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Over recent years, the approach to the teaching of mathenatics has changed considerably in recognition of the need to provide a more effective programme of mathemátical education in schools and colleges. There is general agrement that curricula and teaching methods require modernization. Reforms have been proposed by various organizations with the aims of promoting an the basic structure of mathematics and ôf eliminăing outmoded traditional material. In various modern programmes, attention has been concentrated programmes, attention has been concentrated Upoß algebra, analysis and geometry treated in a more advanced and abstract way than formerly. The traditional apptoach, by which these subjects were compartumentatized, has been discarded and the present aim is to achieve a unified approach by whicb the relationships between these subjects are fully exploited and the underlying unity of mathematics is exbibited. It has been deemed desirable and practicable to introduce topics, formerly reserved for more advanced courses, at an earlier stage, e.g. the concepts and language of set theory are now widely recognized as providing an excellent medium for promoting the understanding and appreciation of a wide range of range mathematical topics. This volume presents a number of modern topics suitable not only for students who are proceeding to the study of mathematics, science or engineering but also as a programme of general education on the reasonable assumption tbat modern mathematics can make an important contribution in the field of liberal education. Whilst the presentation of these topics is non-traditional, students, whose earlier mathematicaf education has proceeded on traditional lines, should experience no handicap. Topics Geometry of vectors Scalar and vector products Differentiation of vectors Vector integration Dynamics of a particle Probability theory Boolean algebras Residue classes Groups