An Implementation of the Solution to the Conjugacy Problem on Thompson\u27s Group V

We describe an implementation of the solution to the conjugacy problem in Thompson\u27s group V as presented by James Belk and Francesco Matucci in 2013. Thompson\u27s group V is an infinite finitely presented group whose elements are complete binary prefix replacement maps. From these we can construct closed abstract strand diagrams, which are certain directed graphs with a rotation system and an associated cohomology class. The algorithm checks for conjugacy by constructing and comparing these graphs together with their cohomology classes. We provide a complete outline of our solution algorithm, as well as a description of the data structures which store closed abstract strand diagrams and contain methods to simplify and compare them. The final conjugacy checking program runs in cubic time

Objectworlds : a class of computer-based discovery learning environments

It is possible to discern a class of Computer-Based Discovery Learning Environments which centre on novel, concept rich,simulated objects and which include simple but general functions with which the objects may be manipulated. This thesis provides a history of this class of environments, which we call objectworlds, and we also give them a strict definition. We describe Gravitas, a new objectworld we have built, which allows learners to work with objects that behave like gravitating masses moving in a two dimensional space.Gravitas contains a powerful programmable interface to the objects, in the form of a set of Logo commands, and a functionally equivalent but easier to use graphical interface which is controlled by the mouse. We show that the combination of interfaces helps learners to explore the world of these objects more effectively.We contrast the educational experiences learners are afforded by objectworlds with those offered by two closely related kinds of Discovery Learning Environment: Simulations and Modelling Systems. We also describe a psychological framework which provides a useful way of thinking about the construction of computer simulated objects for discovery learning applications

Glosarium Matematika

273 p.; 24 cm

The life and work of Major Percy Alexander MacMahon

This thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854 - 1929). His early life as a soldier in the Royal Artillery and events which led to him embarking on a career in mathematical research and teaching are dealt with in the first two chapters. Succeeding chapters explain the work in invariant theory and partition theory which brought him to the attention of the British mathematical community and eventually resulted in a Fellowship of the Royal Society, the presidency of the London Mathematical Society, and the award of three prestigious mathematical medals and four honorary doctorates. The development and importance of his recreational mathematical work is traced and discussed. MacMahon's career in the Civil Service as Deputy Warden of the Standards at the Board of Trade is also described. Throughout the thesis, his involvement with the British Association for the Advancement of Science and other scientific organisations is highlighted. The thesis also examines possible reasons why MacMahon's work, held in very high regard at the time, did not lead to the lasting fame accorded to some of his contemporaries. Details of his personal and social life are included to give a picture of MacMahon as a real person working hard to succeed in a difficult context