Mathematics for the Modern World with a Foundation Year (BSc)
- Subject area: Mathematics
- UCAS code: G303
- Next intake: September 2027
- Duration: 4 years
- Mode: Full time
Why study this course
Prepare for a future of discovery and innovation with the Foundation Year in Mathematics - your gateway to modern, real-world mathematical study and career opportunities.
Alternative route to study
Successful completion of the foundation year will allow you to progress onto the first year of one of the corresponding BSc degree programmes.
Building foundational knowledge
Get confident with key maths topics and build the skills to think deeply, ask questions, and explore new ideas.
Supporting industry demands
You’ll be ready to use your maths skills in exciting careers across tech, finance, education, and beyond.
Skills development
Our focus on creativity and communication will build confidence in sharing ideas, thinking flexibly, and using maths to solve problems in new ways.
Maths for emerging technologies
Explore cutting-edge applications of maths in areas like AI, computer assisted proof, big data analytics, and mathematics for global impact.
This is a four-year full-time degree programme consisting of 120 credits a year, including a Foundation Year.
The Foundation Year is designed to offer a dynamic and supportive environment that develops the core skills and knowledge needed for a degree programme that blends the study of essential mathematical concepts with emerging, future-facing topics. When you have successfully passed the foundation year you will progress to the first year of the corresponding BSc degree programme.
The BSc will give you the same strong mathematical foundations as a traditional maths degree, with a focus on where maths is heading and how it’s transforming our world. You’ll explore real-world problems and learn how maths can be used to create change in areas like sustainability, cybersecurity, data ethics and global development.
You’ll learn about the maths underpinning environmental modelling, resource optimisation, and cryptographic algorithms, equipping you with the skills to contribute to a responsible future. You’ll tackle creative projects that blend maths with entrepreneurship, communications, and emerging technologies.
Alongside problem-solving and theory, you’ll develop essential skills in communication, teamwork, and leadership. You’ll learn how to present ideas clearly, work with different audiences, and use data responsibly and ethically. Whether you're programming with the latest software, investigating patterns through statistics, or pitching mathematical solutions to real-world issues, you’ll be stretching your creativity as much as your logic.
You’ll graduate with a solid understanding of mathematics and how to apply your skills in versatile and dynamic ways. You’ll have the confidence to step into industries that rely on maths to drive progress, spark innovation, and shape a better future.
Subject area: Mathematics
Entry requirements
We accept a combination of A-levels and other qualifications, as well as equivalent international qualifications subject to entry requirements. Typical offers are as follows:
A level
AAB-BBB. Must not include A-level Maths (unless at grade C or below).
Extended/International Project Qualification: Applicants with grade A in the EPQ/IPQ will typically receive an offer one grade lower than the standard offer. Please note that any subject specific requirements must still be met.
- Our grade range covers our standard offer and contextual offer. We carefully consider the circumstances in which you've been studying (your contextual data) upon application. Eligible students will be given an offer that is lower than the standard offer (usually the middle or lower end of the advertised grade range).
- Where there is no grade range advertised and/or where there are selection processes in place (like an interview) you may receive additional consideration in the selection process.
Learn about eligible courses and how contextual data is applied.
International Baccalaureate
34-31 overall or 666-665 in 3 HL subjects. Must not include HL Maths (unless at grade 5 or below).
Baccalaureate Wales
From September 2023, there will be a new qualification called the Advanced Skills Baccalaureate Wales (level 3). This qualification will replace the Advanced Skills Challenge Certificate (Welsh Baccalaureate). The qualification will continue to be accepted in lieu of one A-Level (at the grades listed above), excluding any specified subjects.
GCSE and other essential requirements
You must have or be working towards:
- English language or Welsh language at GCSE grade C/4 or an equivalent (such as A-levels). If you require a Student visa, you must ensure your language qualification complies with UKVI requirements.
We do not accept Critical Thinking, General Studies, Citizenship Studies, or other similar equivalent subjects.
We will accept a combination of BTEC subjects, A-levels, and other qualifications, subject to the course specific grade and subject requirements.
English language requirements
GCSE
Grade C or grade 4 in GCSE English Language.
IELTS (academic)
At least 6.5 overall with a minimum of 5.5 in each subskill.
