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The Council for the Indian School Certificate Examinations (CISCE) [1] is a non-governmental privately held national-level [2] [3] board of school education in India that conducts the Indian Certificate of Secondary Education (ICSE) Examination for Class X and the Indian School Certificate (ISC) for Class XII.
The ICSE Examination is a school examination and the standard of the examination pre-supposes a school course of ten years duration (Classes I-X). The Indian Certificate of Secondary Education Examination will ensure a general education and all candidates are required to enter for six or more subjects and Socially Useful Productive Work (SUPW).
Around 19 school boards from 14 states have adopted or adapted the books. [11] Those who wish to adopt the textbooks are required to send a request to NCERT, upon which soft copies of the books are received. The material is press-ready and may be printed by paying a 5% royalty, and by acknowledging NCERT. [11]
Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician. Mancosu, P. (ed., 1998), From Hilbert to Brouwer. The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press, Oxford, UK.
Later most exercises involve at least two digits. A common exercise in elementary algebra calls for factorization of polynomials. Another exercise is completing the square in a quadratic polynomial. An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1]
The book was fundamental in the development of two main disciplines, the foundations of mathematics and philosophy. Although Bertrand Russell later found a major flaw in Frege's Basic Law V (this flaw is known as Russell's paradox , which is resolved by axiomatic set theory ), the book was influential in subsequent developments, such as ...
The book expands on the material (approximately 100 pages) [1] in the "Mathematical Preliminaries" [2] section of Knuth's The Art of Computer Programming. Consequently, some readers use it as an introduction to that series of books. Concrete Mathematics has an informal and often humorous style. The authors reject what they see as the dry style ...
The spherical law of sines was discovered in the 10th century: it has been attributed variously to Abu-Mahmud Khojandi, Nasir al-Din al-Tusi and Abu Nasr Mansur, with Abu al-Wafa' Buzjani as a contributor. [16] Ibn Muʿādh al-Jayyānī's The book of unknown arcs of a sphere in the 11th century introduced the general law of sines. [23]