iosr-Jm   Volume-5 ~ Issue-4

Abstract: The British colonial masters in Nigeria did not encourage the teaching of science in the schools. At best science was taught as Nature Study and General Science. There was also shortage of middle-level manpower besides the gross shortage of qualified science teachers. To combat the acute shortage of qualified science teachers in Nigeria the Special Entry Preparatory programme (SEPP) was instituted in the University of Lagos to absorb and upgrade the unqualified science teachers to the level of graduate science teachers with education background. The SEPP students were brought up to the advance level of General Certificate in Education (GCE A/L) which was the required qualification for direct admission into the university. Mathematics was one of the science-education courses taught through distance learning for a B.Sc degree. Using the Mann-Whitney test the performance of successful SEPP students was compared with those of "direct" students in the six courses offered. The two groups performed at the same level in four courses while outdoing each other in each of the remaining two courses.

Key Words: Distance Education, Special Entry Preparatory Programme (SEPP), Direct Entry.

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Abstract: We know that the smallest positive integer f such that a f  1 mod m is called the exponent of 'a' modulo m and is denoted by expma. We say that 'a' is a semi-primitive root mod m if expma = 2  (m) . In this paper we discuss the properties of the semi primitive roots and examine for which prime 2 is a semi-primitive root. If S is the sum of semi-primitive roots less than p then we proved that p p S )mod 2 1 (    .Also we proved that if 'a' is a semi primitive root then 'a' is a quadratic residue, converse need not be true. It was established that whenever a is a semi-primitive root mod p where p is of the form 4n+3 then –a is a semi primitive root and if p = 4n+1 then expm (–a) = 4 p 1 .We establish that 2 is semi-primitive root for mod p whenever 'p' is of the form 2q+1where 'q' is an odd prime of the form 4n+3 and if 4n+1,8n+3 are primes then –2 is a semi-primitive root mod 8n+3 by using Gauss Lemma [1].

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Abstract: The aim of this paper is to develop the implicit finite difference scheme for space fractional soil moisture diffusion equation (SFSMDE) with initial and boundary conditions. We prove that the scheme is unconditionally stable and convergent. Also, as an application of this scheme numerical solution for space fractional soil moisture diffusion equation is obtained by Mathematica software. Keywords: Space fractional, Soil moisture diffusion equation, Finite difference scheme, Fractional derivatives, Mathematica.

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