TOEFL iBT
At least 90 overall with a minimum of 17 for writing, 17 for listening, 18 for reading, and 20 for speaking.
PTE Academic
At least 69 overall with a minimum of 59 in all communicative skills.
Trinity ISE II/III
II: at least two Distinctions and two Merits.
III: at least a Pass in all components.
Other accepted qualifications
Please visit our English Language requirements page for more information on our other accepted language qualifications.
Criminal convictions
You are not required to complete a DBS (Disclosure Barring Service) check or provide a Certificate of Good Conduct to study this course.
If you are currently subject to any licence condition or monitoring restriction that could affect your ability to successfully complete your studies, you will be required to disclose your criminal record. Conditions include, but are not limited to:
- access to computers or devices that can store images
- use of internet and communication tools/devices
- curfews
- freedom of movement, including the ability to travel to outside of the UK or to undertake a placement/studies outside of Cardiff University
- contact with people related to Cardiff University.
Other qualifications from inside the UK
BTEC
DDD-DDM in a BTEC Extended Diploma in any subject.
T level
Acceptance of T Levels for this programme will be considered on a case-by-case basis by the Academic School. Consideration will be given to the T Level grade/subject and grades/subjects achieved at GCSE/Level 2.
Please see our admissions policies for more information about the application process.
Tuition fees for 2027 entry
Your tuition fees and how you pay them will depend on your fee status. Your fee status could be home, island or overseas.
Learn how we decide your fee status
Fees for home status
We are currently awaiting confirmation on tuition fees for the 2027/28 academic year.
1 Home status tuition fees are charged at the maximum fee set by the Government each year. If the tuition fee cap changes before you start your course, we’ll email you to let you know. We’ll explain any changes to your tuition fees, and allow you to withdraw without penalty if you decide not to study with us.
Tuition fees may increase for subsequent years of your course if the fee cap changes. Learn what happens if tuition fees increase.
Fees for overseas status
We are currently awaiting confirmation on tuition fees for the 2027/28 academic year.
Additional costs
You may be required to cover additional costs that are either not essential or are basic costs that a student should be expected to cover themselves. This includes but is not limited to laptop computers, calculators, general stationery, and textbooks (assumed to be available in the library). This will be clearly detailed in all programme information and in any verbal instructions given by tutors.
Course specific equipment
We provide a range of high-spec PCs for students to access, but we do recommend you acquire a laptop computer or tablet to be able to access digital learning materials and run specific software. Free access to specialist software will be arranged by the school as required for study, in all cases for campus use, and when possible individual licenses will be provided.
We recommend that you have a scientific calculator. This will be necessary for completing some calculations and supporting your understanding of material introduced during the programme. Note that graphics calculators are not allowed in any examinations.
Accommodation
We have a range of residences to suit your needs and budget. Find out more on our accommodation pages.
Living costs
We're based in one of the UK's most affordable cities. Find out more about living costs in Cardiff.
Course structure
This is a four-year full-time degree programme consisting of 120 credits a year, including a Foundation Year.
The programme includes a carefully chosen balance of essential mathematical topics and contemporary emerging fields of study. It is structured in such a way that you will acquire over successive years high-level skills of mathematical study and interpretation to become an independent and critical thinker, equipped for professional employment.
In order to successfully progress from the Foundation Year (Year 0), you must satisfy the following criteria:
Successfully obtained a minimum of 120 credits from Year 0 of the programme and achieved a year average of at least 50%.
The modules shown are an example of the typical curriculum and will be reviewed prior to the 2027/2028 academic year. The final modules will be published by September 2027.
Preliminary year
The Foundation Year is a supportive introduction to university-level study, providing a gateway into a degree programme designed for the modern mathematician. You will gain a strong grounding in essential mathematics including Algebra, Calculus, and Statistics. In addition, you’ll develop mathematical communication and problem-solving skills.
| Module title | Module code | Credits |
|---|---|---|
| Introduction to Mechanics | EN0016 | 20 credits |
| Introduction to Algebra | EN0017 | 20 credits |
| Introduction to Trigonometry | EN0018 | 10 credits |
| Introduction to Calculus | EN0019 | 20 credits |
| Statistics and Data | MA0502 | 20 credits |
| Mathematical Investigations, Skills, and Culture | MA0901 | 30 credits |
Year one
Year One contains a foundational core in mathematical topics, alongside the exploration of contemporary applications of the subject and development core competencies for the technology-enhanced careers of the future.
