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It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation : any index may appear at most twice and furthermore a raised index must contract with a lowered index.
Until 2014, the Standard Grade section of the site had 12 subjects: Biology, History, Chemistry, Computing Studies, Maths, English, Modern Studies (a course exclusive to Scotland), French, Physical Education, Geography, and Physics. [9] The site was updated in 2014 to replace the Standard Grade section with National 4 and National 5 sections.
Key Stage 3 (commonly abbreviated as KS3) is the legal term for the three years of schooling in maintained schools in England and Wales normally known as Year 7, Year 8 and Year 9, when pupils are aged between 11 and 14. In Northern Ireland the term also refers to the first three years of secondary education.
The National Curriculum for England is the statutory standard of school subjects, lesson content, and attainment levels for primary and secondary schools in England. It is compulsory for local authority-maintained schools, but also often followed by independent schools and state-funded academies.
The assessments were introduced following the introduction of a National Curriculum to schools in England and Wales under the Education Reform Act 1988.As the curriculum was gradually rolled out from 1989, statutory assessments were introduced between 1991 and 1995, with those in Key Stage 1 first, following by Key Stages 2 and 3 respectively as each cohort completed a full key stage. [2]
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
CGP Revision Guides is the main product line published by CGP, covering a range of school subjects at KS1, KS2, KS3, 11+, 13+, GCSE, A-level and SATs. [3] CGP's books often incorporate a witty and humorous tone, occasionally informal and colloquial, making them clear and easy to understand.
Ricci calculus, and index notation more generally, distinguishes between lower indices (subscripts) and upper indices (superscripts); the latter are not exponents, even though they may look as such to the reader only familiar with other parts of mathematics.