: Introduces the basics of quantum theory and its applications.
• Mathematical Methods: Introduces methods for obtaining approximate solutions to problems involving small parameters.
• Graph Theory: Investigates the mathematics of graphs and their applications.
• Knots and Surfaces: Studies knots, links, and surfaces in an elementary way.
• Codes and Cryptography: Explores error-correcting codes and cryptography.
• Sampling Theory and Design of Experiments: Introduces methods for obtaining samples from finite populations and designing experiments.
• Time Series: Introduces methods for analyzing data observed repeatedly over time.
• Undergraduate Ambassadors Scheme in Mathematics: Provides an opportunity for students to gain experience in mathematics education through mentoring in local schools.
• Skills Development in Mathematics and Statistics: Consolidates skills development across various areas of the curriculum.
• Stochastic Processes and Finance: Studies martingales and diffusions and their applications in finance.
• Evolution of Terrestrial Ecosystems: Examines the evolution of terrestrial ecosystems.
• Sustainable Agro-Ecosystems: Highlights threats to global sustainability and considers sustainable management of agro-ecosystems.
• Speech Processing: Investigates the representation and processing of speech.
• History of Astronomy: Provides an introduction to the historical development of modern astronomy.
• Human Planet: Examines the historical, social, cultural, and political dimensions of sustainability.
• Topics in Evolutionary Genetics: Examines current research areas in evolutionary genetics.
• Reinforcement Learning: Teaches the theory and implementation of reinforcement learning.
• Globalising Education: Considers the global context of education.
• Pain, Pleasure, and Emotions: Explores recent advances in the study of the affective mind.
• Advanced Topics in Algebra A: Studies algebraic structures like fields, groups, and rings.
• Advanced Topics in Waves and Fluid Dynamics A: Covers concepts and techniques in waves and fluid dynamics.

Year 5:

• Core Modules:
• Mathematics and Statistics Project:
Involves the completion of a substantial project on an advanced topic in mathematics or statistics.
• Optional Modules:
• Machine Learning:
Introduces the theory and application of machine learning.
• Financial Mathematics: Explores the mathematical ideas behind modern finance.
• Functional Analysis: Studies infinite-dimensional vector spaces equipped with extra structure.
• Further Topics in Mathematical Biology: Focuses on mathematical modeling of biological phenomena.
• Topics in Mathematical Physics: Introduces advanced concepts and techniques in modern mathematical physics.
• Generalised Linear Models: Introduces the theory and application of generalised linear models.
• Sampling Theory and Design of Experiments: Introduces methods for obtaining samples from finite populations and designing experiments.
• Time Series: Introduces methods for analyzing data observed repeatedly over time.
• Mathematical Modelling of Natural Systems: Provides a practical introduction to techniques for modeling natural systems.
• Further Topics in Number Theory: Treats examples of further topics in number theory.
• Probability and Random Graphs: Studies models of random trees, graphs, and networks.
• Probability with Measure Theory: Introduces the modern basis for probability theory.
• Advanced Particle Physics: Provides a comprehensive understanding of modern particle physics.
• Medical Statistics: Introduces an important application of statistics: medical research.
• Bayesian Statistics and Computational Methods: Introduces the Bayesian approach to statistical inference and computational methods.
• Advanced Topics in Algebra A: Studies algebraic structures like fields, groups, and rings.
• Advanced Topics in Algebra B: Studies algebraic structures like fields, groups, and rings.
• Advanced Topics in Waves and Fluid Dynamics A: Covers concepts and techniques in waves and fluid dynamics.
• Advanced Topics in Waves and Fluid Dynamics B: Covers concepts and techniques in waves and fluid dynamics.
• Algebraic Topology: Covers algebraic topology, following on from metric spaces.
• Analytical Dynamics and Classical Field Theory: Discusses Newton's laws of mechanics and their influence on field theory.
• Stochastic Processes and Finance: Studies stochastic processes and their applications in finance.

Assessment:

• Variety of methods: Assessment methods include quizzes, examinations, presentations, participation in tutorials, projects, coursework, and other written work.

Teaching:

• Lectures: Students learn through lectures, which provide a comprehensive overview of the subject matter.
• Problem classes: Small group problem classes allow students to practice their skills and receive feedback from tutors.
• Research projects: Students engage in research projects to develop their independent research skills.
• Programming classes: Some modules include programming classes to enhance students' computational skills.

Careers:

• Wide range of opportunities: Graduates with strong mathematics skills are highly sought after in various fields, including banking, insurance, software development, data science, and security agencies.
• Employer examples: Organizations that have hired Sheffield maths graduates include AstraZeneca, BAE Systems, Barclays, Bet365, Dell, Deloitte, Goldman Sachs, GSK, HSBC, IBM, Lloyds, PwC, Unilever, the Civil Service, and the NHS.

Other:

• Student society: The Sheffield University Mathematics Society (SUMS) organizes activities throughout the year, fostering a sense of community among students.
• Facilities: Students have access to classrooms, lecture theatres, computer rooms, and social spaces in the Hicks Building.

Please use 2024-25 information as a guide. £9,250Home students 2024 annual tuition fee£25,540Overseas students 2024 annual tuition fee