| Module title | Module code | Credits |
|---|---|---|
| Computing for Mathematics | MA1003 | 20 credits |
| Foundations of Mathematics I | MA1005 | 20 credits |
| Foundations of Mathematics II | MA1006 | 20 credits |
| Linear and Differential Equations | MA1011 | 20 credits |
| Probability and Statistics | MA1502 | 20 credits |
| Mathematical Creativity, Communication and Exploration | MA1901 | 20 credits |
Year two
Year Two of the programme builds upon the foundational mathematics introduced in Year One alongside forward thinking content to develop analytical thinking, problem solving techniques and innovation.
| Module title | Module code | Credits |
|---|---|---|
| Linear Algebra and Multivariable Calculus | MA2012 | 20 credits |
| Probability Theory and Stochastic Simulation | MA2503 | 20 credits |
| Operational Research | MA2601 | 20 credits |
| Modern Mathematical Computing | MA2702 | 20 credits |
| Entrepreneurship | MA2902 | 20 credits |
| Module title | Module code | Credits |
|---|---|---|
| Abstract Algebra | MA2015 | 20 credits |
| Mechanics | MA2304 | 20 credits |
Year three
The final year of the programme includes a range of contemporary modules with focus on modern applications of mathematics and investigations into how mathematics is providing insight to global challenges and supporting future living. Some optional modules in the final year will depend on having studied appropriate modules in Year Two. Personal Tutors will be available to guide you through the options available.
| Module title | Module code | Credits |
|---|---|---|
| Mathematics for Global Impact | MA3907 | 30 credits |
| Module title | Module code | Credits |
|---|---|---|
| Big Data Technologies | MA3509 | 20 credits |
| Mathematics of AI and Deep Learning | MA3702 | 10 credits |
| Developing Mathematics Teachers for Future Generations | MA3905 | 20 credits |
| Student Driven Topics in Mathematics | MA3906 | 20 credits |
| Algebraic Topology | MA3008 | 10 credits |
| Differential Geometry of Curves and Surfaces | MA3010 | 10 credits |
| Introduction to Number Theory 2 | MA3011 | 10 credits |
| Algebra II: Rings | MA3014 | 10 credits |
| Algebra III: Fields | MA3015 | 10 credits |
| Complex Analysis and Functional Series | MA3019 | 20 credits |
| Knot Theory | MA3022 | 10 credits |
| Methods of Applied Mathematics | MA3304 | 20 credits |
| Fluid Dynamics | MA3305 | 20 credits |
| Solid Mechanics | MA3306 | 20 credits |
| Stochastic Processes for Finance and Insurance | MA3503 | 20 credits |
| Statistical Modelling | MA3507 | 20 credits |
| Time Series | MA3508 | 10 credits |
| Algorithms and Heuristics | MA3602 | 10 credits |
| Optimisation | MA3603 | 20 credits |
| Game Theory | MA3604 | 10 credits |
The University is committed to providing a wide range of module options where possible, but please be aware that whilst every effort is made to offer choice this may be limited in certain circumstances. This is due to the fact that some modules have limited numbers of places available, which are allocated on a first-come, first-served basis, while others have minimum student numbers required before they will run, to ensure that an appropriate quality of education can be delivered; some modules require students to have already taken particular subjects, and others are core or required on the programme you are taking. Modules may also be limited due to timetable clashes, and although the University works to minimise disruption to choice, we advise you to seek advice from the relevant School on the module choices available.
Learning and assessment
The home for the School of Mathematics is Abacws - a world-leading facility designed in collaboration with students and academic staff to create interdisciplinary, flexible and creative workspaces, with innovative teaching areas being a key feature. Classes will include lectures, practical tutorials, workshops, and staff and student-led seminars. Independent learning is encouraged throughout the course with increasing emphasis on scholarly research to explore new ideas and connect academic theory to practical real-world scenarios.
How will I be supported?
