If you already excel in mathematics, summer is an opportunity to go further. These advanced mathematics courses are designed for high achievers who want depth, challenge and exposure to university-style learning. Studying alongside equally motivated peers, you are encouraged to think rigorously, question assumptions and explore mathematics well beyond the school syllabus.
Set in world-leading academic cities such as Oxford, Cambridge, London and Boston, these programmes offer more than subject enrichment. Students learn in environments shaped by centuries of mathematical discovery, gaining first-hand experience of what advanced mathematical study feels like. Small classes, expert tutors and demanding content work together to stretch able students and sharpen analytical thinking.
These courses are particularly well suited to students aiming for:
You will strengthen your ability to tackle complex concepts, build confidence with advanced material and gain insight into the expectations of higher-level study. By the end of the course, you will leave academically stretched, motivated and focused on your next steps.
If you are aged 18–24, these mathematics courses provide an intellectually demanding setting for those with a strong academic foundation who want to deepen their expertise. Whether preparing for postgraduate study, building deeper mathematical understanding or developing a more sophisticated problem-solving approach, you are given the space to engage seriously with advanced mathematical ideas.
Studying mathematics in Oxford or Cambridge places students in an environment where precision, independence and academic curiosity are expected. Teaching is tutorial-based and discussion-driven, encouraging students to:
If you are a graduate, gap-year student, or undergraduate seeking academic enrichment, these courses offer both challenge and clarity. You will sharpen analytical skills, reinforce confidence in advanced concepts and gain clearer direction for future academic or professional paths. You will leave with stronger mathematical insight, renewed focus and a clearer sense of where your abilities can take you next.
Oxford
Oxford has a long tradition of mathematics and mathematical logic.
Roger Penrose – Mathematician and mathematical physicist; taught at Oxford
John Wallis – One of the founders of calculus; Savilian Professor of Geometry at Oxford
Charles Dodgson (Lewis Carroll) – Lecturer in mathematics at Oxford; author and logician
Cambridge
Cambridge is one of the most influential centres of mathematics in the world.
Isaac Newton – Developed calculus; Lucasian Professor of Mathematics
Alan Turing – Pioneer of computer science and mathematical logic; studied and worked at Cambridge
Srinivasa Ramanujan – Extraordinary mathematical genius; worked at Cambridge
Mary Cartwright – Influential mathematician in dynamical systems; Girton College, Cambridge
London (University of London institutions, especially UCL)
London has played a key role in the development of modern mathematics, statistics and logic.
Augustus De Morgan – Founding Professor of Mathematics at University College London; pioneer of mathematical logic and algebra; best known for De Morgan’s laws.
Karl Pearson – Professor at UCL and a founder of modern statistics; introduced correlation, regression and key statistical methods still used today.
Ronald Fisher – One of the most influential statisticians of all time; associated with UCL early in his career; developed statistical inference, experimental design and foundational ideas in data analysis.
Boston (Harvard, MIT and the Boston academic cluster)
Boston is a global hub for modern mathematics and applied mathematics.
Norbert Wiener – Founder of cybernetics; MIT professor
John Nash – Nobel laureate and mathematician; studied at MIT
Isadore Singer – Co-creator of the Atiyah–Singer Index Theorem; MIT
Studying mathematics in Oxford, Cambridge, London or Boston means learning in places where:
These environments continue to attract high-achieving students who want depth, rigour and intellectual heritage—not just classroom instruction.
Here are some of the outstanding courses At A Glance
Pre-University Mathematics – Bucksmore Education (Ages 15–18 | Oxford University Colleges | 2 or 4 weeks | Fees from £3,195 | June–August 2026)
At a Glance
An immersive introduction to university-level mathematics for ambitious students aged 15–18, delivered in Oxford University colleges. This course combines theoretical mathematics with applied modelling, covering core foundations such as algebra, calculus, probability and statistics. Students learn how to analyse real-life phenomena through logical reasoning, hypothesis testing and structured problem-solving, preparing them for mathematically intensive university courses.
