Summer enrichment · Ages 11 to 17 · UK-wide, online

Online maths summer school in the UK

The UK's best known maths summer school, the UKMT National Mathematics Summer School, is a free week away that students cannot apply for: invitations go by lottery to a small share of top scorers in the Intermediate Mathematical Challenge. Modern Age Coders is not connected with UKMT. Over the summer we teach the same kind of maths, number theory, combinatorics, graphs, induction and proof writing, live online through our olympiad and competition course, for pupils aged 11 to 17, as a group or 1-on-1. This page explains the UKMT summer school from UKMT's own pages, lists other programmes, and lays out a five-day online summer plan with worked examples.

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UKMT, Oxford and King's pages read 31 October 2026 · Not linked to UKMT or any summer school

What is the UKMT maths summer school, and how do students get in?

The National Mathematics Summer School is a one-week residential event run by the UK Mathematics Trust for students aged 14 to 16. Nobody applies: UKMT sends invitations through schools in March to students chosen at random from the top 1.5 per cent of Intermediate Mathematical Challenge results, in Years 10 to 11 in England and Wales, S3 to S4 in Scotland and Years 11 to 12 in Northern Ireland, with only one student per school. UKMT says it usually runs three events a year from the start of August. Modern Age Coders has no link with UKMT; we teach summer school topics live online on our olympiad course to any pupil aged 11 to 17, in groups of 15 to 20 or 1-on-1.

Where to begin

Three courses for a summer of maths

Choose by age and appetite. Each card opens a syllabus you can compare with the summer school topic list.

Maths Olympiad & Competition Course course thumbnail

SSU / 01

Olympiad and summer school topics

Number theory, combinatorics, geometry, graphs and induction, with written solutions, for ages 13 to 17.

Open the syllabus →
Middle School Math Competitions course thumbnail

SSU / 02

Junior competition maths

Puzzle-rich problem solving for ages 11 to 14, the years before an IMC score counts.

Open the syllabus →
Maths Through Coding course thumbnail

SSU / 03

Maths through coding

A summer project that uses Python to explore patterns, for ages 10 to 15 who like both.

Open the syllabus →

UKMT summer school

What happens at the UKMT National Mathematics Summer School?

A week of maths sessions, problem solving in groups and evening activities, run by volunteers who are often maths teachers or former attendees. The table sets out the facts as UKMT publishes them.

UKMT National Mathematics Summer School, from UKMT's summer schools page read 31 October 2026
QuestionWhat UKMT says
What is it?Residential events, "one week long", for young people with an interest in maths
When?"Usually from the start of August onwards"; three events a year, Sunday to Friday
Ages and years14 to 16; Years 10 to 11 in England and Wales, S3 to S4 in Scotland, Years 11 to 12 in Northern Ireland
How are students chosen?At random from the top 1.5% of Intermediate Mathematical Challenge results
How do invitations arrive?"Invitations are sent through schools in March"
LimitsOne student per school; a school cannot send students two years in a row
EligibilityUK passport holders not requiring a visa, with UK-based emergency contacts
Who teaches?Volunteers, with Enhanced DBS checks and safeguarding training
TopicsNumber Theory, Geometry, Combinatorics, Graph Theory, Proof by Induction, Writing Maths, Maths at University, Repetition and Chaos, Polyhedra, Logic Puzzles and more

Seniors: going back a second time

UKMT invites past Juniors to apply to return as Seniors, with "one Senior per group of six Juniors". Volunteers highlight suitable students, and Senior applications "usually go out in December".

Seniors get more specialised sessions that push beyond the secondary curriculum into university topics.

If the school does not enter the IMC

UKMT's answer is that "entering IMC as a visiting student may be possible" at another local school, which is under no obligation to agree.

For pupils whose school does enter, the first job each year is simply to sit the Intermediate Challenge, which our intermediate olympiad page covers.

Source: UK Mathematics Trust, National Mathematics Summer School, read 31 October 2026. UKMT does not charge invited students in what we read; we print no fees for any programme. Modern Age Coders is not connected with UKMT.