At the start of each year, you will be given a guide to module aims, learning outcomes, methods of assessment, module syllabuses, and reading lists. You will also have access to relevant multimedia resources, presentations, lecture handouts, exercises, and further links via the Learning Central virtual learning environment.
You will be allocated a personal tutor, a member of the academic staff who will provide pastoral support and academic advice during your course. Personal tutors will also guide you through module choice as different options become available throughout the programme.
All lecturing staff can be contacted by email and have either an ‘open door’ policy for students with specific queries about course material, or a system to book meeting times. Student Hubs will also be available to support any administrative queries.
The University offers a range of services including Student Futures, the Counselling Service, the Disability and Dyslexia Service, the Student Support Service and excellent libraries and resource centres.
Further learning support is also available via the University wide Maths Support Service. This provides relaxed and informal drop-in sessions where students are encouraged to discuss any elements of their studies with a tutor on a one-to-one or small group basis.
How will I be assessed?
A range of assessment approaches are utilised throughout the programme. These reflect the outcomes associated with the specific modules and include:
- written examination (at the end of the autumn or spring semesters)
- group based and individual project work
- problem solving exercises
- written reports
- computer programs
- oral assessments
Feedback on progress is typically provided through a combination of discussion in class, comments relating to submitted work, and review of outline solutions to problems. This provides you with opportunity to reflect on your progress and develop independent learning strategies. You are also encouraged to discuss any queries related to specific modules with individual lecturers.
What skills will I practise and develop?
The Learning Outcomes for this Programme describe what you will achieve by the end of your programme at Cardiff University and identify the knowledge and skills that you will develop. They will also help you to understand what is expected of you.
On successful completion of your Programme you will be able to:
Knowledge & Understanding:
- demonstrate foundational knowledge and understanding of core areas of mathematics and some specialist areas
- analyse the scope and breadth of mathematics as a discipline, and its applications to the modern world
- critically assess the development of mathematical ideas and its impact on (global) societal challenges including those relating to climate change, public health, and technological innovation
Intellectual Skills:
- formulate problems mathematically and make hypotheses
- solve problems formulated within established mathematical frameworks in core areas of mathematics and some specialist areas, and draw valid inferences from the solutions
- reason using logical arguments, including identifying assumptions made and the conclusions drawn
- apply concepts and principles in evolving contexts, showing judgement in the selection and application of tools, techniques, models and algorithms
Professional Practical Skills:
- apply modern mathematical tools to support and critically assess decision making in uncertain contexts
- perform calculations and manipulations with precision and rigour within the body of knowledge
- write and run computer code in at least one programming language to analyse problems mathematically
- perform mathematical and statistical analyses to gain insights from data, including drawing inferences from sample data
- identify appropriate mathematical techniques to solve problems in core areas of mathematics and some specialist areas
Transferable/Key Skills:
- effectively communicate mathematical ideas to a variety of audiences in multiple formats
- demonstrate creativity and criticality in problem solving
- locate, critically evaluate, and interpret data and information in an effective manner
- make effective contributions to group work to achieve a specific aim
Careers and placements
Career prospects
This programme is designed to meet the evolving needs of academia and industry with a blend of foundational mathematical knowledge and cutting-edge skills to enable students to pursue diverse careers in technology, finance, healthcare, education, and beyond. It prepares graduates to excel in both traditional roles and emerging fields requiring advanced mathematical expertise.
For students pursuing academia, the programme provides a rigorous pathway to research and advanced study. Opportunities for exploration of emerging areas, independent projects, and exposure to current research trends will develop intellectual curiosity and critical inquiry. The content will also demonstrate how technology can accelerate mathematical exploration and innovation.
Industry increasingly requires mathematicians who can solve real-world problems with technical expertise and practical skills. By embedding computational methods, data analytics, and operational research throughout the curriculum, this programme aligns with these demands.
Placements
Through specific modules included in the programme, students will support the planning and delivery of Outreach and Public Engagement events. This will encourage the development of essential communication skills and inspire the next generation of students to engage with the future world of mathematics.
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HESA Data: Copyright Higher Education Statistics Agency Limited 2021. The Higher Education Statistics Agency Limited cannot accept responsibility for any inferences or conclusions derived by third parties from its data. Data is from the latest Graduate Outcomes Survey 2019/20, published by HESA in June 2022.
