https://www.um.edu.mt/library/oar/handle/123456789/36166 Thu, 16 Apr 2026 13:47:35 GMT 2026-04-16T13:47:35Z https://www.um.edu.mt/library/oar/handle/123456789/24500 Title: Random numbers Abstract: It is very difficult to define 'randomness'. However a simple definition of Random Numbers would be as follows: Random numbers can be defined as a sequence of numbers which do not follow a regular pattern. Thus one cannot possibly guess the value of the next number in the sequence, as this may be bigger, equal or smaller than its previous values or set of values. An example of a random number sequence is: 1, 7, 13, 24, 8, 3, 6, 50, 39, 86, 87, 2, ... We describe how random sequences may be generated, and tested for randomness. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24500 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24499 Title: On perfect numbers Abstract: A Perfect number is a number which is the sum of its proper divisors. A Mersenne Prime is a prime number of the form 2k - 1. We discuss a relation between these two types of numbers and deduce various properties of perfect numbers. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24499 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24498 Title: Interlacing and carbon balls Abstract: The Interlacing Theorem gives a relation among the eigenvalues of a n x n matrix A and those of a (n -1) x (n -1) principal submatrix. We deduce the Generalized Interlacing theorem which interlaces the eigenvalues of a k x k principal submatrix of A with those of A. We apply this theorem to the hypothetical Carbon ball C40 which has two dodecahedral 6 pentagon caps. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24498 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24497 Title: Foreword [The Collection, 7] Editors: Sciriha, Irene; Telenta, Tanya Abstract: Why do mathematical giants like Evariste Galois dedicate their lives to edge-breaking discoveries, very often unacknowledged by their contemporaries? The truth is that mathematics is both a science and an art. It possesses a magical power that disciplines the mind. The discovery of the laws of nature and the setting up of hypothetical ordered worlds that obey axioms allow us to share in the joy of creation. It is with great satisfaction that we see our students producing original work that enables them to experience the thrill of unlocking the mysteries, signs and wonders of mathematics. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24497 2003-01-01T00:00:00Z