Who is invited

How many students get a UKMT summer school place?

Very few, and luck plays a large part. UKMT publishes its own 2024 figures, and they explain why a high scorer can miss out.

  1. UKMT starts with all Intermediate Mathematical Challenge results: "somewhere around 226,000 in 2024".
  2. It takes the top 1.5 per cent of scorers in the eligible years.
  3. It selects one student at random from each school, which in 2024 gave 843 students, leaving out schools that sent someone the previous year.
  4. A second lottery chooses the final invitations: "108 Juniors in 2024".
  5. If a student declines, the place goes by lottery to another school and student.

Our arithmetic on those figures

108 invitations against about 226,000 results is roughly one invitation for every 2,100 results, by our calculation. Even among the 843 shortlisted after the one-per-school step, about one in eight was invited.

UKMT is open about why: it wants wider access, so it spreads places across schools rather than taking the top scores.

What that means for a family

A summer school invitation is a lovely surprise, not a plan. A strong scorer from a school with several strong scorers may never be the one drawn.

If your child loves the kind of maths on that topic list, it makes sense to find a way to do it every summer, invited or not.

Figures quoted from UKMT's summer school FAQ, read 31 October 2026. The one-in-2,100 and one-in-eight ratios are our own arithmetic on UKMT's numbers.

Other programmes

What other maths summer schools are there for UK students?

A handful of university-linked programmes, each with its own age and entry rule. We list only what the organisers say on their own pages, and we print no fees.

Other maths summer programmes open to UK students, from the organisers' pages read 31 October 2026
ProgrammeWho forLengthEntry
PROMYS Europe (with the University of Oxford Mathematical Institute, Wadham College and the Clay Mathematics Institute)At least 16, pre-university, ordinarily resident in EuropeA 6-week programme of intensive number theoryApplication with problems; applications open each January
King's College London Mathematics School summer schoolYear 11 students planning A level Maths and PhysicsFive daysKing's says its summer schools are completely free
UKMT National Mathematics Summer SchoolAges 14 to 16, by year groupOne week, residentialInvitation only, by lottery

Oxford's PROMYS Europe page was last updated in February 2024, so check the programme's own site for the current year. There are also paid commercial summer camps in maths and coding; we do not review or price them here. For coding over the holidays, our online coding summer course page covers the options.

Sources: University of Oxford, PROMYS Europe; King's Maths School, outreach for students. We are independent of both.

A five-day plan

What could an online maths summer school week cover?

Here is a five-day plan we wrote around topics on UKMT's own list, with one worked example a day. It is our programme, not UKMT's, and it suits ages 13 to 17; younger pupils take each day more slowly.

Our five-day online summer plan
DayTopicThe ideaOne problem (ours)
1Combinatorics: the pigeonhole principleMore objects than boxes forces a shared boxPick any six numbers from 1 to 10; show two of them add to 11
2Logic: invariantsFind what never changesThe difference game on 1 to 10, below
3Graph theoryCount from both endsShow the number of people with an odd handshake count is even
4Proof by inductionOne step, then every stepShow 2 to the power n exceeds n squared from n = 5 onwards
5Writing mathsA solution is for a readerRewrite a correct but muddled solution so a stranger can follow it

Day 1 and Day 2, worked

Pigeonhole: split 1 to 10 into the five pairs 1 and 10, 2 and 9, 3 and 8, 4 and 7, 5 and 6. Each pair adds to 11. Six numbers in five pairs means two land in the same pair, and those two add to 11.

Invariant: write 1 to 10 on a board. Repeatedly rub out two numbers and write their difference. Can the last number be 0? The sum starts at 55, which is odd. Replacing a and b by their difference changes the sum by an even amount, so the sum stays odd, and the last number is odd. It can never be 0.

Day 3 and Day 4, worked

Graphs: add up everyone's handshake count. Each handshake is counted twice, once by each person, so the total is even. A sum of whole numbers is even only if it contains an even number of odd terms. So an even number of people shook an odd number of hands.

