https://www.um.edu.mt/library/oar/handle/123456789/23639 2026-04-05T06:08:11Z https://www.um.edu.mt/library/oar/handle/123456789/24453 Title: The Collection X Editors: Sciriha, Irene; Walker, Ian G. Abstract: Tenth issue of The Collection, a journal by the Department of Mathematics at the University of Malta. 2004-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24452 Title: Teaching mathematics using excel Abstract: 'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000) 2004-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24451 Title: Note on approximation by nonlinear optimization Abstract: The purpose of this note is to discuss the use of nonlinear optimization techniques to solve approximation problems typical for example in signal identification. Different techniques based on classical and modern approaches to time series are available. The presented idea considers cases when signals are composed of a finite number of certain nonlinear functions distinct in their parameter sets, and realization of an additive random error. The focus is given to the sums of parameterized trigonometric functions. As the random error probability distribution is assumed unknown, the common LSQ criterion is replaced with its parameterized generalization. The obtained unconstrained non-smooth minimization problem can be solved either directly or after a smooth reformulation to the constrained problem. The initial values for computational procedures are estimated using heuristics and suitable statistical techniques, e.g., periodograms. The ideas are illustrated by simple explanatory examples accompanied by figures. Test results are shown for MS Excel Solver, MATLAB is used for visualization. 2004-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24449 Title: Abelian sandpiles Abstract: The Abelian Sand pile (AS) is a model originally introduced by physicists to simulate what is known as "self-organized complexity". Models exhibiting this phenomenon typically have some form of "avalanche dynamics" , where "stress" is built up until system becomes unstable. On reaching instability, the system reorganizes itself quickly to re-attain stability. Examples are sandpile or avalanche. Although the AS is primarily a physical model, it has a very interesting algebraic structure which merits investigation. 2004-01-01T00:00:00Z