What This Course Offers
University-style teaching focused on both theory and application; coverage of advanced mathematical foundations relevant to mathematics, physics and data analysis; development of transferable skills including logical reasoning, modelling and analytical thinking; workshops, case studies and real-world projects; 23 hours of academic tuition per week; guest lectures from inspiring speakers; accommodation in Oxford University colleges including St Hilda’s College; a formal graduation ceremony in an Oxford hall; weekly excursions including two full-day and one half-day trip; all-inclusive fees covering meals, academic materials, excursions, insurance and airport transfers (conditions apply).
Who This Course Is For
This course is suited to motivated students who want a structured introduction to university-level mathematics and a realistic insight into undergraduate study. It is ideal for those considering degrees in mathematics, engineering, physics, computer science or related fields, and for students who want to strengthen academic confidence, analytical thinking and readiness for the rigour of university study in an authentic Oxford setting.
Mathematics – Oxford Summer Courses (Ages 16–17 | Cambridge University Colleges | 2 weeks | Fees from £6,995 | June–August 2026)
At a Glance
A challenging and theory-focused mathematics programme for academically strong students aged 16–17, delivered in the historic setting of Cambridge University colleges. This course goes beyond calculation to explore mathematical reasoning, proof, and rigorous argument. Students develop a deep understanding of fundamental theory and learn how to apply mathematical thinking to complex problems, future study and real-world contexts.
What This Course Offers
Tutorial-style teaching with qualified academics, including 1:1 or 2:1 tutorials and small seminars of no more than eight students; completion of two pieces of independent academic work with personalised feedback; academic skills masterclasses focused on critical thinking; tutorial Q&A sessions; expert talks exploring future academic and career pathways; accommodation in Cambridge University colleges with daily breakfast and evening meals included; social activities, day trips and programmed excursions; a graduation ceremony; airport transfers (UK courses only, conditions apply); access to Oxford Summer Courses Foundations; certificate of completion and a letter of recommendation from your tutor.
Who This Course Is For
This course is suited to high-achieving students who enjoy abstract thinking, logical reasoning and mathematical proof. It is ideal for those considering mathematically intensive degrees and for students who want to strengthen their ability to reason rigorously, write precise arguments and approach advanced mathematics with confidence in a university-style academic environment.
Mathematics in Boston – Immerse Education (Ages 15–18 | Boston | 2+ weeks | Fees from £7,495 | June–August 2026)
At a Glance
A rigorous, university-style mathematics programme for high-achieving students aged 15–18, delivered in Boston, one of the world’s leading centres for science, technology and innovation. Students study advanced topics including calculus, linear algebra, probability and differential equations, while developing strong analytical, logical and problem-solving skills. The course places a strong emphasis on applying mathematics to real-world contexts such as engineering, economics, computer science and cryptography.
What This Course Offers
In-depth academic modules in calculus, probability and linear algebra; small-group classes with an average class size of seven; 1:1 tutorials with experienced academic tutors; completion of a personal academic project suitable for university applications; personalised tutor evaluation and feedback; 40+ hours of tuition over two weeks; guest speaker sessions; mentoring support; accommodation at Suffolk University with breakfast and dinner included; tailored cultural and social activities; optional visits to Harvard University and MIT; a formal graduation ceremony with certificates; full pastoral support from the Immerse team.
Who This Course Is For
This course is designed for confident, academically strong students who want to experience university-level mathematics in an international academic setting. It is ideal for students considering mathematically intensive degrees and those who enjoy independent research, abstract thinking and applying mathematical theory to complex, real-world problems while preparing for future study at top universities.
Mathematics in London – Academic Insights (Ages 15–18 | London | 2 weeks | Fees from £7,495 | Summer 2026)
At a Glance
A university-style mathematics programme for high-achieving students aged 15–18, set in London’s vibrant academic and cultural environment. This course deepens understanding of mathematical theory while preparing students for university-level study. Core topics include calculus, algebra, probability, linear algebra, discrete mathematics and mathematical modelling, with a strong focus on logical reasoning, analytical thinking and real-world application across science, technology and economics.
What This Course Offers
Small-group academic seminars and 1:1 tutorials led by experienced tutors; 40+ hours of tuition over two weeks; completion of a personal academic project applying theory to real-world problems; personalised tutor evaluation and feedback; guest speaker sessions; mentoring support from UCL students; accommodation in UCL college residences with breakfast and dinner included; tailored cultural and social activities; excursions including museum visits, Thames boat trips and a full-day visit to Oxford or Cambridge; formal graduation ceremony; certificate of attendance; full pastoral support throughout the programme.
