IT is not often you hear a teenage girl squeal "Yipee, a theorem!" halfway through a maths lesson, without a hint of sarcasm.
But this is no ordinary class. It is part of the summer-school programme at England's first Gifted and Talented Academy.
One hundred pupils, judged to be in the top 1 to 5 per cent of the country, are spending two weeks into the three-week residential course at Warwick University.
The 90 minute lesson begins with Euclidean and non-Euclidean geometry and ends with the geometry of perspectives. The class, run by university lecturer Dave Wood, spans an age range of 11 to 16 years. It is lively and extremely challenging for both tutors and students. Mr Wood said: "They are more on-the-ball than some undergraduates. They want to know the answers before I've even got into the explanation."
Lizz Paley took maths GCSE this summer. The 14-year-old works using different books from her classmates at Holmfirth high school, Huddersfield. She had no real expectations of the academy, but she is surprised at how "normal" people are.
Outside the seven hours of classes a day, students are chaperoned and entertained by a small army of residential assistants, in the mould of American-style camp leaders.
Their presence is important when 11-year-olds are wandering around Warwick's huge, leafy, campus and they keep an eye on discipline. Simon Parkes, the head assistant, a mature student and a former soldier, tells pupils to stop putting things down the toilet and cut out the backchat at the end of the evening or face an early curfew.
As The TES revealed last month, state-school pupils make up most of the group and one in three is from an ethnic-minority background.
However, there seem to be few African-Caribbean faces and "state school" is a label that disguises a wide spectrum of institutions.
Simone Milani, a pupil at La Sainte Union convent school, north London, who has chosen to study philosophy, said middle-class children dominated the academy. She also fears the proposed introduction of fees, which she thinks will result in lost talent and make the academy elitist.
However, Zoya Street, from Wickersley comprehensive, Rother-ham, applauds the academy's diversity. The 14-year-old, who is on the creative writing course, is one of 40 children from schools in deprived urban areas served by the Excellence in Cities scheme.
She said: "At school we have to do a set task, exactly how the teacher tells you I Here, we take our inspiration from an idea and there is a lot of focus on poetry. I keep scribbling down thoughts on my paper."
Zoya achieved level 8 in maths and level 7 in English in her national curriculum tests. But she insists she is "not a genius or anything like that". One of the academy's aims - to motivate bright pupils - seems to have been achieved. Zoya wants to be a journalist, but mainly to fund her ambition to write novels.