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Advanced Level (A-Level) Mathematics is a qualification of further education taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college.
Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may ...
However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four. [2]
Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. [2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. [4]
A qualification in Further Mathematics involves studying both pure and applied modules. Whilst the pure modules (formerly known as Pure 4–6 or Core 4–6, now known as Further Pure 1–3, where 4 exists for the AQA board) build on knowledge from the core mathematics modules, the applied modules may start from first principles.
[1] [2] It is regarded as one of the most difficult and intensive mathematics courses in the world. Roughly one third of the students take the course as a continuation at Cambridge after finishing the Parts IA, IB, and II of the Mathematical Tripos resulting in an integrated Master's (M.Math), whilst the remaining two thirds are external ...
A Bachelor of Mathematics (abbreviated B.Math, BMath or BMaths) is an undergraduate academic degree awarded for successfully completing a program of study in mathematics or related disciplines, such as applied mathematics, actuarial science, computational science, data analytics, financial mathematics, mathematical physics, pure mathematics, operations research or statistics.
Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .