Council officers are recommending the new four-storey sixth form should be built on the site of the former Barry House office block in London Road.
The college, run by the Rigby Education Trust, will eventually house up to 260 students in two year groups.
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It will be called the Lancaster University School of Mathematics and is a collaboration between the university and Cardinal Newman College.
It will be financed by the Department of Education and run by the Rigby Trust.
A report to the committee says: “As a specialist teaching facility, the curriculum is focused entirely on mathematics, the sciences and computing.
"These functions are stacked within a ‘teaching wing’ on the north side of the building, for clear way finding and easy travel between classes, with a large auditorium on the south side.
“The auditorium has capacity for up to 400 to be seated on retractable bleacher seating. The size would also allow exams to be accommodated in the space.”
The application says the building will be “well-designed with significant architectural interest.”
Contractors moved in this week and will dismantle Barry House in three stages. Work is expected to take six weeks.
The office block will be taken down piece by piece, starting with the middle third, then the section nearest to Primrose Hill and finally the end closest to the Olive School next door.
Around 1,000 tonnes of concrete will be taken away, crushed up and recycled to be used to level the site before building begins.
Councillors have been told feasibility studies have established that the old office block, which has been empty for some time, is unsuitable for adaptation or refurbishment.
The new state-of-the-art A-Level college will take some of the most promising young mathematicians in Lancashire. The county will be only the fourth area on the country to have such a facility.
Cardinal Newman principal Nick Burnham said that such “maths communities” are already thriving at the three other specialist colleges that are up and running elsewhere.
“The school will appeal to a certain type of mathematician who lives and breathes maths and seeks out other mathematicians so that they can spend their day just talking about the subject, ” he explained. “These will be classes of very bright students.”