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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]
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]
In the Class 7 textbook topic titled “Our Pasts-2”, pages 48 and 49 have been excluded. These pages mentioned “Mughal Emperors: Major campaigns and events.” The deletions also affected Biology and Chemistry textbooks as the theory of evolution and the periodic table were also purged from class 10 NCERT textbooks. [35] [36]
At 2-year public institutions, where low-income students are more likely to pursue a degree program and tuition and fees are lower, the average estimated cost of books and supplies per first-time, full-time student was $886 in academic year 2003–2004, representing almost three-quarters of the cost of tuition and fees.
If p is composite, the probability that the test declares it a strong probable prime anyway is at most 1 ⁄ 4, in which case p is a strong pseudoprime, and a is a strong liar. Therefore after k non-conclusive random tests, the probability that p is composite is at most 4 −k, and may thus be made as low as desired by increasing k.
For example, in the case of p = 10, a = 4, b = 15, composite number 10 divides ab = 4 × 15 = 60, but 10 divides neither 4 nor 15. This property is the key in the proof of the fundamental theorem of arithmetic. [note 2] It is used to define prime elements, a generalization of prime numbers to arbitrary commutative rings.
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only k {\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k {\displaystyle k} that is independent of n {\displaystyle n} ; this number k ...
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...