Degree overview

Together these courses will take up half of your first year; a full year is 120 credits.

Introduction to Linear Algebra

You will learn more about vectors, matrices and systems of linear equations. You may have met some of the early ideas at school but throughout the course you will learn about new abstract concepts. You will use the mathematical ideas encountered in practical contexts but also lay the foundations for your study of pure mathematics in subsequent years.

Calculus and its Applications

Calculus is the most fundamental tool in the study of mathematics and is vital for many of its applications. This course will revise some of the calculus you studied at school and develop it further but will treat it with the rigour required at university level.

Proofs and Problem Solving

This course introduces the fundamental skills needed for advanced study in pure mathematics. You will develop the skill of reading, understanding and using the precise language of professional mathematicians and learn to construct your own rigorous proofs. During the course you will also engage with many problems, obtaining the practice required to become an effective problem-solver.

The other half of your first year will be spent studying optional courses. These can either be outside subjects or optional mathematics courses. If studying a joint honours programme, a portion of this time will be taken up by studying compulsory courses from your second degree subject.

Outside subjects

Outside courses can be chosen from across the University, provided the timetable fits. Popular choices include, but are not limited to, physics, informatics (computer science), economics, business, philosophy and languages.

Examples of outside subjects

If studying the MA (Hons) Mathematics programme, you will typically choose one subject and study this in both Years 1 and 2. Other programmes allow for more variety.

Optional mathematics courses

Fundamentals of Algebra and Calculus

This is an introductory online course in University Mathematics which provides extra preparation in key topics from advanced mathematics. The course introduces and develops a range of topics that incoming undergraduates may not have previously studied, or may benefit from studying in more depth.

Introduction to Data Science

This is an introductory course in data science and statistical thinking. You will learn to explore, visualise, and analyse data to understand natural phenomena, investigate patterns, model outcomes, make predictions and do so in a reproducible and shareable manner. You will work on problems and case studies inspired by and based on real-world questions and data, and will also gain experience in R, a statistical computing language.

Students on all of our programmes will take the following compulsory courses.

Several Variable Calculus and Differential Equations

This course builds on the calculus from Year 1, by extending the ideas to functions of more than one variable. You will learn about partial derivatives and multiple integrals, as well as methods for solving first and second order differential equations.

Fundamentals of Pure Mathematics

You will learn about real analysis – including a rigorous treatment of limits, continuity, differentiability and infinite series – as well as being introduced to group theory and the mathematics of symmetry.

The following courses are either core or optional depending on your degree programme:

• Probability

• Statistics

• Computing and Numerics

• Facets of Mathematics

You can see which courses are compulsory for your particular programme of interest by looking at the relevant entry in the University's online degree finder.

Mathematics Degree Finder | University of Edinburgh

You will continue studying outside subjects. These can lead on from the ones taken in Year 1, or can be completely different.

If studying the MA (Hons) Mathematics programme, you will continue to study the one outside subject you chose in Year 1.

If studying a joint honours programme, a portion of this time will be taken up by studying compulsory courses from your second degree subject.

For students taking the accelerated programme, you will study the compulsory core Year 2 mathematics courses for your programme, as well as courses that cover the compulsory material from Year 1:

• Accelerated Algebra and Calculus
• Accelerated Proofs and Problem Solving

As a result, you will have very little time left to study other subjects. Most students have space for just one course from another subject.

Our students will take between two and four of our core Honours courses:

• Honours Algebra
• Honours Analysis
• Honours Complex Variables
• Honours Differential Equations

If studying one of our Mathematics degrees (BSc, MA, or MMath), all four of these courses are compulsory. If you are taking a joint honours programme, or are taking a specialised mathematics degree (e.g. BSc Mathematics and Statistics, or Applied Mathematics), you will be required to take a selection of these Honours courses, which will vary depending on your programme.

These courses provide an excellent grounding in advanced mathematics and prepare you for the options available later in your programme.

Employability Skills component

Each honours course contains a skills component. This enables you to develop valuable employability skills such as:

• programming
• group work
• presentation skills

The rest of your time will be spent studying other courses from the School of Mathematics. This is the stage of the degree when you will begin to specialise and narrow your mathematical focus.

Current optional courses include:

• Financial Mathematics
• Introduction to Number Theory
• Statistical Computing

As a Year 4 student, you will complete at least one of the following.

Research project (20 or 40 credits)

The opportunity to research a new area of mathematics! Completing the project allows you to research a topic in depth and provides you with lots of transferable skills, such as communication skills (written and verbal) and the ability to explain complex ideas in a new way. The project can be done as a group or individually.

Mathematical Education (20 credits)

If you choose this option, you will learn about the theories of learning and teaching mathematics. Then you will put your knowledge into practice, undertaking short placements at local primary schools or organising revision sessions for local Advanced Higher students.

Statistical Case Studies (20 credits)

This course allows you to undertake consultancy-style projects as part of a team. Projects will be focused on data analysis problems using complex, real-world data.

The rest of your time will be spent studying a selection of mathematics courses.

You can choose from a wide range of options reflecting the diversity of research interests in the School. We offer a large selection of courses in:

• pure mathematics

• applied mathematics

• statistics

• operational research

• financial mathematics

• mathematical biology

• mathematical education

Research project (40 credits)

You will complete a substantial research project, under the guidance of an experienced mathematician. This accounts for a third of your final year.

Optional mathematics courses (80 credits)

The rest of your time will be spent studying masters level mathematics courses. Again, the  course selection is influence by the varied research interests in the School.