Induction: at n = 5, 32 beats 25. If 2 to the n exceeds n squared, then 2 to the n plus 1 exceeds 2n squared, and 2n squared minus (n plus 1) squared equals n squared minus 2n minus 1, which is positive for n of 3 or more. So the claim passes from each n to the next.

Day 5 matters most. UKMT lists Writing Maths as a session of its own, and olympiad markers reward a clear argument over a bare answer. On our Day 5 each pupil takes one of their own solutions from the week, rewrites it for a reader who was not in the room, and has it read and returned by a teacher. A pupil who does that once a week for a summer writes very differently by September.

The plan, the problems and the worked solutions are ours. The topic names in the second column echo UKMT's published topic list.

Shaping a summer

How should a keen pupil spend a maths summer?

Our suggestion, not a rule: a little maths often, one long problem a week, and something written down. Holidays should still feel like holidays.

A sample six-week summer, our suggestion
WeekThemeTime
1Pigeonhole and countingTwo sessions plus an hour of problems
2Invariants and gamesTwo sessions plus a written solution
3Number theory: remainders and primesTwo sessions plus an hour of problems
4Graphs and networksTwo sessions plus a written solution
5Induction and sequencesTwo sessions plus an hour of problems
6Writing week: revise three solutionsOne session plus rewriting

If an invitation does come

Go. A residential week with other keen students and volunteers who love maths is something online lessons cannot copy, and UKMT's pages describe evening activities, a quiet room and pastoral leads.

The weeks around it are where online lessons help, either to prepare or to keep going afterwards.

For younger pupils

Pupils aged 11 to 13 are below the UKMT summer school age. A gentler summer of puzzles and competition maths builds the habits that a later IMC score depends on.

Our junior olympiad page and online maths circle page show what that looks like.

Stages

Four summers, four steps

A rough path through the summers between Year 7 and Year 11, in our own terms.

Our summer stages
StageTypical yearSecure when
1. PuzzlesYear 7Enjoys a problem that takes twenty minutes
2. TechniquesYear 8Recognises pigeonhole, parity and case-splitting
3. ArgumentsYear 9Writes a short proof a classmate accepts
4. Olympiad styleYear 10 and 11Tackles unseen olympiad problems with a written solution

Why summer works

Without homework and tests, a pupil can stay with one problem for an afternoon, which is how these topics are really learned.

Short, regular sessions keep the habit through August.

After the summer

The autumn brings UKMT challenges; see our olympiad training guide.

Sixth formers can turn to STEP preparation.

All related courses

Courses for a maths or coding summer

Grouped by age. Every syllabus is on its course page.

I

Younger pupils

Ages 8 to 12

UK / SSU / 01

Mental maths for kids

Quick, confident number sense.

Open the syllabus

UK / SSU / 02

Python and AI for kids

A coding summer for ages 8 to 12.

Open the syllabus
II

Competition maths

Ages 11 to 17

UK / SSU / 03

Junior competition maths

Problem solving for ages 11 to 14.

Open the syllabus

UK / SSU / 04

Olympiad maths

The summer school topic list, every week.

Open the syllabus

UK / SSU / 05

Maths through coding

Patterns explored with Python.

Open the syllabus
III

Sixth form

Ages 16 to 18

UK / SSU / 06

TMUA and STEP preparation

Admissions maths for future maths students.

Open the syllabus

UK / SSU / 08

Python for teens

A coding summer for ages 13 to 18.

Open the syllabus

How summer lessons run

Live sessions through the holidays

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. In the holidays a 1-on-1 plan can meet more often than once a week if a pupil wants a concentrated summer. Lessons are booked in UK time, and our teachers in India adjust to the UK day.

Weekday morning

Holiday sessions while school is out.

Weekday afternoon

Group batches by stage.

Weekend morning

For families away during the week.

One topic a week

A summer theme per week, built from first ideas to hard problems.

Problems between sessions

A short set to try alone, discussed at the next session.

