https://www.um.edu.mt/library/oar/handle/123456789/23638 Tue, 07 Apr 2026 13:06:57 GMT 2026-04-07T13:06:57Z https://www.um.edu.mt/library/oar/handle/123456789/24501 Title: Crystallography and symmetry groups Abstract: Crystals are assemblages of very small basic units of matter repeated periodically in 3 dimensions. The connection with group theory is that each pattern can be characterized by its symmetry group. It turns out that there are only 230 of these so-called crystallographic space groups amongst which are 22, which crystallographers prefer to regard as distinct, but which, from an abstract point of view, form 11 pairs of isomorphic groups. Thus the space groups fall into 219 isomorphism classes. The enumeration of these space groups is built upon the 14 lattices determined by Bravais. Since the enumeration is quite complicated, we here look at some of the corresponding ideas involved in the analogous 2-dimensional problem where 17 groups, no two of which are isomorphic, arise. First recall that an isometry of the plane R2 is a distance- preserving mapping of R onto itself. Amongst such isometries are translations, rotations, reflections (in lines) and glide reflections. The latter being the result of an ordinary reflection in some line 1 followed by a translation parallel to 1. Figure 1 adequately describes these movements. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24501 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24440 Title: On hand shakes : a combinatorial problem Abstract: A number n of couples meet at one of the couples' homes. The female host (Fh) notices that no two of the people present (excluding herself) shake hands with the same number of people. No person shakes hand with the partner. With how many people does her husband (Hh) shake hands? Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24440 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24434 Title: The Collection VIII Editors: Sciriha, Irene Abstract: Eighth issue of The Collection, a journal by the Department of Mathematics at the University of Malta. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24434 2003-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24433 Title: Generation of prime numbers Abstract: Introduction Prime numbers are by definition numbers which are only divisible by one and by themselves. It can be proved that such numbers are infinite, as are after all, the Real Numbers, or the Natural numbers. In the following pages will be trying to shed some light over the following unanswered question: "Is it possible to come up with some form of equation with which one can generate such numbers?" It is interesting to know that ever since Antiquity, mathematicians have always been haunted by this infamous question which, in virtue seems to have no straight forward answer. Wed, 01 Jan 2003 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/24433 2003-01-01T00:00:00Z