Mathematics MMath

Program Overview

The Mathematics MMath program at the University of Sheffield provides students with advanced mathematical tools and problem-solving skills, preparing them for a career in research, academia, or industry. The program emphasizes tackling intriguing problems, building a solid foundation in mathematical concepts, developing real-world problem-solving skills, and conducting a major research project, equipping graduates with expertise in various sectors, including finance, software development, data science, and academia.

Program Outline

Degree Overview:

The Mathematics MMath program at the University of Sheffield is a four-year, full-time program designed to prepare students for a career in research, whether in academia or industry. The program focuses on developing advanced mathematical tools and problem-solving skills, equipping students to tackle complex real-world challenges. The program's objectives include:

• Tackling intriguing mathematics problems: Students will delve into a wide range of mathematical concepts and theories, exploring both abstract research problems and practical applications.
• Developing advanced problem-solving skills: The program emphasizes the development of logical and analytical thinking, enabling students to approach problems in a structured and efficient manner.
• Gaining experience in real-world problem-solving: Students will have the opportunity to apply their knowledge to real-world scenarios, working on research projects that address current challenges in various fields.
• Building a strong foundation for a successful career: The program incorporates career and employability skills development, preparing students for a variety of career paths in mathematics, data science, finance, and other related fields.
• Conducting a major research project: In their final year, students will undertake a significant research project, collaborating with active researchers and contributing to the advancement of their chosen field.

Outline:

The Mathematics MMath program is structured across four years, with a focus on core modules in the first two years, followed by a wide range of optional modules in the third year, and culminating in a major research project in the fourth year.

Year 1:

• Core Modules:
• Mathematics Core:
Covers fundamental concepts in calculus, linear algebra, and mathematical modeling, providing a foundation for subsequent courses.
• Foundations of Pure Mathematics: Introduces basic constructions in pure mathematics, including axioms, proofs, and abstract algebraic structures.
• Mathematical Modelling: Explores the application of mathematics to scientific questions, introducing techniques like differential equations and calculus.
• Probability and Data Science: Introduces probability theory and data science tools, including statistical inference and machine learning.
• Mathematical Investigation Skills: Develops computer literacy and presentation skills, including programming in Python and using LaTeX for mathematical typesetting.

Year 2:

• Core Modules:
• Mathematics Core II:
Builds upon Year 1's core modules, focusing on foundational skills and knowledge for both higher mathematics and future careers.
• Differential Equations: Explores the theory and application of differential equations, a crucial tool in applied mathematics.
• Analysis and Algebra: Delves deeper into the theory behind familiar mathematical concepts, providing a rigorous foundation for advanced study.
• Optional Modules:
• Stochastic Modelling:
Introduces models for processes with random fluctuations over time, relevant to fields like queueing theory and population dynamics.
• Vector Calculus and Dynamics: Applies vector calculus to understand the dynamics of physical systems, including fluids and solids.
• Group Theory: Explores the properties of groups, a fundamental algebraic structure with applications in various areas of 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 solving mathematical problems and exploring numerical solutions.

Year 3:

• Optional Modules:
• Topics in Mathematical Biology:
Focuses on mathematical modeling of biological phenomena, including epidemics, predator-prey dynamics, and cell biology.
• Introduction to Relativity: Introduces Einstein's theory of relativity and its physical consequences.
• Topics in Number Theory: Explores concepts like prime numbers, congruences, and quadratic reciprocity.
• Metric Spaces: Extends ideas of convergence to the more general framework of metric spaces.
• Complex Analysis: Introduces the study of complex-valued functions of a complex variable, a central area of mathematics.
• Combinatorics: Explores the mathematics of selections and combinations, with applications in counting and pairing problems.
• 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, focusing on the ethical and regulatory constraints of medical experimentation.
• Financial Mathematics: Explores the mathematical ideas behind modern finance, including the Capital Asset Pricing Model and the Black-Scholes option pricing formula.
• Bayesian Statistics: Develops the Bayesian approach to statistical inference, providing an alternative to conventional frequentist methods.
• Machine Learning: Introduces the theory and application of machine learning, a field at the interface of computer science and statistics.
• Generalised Linear Models: Explores the theory and application of generalised linear models, which can be used to investigate relationships between variables.
• Probability and Random Graphs: Studies models of random trees, graphs, and networks, relevant to fields like social networks and communication networks.
• Mathematical Modelling of Natural Systems: Introduces techniques for modeling natural systems, using differential equations, scientific computing, and mathematical reasoning.
• Operations Research: Covers mathematical programming algorithms for solving constrained optimization problems.
• Quantum Theory: Introduces the basics of quantum theory and its applications in various technologies.
• Mathematical Methods: Introduces methods for obtaining approximate solutions to problems involving small parameters.
• Graph Theory: Investigates the mathematics of graphs and their applications in various fields.
• Knots and Surfaces: Studies knots, links, and surfaces, using algebraic invariants to classify them.
• Codes and Cryptography: Explores error-correcting codes and cryptography, including their mathematical foundations and real-life applications.
• Sampling Theory and Design of Experiments: Introduces methods for efficiently collecting data in various settings, including sample surveys and physical experiments.
• Time Series: Covers methods for analyzing data observed repeatedly over time, relevant to fields like economics and engineering.
• Undergraduate Ambassadors Scheme in Mathematics: Provides an opportunity for students to gain experience in mathematics education by mentoring students in local schools.
• Skills Development in Mathematics and Statistics: Consolidates skills development across various areas of the mathematics and statistics curriculum.
• Stochastic Processes and Finance: Studies martingales and diffusions, two classes of stochastic processes relevant to financial phenomena.
• Evolution of Terrestrial Ecosystems: Examines the evolution of terrestrial ecosystems from the Ordovician period to the present day.
• Sustainable Agro-Ecosystems: Highlights threats to global sustainability, focusing on food production and ecosystem functioning.
• Speech Processing: Investigates the representation of speech in various domains and computational approaches to speech parameter extraction.
• 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: Explores current research areas in evolutionary genetics.
• Reinforcement Learning: Teaches the theory and implementation of reinforcement learning.
• Globalising Education: Considers the extent to which education can be viewed as a global context with a shared meaning.
• Pain, Pleasure, and Emotions: Explores recent advances in the study of the affective mind, considering theoretical work in the philosophy of mind and empirical research in affective cognitive science.
• Advanced Topics in Algebra A: Studies algebraic structures like fields, groups, and rings, with applications in number theory, polynomial roots, and algebraic geometry.
• Advanced Topics in Waves and Fluid Dynamics A: Covers concepts and techniques in waves and fluid dynamics, including wave propagation, viscous fluid flow, and boundary layers.