Writing counts

At least one full written solution each week, read by the teacher.

Group or 1-on-1

15 to 20 pupils at one stage, or a single pupil.

Away for a week

Holidays are expected; sessions move rather than vanish.

Into the autumn

The same group can carry on when term starts.

Student work

Student projects

Things our students made in maths and code. More are collected in student labs.

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Fees

Fees for summer maths

Billed monthly, so a family can book just the summer months and stop in September, or carry on. The first session is free.

Free first class

USD 0

no card required

  • A taster session on one summer topic
  • Advice on stage and group
  • Only a phone number to book
Book it

Group batch

USD 100

a month, billed in US dollars

  • 15 to 20 pupils at one stage
  • A weekly topic and problem set
  • Written solutions read and returned
  • Continues into term if wanted
Start here

One to one

USD 150

a month, billed in US dollars

  • One pupil, one teacher
  • Sessions as often as the summer allows
  • Topics chosen around the pupil
Enquire

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Summer school questions

What families ask about maths summer schools

What is the UKMT summer school?

The National Mathematics Summer School, a one-week residential event run by the UK Mathematics Trust for students aged 14 to 16. UKMT says it runs three events a year, Sunday to Friday, usually from the start of August.

How do you get into the UKMT summer school?

By invitation only. UKMT chooses students at random from the top 1.5 per cent of Intermediate Mathematical Challenge results in the eligible years, one per school, and sends invitations through schools in March.

Can I apply for the UKMT national maths summer school?

No. There is no application for Juniors; the selection is by lottery from IMC results. Past attendees can later apply to return as Seniors, with applications usually going out in December.

How many students go to UKMT summer school?

UKMT says it invited 108 Juniors in 2024, chosen from 843 students shortlisted one per school from the top 1.5 per cent of about 226,000 IMC results. By our arithmetic that is roughly one invitation per 2,100 results.

What do students do at the UKMT summer school?

Maths sessions on topics such as number theory, geometry, combinatorics, graph theory, proof by induction and writing maths, plus group problem solving and evening activities. Volunteers, often maths teachers, lead the sessions.

Are there other maths summer schools in the UK?

Yes. PROMYS Europe, a partnership including the University of Oxford's Mathematical Institute, runs a six-week number theory programme for students aged 16 and over living in Europe, and King's College London Mathematics School runs free summer schools including a five-day programme for Year 11.

Is there an online maths summer school for UK students?

We teach summer school topics live online for ages 11 to 17, open to anyone and not by invitation. It is our own programme, not a UKMT event, and it can continue into term if a pupil enjoys it.

My child is 12. Is there anything for them?

The UKMT summer school is for ages 14 to 16, so not yet. A summer of puzzles and junior competition maths builds the habits a later Intermediate Challenge score needs, and that is what our junior groups do.

Are you linked to UKMT?

No. We describe UKMT's summer school from its own pages so families understand it. We are not connected with UKMT, PROMYS Europe, the University of Oxford or King's.

When do summer lessons run?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Holiday times are agreed in UK time.

Related pages

More for the summer and beyond

Coding summers, circles, masterclasses and competitions.

Online coding summer course

A holiday of real coding projects.

Online maths circles

Long problems with the same group all year.

Maths masterclasses

The Royal Institution series explained.

Intermediate olympiads

Cayley, Hamilton and Maclaurin, after the IMC.

Maths olympiad training

Every UKMT round in one table.

Coding classes in the UK

Our UK hub.

Related pages in this guide

Part of the guide: UK maths enrichment, competitions and able pupils

Enrichment and able pupils

Maths competitions

Computing programmes and competitions

More guides: UK maths exam boards and specification codes · UK maths year by year, Reception to Year 11 · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK university admissions: maths tests and computing applications

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Let us know your child's school year and which topics sound exciting. We teach one summer-style session, then suggest a group or a 1-on-1 plan for the holidays.

Reading first? Every course page sets out its topics, and how we teach explains a session from start to finish.

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