E. A. Maxwell – Författare

As Dr Maxwell writes in his preface to this book, his aim has been to instruct through entertainment. 'The general theory is that a wrong idea may often be exposed more convincingly by following it to its absurd conclusion than by merely announcing the error and starting again. Thus a number of by-ways appear which, it is hoped, may amuse the professional, and help to tempt back to the subject those who thought they were losing interest.' The standard of knowledge expected is fairly elementary. In most cases a straightforward statement of the fallacious argument is followed by an exposure in which the error is traced to the most elementary source, and this process often leads to an analysis which is often of unexpected depth. Many students will discover just how mathematically minded they are when they read this book; nor is that the only discovery they will make. Teachers of mathematics in schools and technical schools, colleges and universities will also be sure to find something here to please them.

Dr Maxwell has written this short book to introduce students (and teachers) to the ideas involved in abstract mathematics. In his preface he states, 'I have often felt that the present plunge into abstraction is too sudden and that there is a need for more elementary work to make the immersion less exhausting.' Dr Maxwell does this by taking various topics from elementary mathematics, and showing what happens when the rules are altered in quite simple ways. He first discusses digital arithmetic, then introduces the idea of a group and illustrates some properties of groups by examples from algebra and geometry.

This is the first volume of a series of four volumes covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. This volume is concerned with the basic ideas and applications of differentiation and integration in relation to algebraic and trigonometric functions, but excluding logarithmic and exponential functions. Integration begins on the 'Riemann integral' basis, and the treatment of curves combines accuracy with simplicity, without shirking the awkward problems of sign. Each section has examples; at the end of each chapter there are problems from school-leaving and open scholarship examinations.

This is the second of a series of four volumes covering all stages of development of the Calculus, from the last years at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies. with their emphasis on rigour. This treatment of algebraic and trigonometric functions is here developed to cover logarithmic, exponential and hyperbolic functions and the expansion of all these functions as power series. There is a chapter on curves and the idea of complex numbers is introduced for the first time. In the two final chapters, the author begins a systematic treatment of methods of integrating functions, introducing principles into what often seems rather a haphazard process. This volume, like the others, is well endowed with examples.

This is the third volume of a series of four volumes covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. The volume treats of the theory of functions of more than one variable. Partial differentiation and multiple integrals are explained in detail. Each section has examples; at the end of each chapter there are problems from school-leaving and open scholarship examinations. This volume is most suitable for the first or second year at British universities.

This is the final volume of a series covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. Dr Maxwell guides the student through the early stages of analysis, while keeping the exposition as clear and uncomplicated as possible. The aim is to instil a knowledge of general method rather than to study the particular functions in detail; in this way the student is led on naturally to apply what they have learnt to move advanced mathematical contexts. Dr Maxwell is, as usual, lucid in his presentation, explaining difficulties in greater detail than is customary in an advanced textbook, and guarding against the pitfalls that await the beginner.

This is a book about powerful mathematical methods rather than a mere catalogue of the properties of conics. The treatment is elegant and refreshing as well as systematic, and throughout the book the author is concerned to lay the foundations of future work. Consequently (unlike too many textbooks) there is little for the student to unlearn when he goes on to more advanced courses. A valuable feature is the large number of carefully selected and graded problems for solution (about 400 in all). When this book was first published, the reviewer in Science suggested that 'this scholarly work should be supplemented by a similar book on the analytic projective geometry of ordinary space'. His suggestion has since been adopted: and the companion volume, E.A. Maxwell's General Homogenous Coordinates in Space of Three Dimensions is now also available.

The purpose of this book is at once modest and ambitious, namely, to provide a short introduction to algebraic geometry in space of three dimensions, to make clear its spirit, and to prepare the way for deeper study. This book will appeal to a reader who has read Maxwell's book on homogenous coordinates in a plane (to which this stands as a second volume) and is in the early stages of second year work at University, It will also be suitable for a class reader who has read further in mathematics generally, but has found the existing detailed accounts of this work too full or too specialised for their own needs, and is in need of an accessible introduction.

The scope and treatment of Dr Maxwell's two-volume course covering the transition from school to university is directed towards training students in algebraic thinking, so that processes do not become too mechanical. The explanations are full, the difficulties of the beginner are foreseen and overcome. Indeed, the course should prove excellent for the lone student as well as for the supervised class. Topics in part one include polynomial theory, equations, inequalities, partial fractions, permutations and combinations, the binomial theorem and series and determinants. The 'feel' of the book may be illustrated by reference to the treatment of partial fractions, which is novel in several ways. A theoretical exposition is given in some detail and varies from standard treatments in leading to a method of calculation that arises directly from it. The book contains many 'drill' examples, which the author considers essential.