Who This Course Is For
This course is designed for confident, academically strong students who want to experience university-level mathematics in a global city setting. It is ideal for those considering mathematically intensive degrees and students who enjoy abstract thinking, problem-solving and applying mathematical concepts to practical challenges, while gaining insight into academic life at a leading university.
Here is a clear comparative table for these courses, showing student outcomes.
| Course + provider | Ages | Main focus of this course | Skills | Skills and qualifications (student outcomes) |
|---|---|---|---|---|
| Mathematics (Cambridge) – Oxford Summer Courses | 16–17 | Mathematical reasoning beyond calculation, focusing on theory, proof and rigorous argument in a Cambridge college setting. | Logical reasoning; constructing and testing proofs; critical thinking; independent academic work. | Stronger ability to write and defend mathematical arguments; experience of tutorial-style learning; certificate of completion and tutor reference supporting university applications. |
| Pre-University Mathematics (Oxford) – Bucksmore Education | 15–18 | University-level mathematics through theoretical and applied modelling, linking maths to physics and data analysis. | Modelling real-life phenomena; logical reasoning; analysing problems; proposing hypotheses; testing solutions. | Greater readiness for mathematically intensive undergraduate study; improved analytical confidence; experience of university-style study; certificate of completion. |
| Mathematics in London – Academic Insights | 15–18 | University-style mathematics in London covering calculus, algebra, probability, linear algebra and mathematical modelling. | Logical and analytical thinking; problem-solving; applying theory to real-world systems and data; independent project skills. | Completed academic project demonstrating research and critical thinking; increased confidence with university-level maths; certificate of attendance and personalised academic evaluation. |
| Mathematics in Boston – Immerse Education | 15–18 | Rigorous introduction to university-level mathematics, applying theory to science, engineering, economics and computing. | Analytical and logical reasoning; independent research; applying maths to real-world problems; advanced problem-solving. | Completed personal academic project suitable for university applications; strengthened academic profile; certificate of attendance and tutor evaluation. |
| Mathematics – Reach Cambridge | 13–18 | Rigorous introduction to university-level mathematics, combining theory with real-world applications. | Theoretical understanding; computational confidence; critical thinking; application of maths across STEM fields. | Clearer understanding of university-level maths expectations; improved confidence with advanced topics; certificate of completion supporting future study choices. |
Cambridge
There is no better place to gain an introduction to university-level mathematics than at Cambridge – a home to numerous Fields Medal winners.
Cambridge
The Mathematics Cambridge summer school at Oxford Summer Courses, designed for 13-15 years old students, provides seminars and small group learning and is priced from £6,995.
Oxford
The Mathematics summer school at Oxford Summer Courses, designed for 13-15 years old students, provides seminars and small group learning and is priced from £6,995.
Oxford
The Mathematics summer school at Oxford Summer Courses, designed for 16-17 years old students, provides tutorials and is priced from £6,995.
Cambridge
The Mathematics Cambridge summer school at Oxford Summer Courses, designed for 16-17 years old students, provides tutorials and is priced from £6,995.
Oxford
The Mathematics summer school at Oxford Summer Courses, designed for 18-24 years old students, provides tutorials and is priced from £6,995.
Cambridge
The advanced Mathematics Cambridge summer school at Oxford Summer Courses, designed for 18-24 years old students, provides tutorials and is priced from £6,995.
Boston
Solve complex problems in Boston, a hub for innovation and home to leading scientific research.
Cambridge
Advance your mathematical thinking in Cambridge, a city that has shaped some of the world’s greatest mathematicians.
Explore advanced mathematical concepts in London, a city where innovation and problem-solving meet global application.
Oxford
Solve complex equations in Oxford, following in the footsteps of world-renowned mathematicians.
Oxford
This programme prepares students to excel in their chosen subjects within the highly competitive higher education environment. Students choose one university-level subject taught at a first-year undergraduate level.
Cambridge
This course is for students interested in studying in the USA. It will provide complete preparation for the SAT, the admission examination required by American universities.