Year 4:

• Core Modules:
• Mathematics and Statistics Project:
Involves the completion of a substantial research project on an advanced topic in mathematics or statistics, under the guidance of a research-active supervisor.
• Optional Modules:
• Machine Learning:
(Same as Year 3)
• Financial Mathematics:
(Same as Year 3)
• Functional Analysis:
Studies infinite-dimensional vector spaces equipped with extra structure, with applications in various areas of mathematics.
• Further Topics in Mathematical Biology: (Same as Year 3)
• Advanced Quantum Mechanics:
Covers quantum mechanics at an intermediate to advanced level, including mathematical formalism, approximate methods, and contemporary topics.
• Topics in Mathematical Physics: Introduces advanced concepts and techniques in modern mathematical physics.
• Generalised Linear Models: (Same as Year 3)
• Sampling Theory and Design of Experiments:
(Same as Year 3)
• Time Series:
(Same as Year 3)
• Mathematical Modelling of Natural Systems:
(Same as Year 3)
• Further Topics in Number Theory:
Explores advanced topics in number theory, building upon previous knowledge.
• Probability and Random Graphs: (Same as Year 3)
• Medical Statistics: (Same as Year 3)
• Bayesian Statistics and Computational Methods:
Introduces Bayesian inference and computational methods for implementing both Bayesian and frequentist inference.
• Advanced Topics in Algebra A: (Same as Year 3)
• Advanced Topics in Algebra B:
(Same as Year 3)
• Advanced Topics in Waves and Fluid Dynamics A:
(Same as Year 3)
• Advanced Topics in Waves and Fluid Dynamics B:
(Same as Year 3)
• Algebraic Topology:
Studies the shape of spaces using algebraic techniques, enabling the use of linear algebra and group theory to study deformations.
• Analytical Dynamics and Classical Field Theory: Discusses the mathematical structures underlying Newton's laws of mechanics and introduces Einstein's theory of gravity.
• Stochastic Processes and Finance: (Same as Year 3)

Assessment:

Students are assessed through a variety of methods, depending on the modules they take. These methods can include:

• Quizzes: Short assessments to test understanding of key concepts.
• Examinations: Formal written assessments to evaluate knowledge and application of concepts.
• Presentations: Oral presentations to demonstrate communication skills and ability to present complex information.
• Participation in Tutorials: Active engagement in small-group discussions to foster critical thinking and problem-solving skills.
• Projects: In-depth investigations of specific topics, requiring research, analysis, and written reports.
• Coursework: Written assignments to demonstrate understanding and application of concepts.
• Other Written Work: Various forms of written assignments, such as essays, reports, and problem sets.

Teaching:

The Mathematics MMath program employs a variety of teaching methods to cater to different learning styles and enhance student engagement. These methods include:

• Lectures: Formal presentations of key concepts and theories by experienced faculty members.
• Problems Classes: Small-group sessions where students work together on problems and receive guidance from instructors.
• Research Projects: Opportunities for students to conduct independent research under the supervision of faculty members.
• Programming Classes: Hands-on sessions to develop programming skills in languages like Python.
The program is taught by a team of highly qualified and experienced faculty members who are actively involved in research and are committed to providing students with a stimulating and supportive learning environment.

Careers:

The Mathematics MMath program opens doors to a wide range of career paths, both in academia and industry. Graduates are highly sought after by employers in various sectors, including:

• Banking, Insurance, and Pensions: Mathematical skills are essential for financial modeling, risk assessment, and actuarial science.
• Software Development: Strong mathematical foundations are valuable for developing algorithms, data structures, and software applications.
• Data Science: The ability to analyze and interpret large datasets is crucial for data-driven decision-making in various industries.
• Student Society: The Sheffield University Mathematics Society (SUMS) organizes activities throughout the year, fostering a sense of community among mathematics students.
• Facilities: Students have access to state-of-the-art facilities, including classrooms, lecture theaters, computer rooms, and social spaces.
• City Experience: Sheffield is a vibrant city with a rich cultural scene, offering a wide range of opportunities for students to explore and enjoy.

Home students 2024 annual tuition fee£9,250 Overseas students 2024 annual tuition fee£25,540