Originally published in 1948, this book was written to provide students with an accessible guide to various elements of mathematics. The text was created for individual working rather than group learning situations. Numerous exercises are included. This book will be of value to anyone with an interest in mathematics and the history of education.

First published in 1946, as the second edition of a 1932 original, this book was intended to provide students with a sound working knowledge of coordinate geometry. The text contains 'a full discussion of the subject up to conics referred to their axes, using both point equations and parametric methods wherever the latter are suitable'. Exercises and examples are also included. This book will be of value to anyone with an interest in coordinate geometry and the history of mathematics.

Originally published in 1936, this book was written with the intention of preparing candidates for the Higher Certificate Examinations. The text was created to bridge the gap between introductions to differential and integral calculus and advanced textbooks on the subject. This volume will be of value to anyone with an interest in differential and integral calculus, mathematics and the history of education.

Originally published in 1924, this book presents an account regarding the direct numerical calculation of elliptic functions and integrals. Notes are incorporated and an appendix section containing examples is also included. This book will be of value to anyone with an interest in the history of mathematics.

Originally published in 1940, this book was aimed at students of science who had not previously been acquainted with algebra and the core mathematical principles. 'It is quite wrong that science students, particularly biology students, should go to their universities without having been made aware of even the existence of a side of mathematics whose importance is becoming more and more apparent'. The book caters for students who wish to develop their mathematical and reasoning skills, necessary to progress in the sciences. Chapters are broad in scope, detailed and varied; chapter titles include, 'The theory of quadratic equations', 'Probability' and 'Statistics'. A multitude of examples are included throughout to reinforce learning and answers can be found at the back. Providing an overview of algebra for school students before entering undergraduate science, this book will be of significant value to anyone with an interest in mathematics and the history of education.

Originally published in 1936, this detailed textbook is a companion to the 1931 publication An Elementary Treatise on Actuarial Mathematics and is intended to provide further examples for learning, practice and revision; 'the inclusion of additional examples in the book as it stood was impracticable, and it appeared that the difficulty could only be overcome by the publication of a supplement to the book'. Contained is a vast selection of examples on finite differences, calculus and probability, in the hope 'that the supplement will prove of value to students, especially to those who have completed the course for the examination'. Notably, most questions purposely hint at solution and refrain from providing a full explanation - 'in only a few instances has the complete solution of the question been given'. This engaging book will be of great value to anyone with an interest in mathematics, science and the history of education.

Originally published in 1929, this book presents a guide to riders in geometry aimed at students of matriculation or School Certificate standard. The text is divided into three main sections: 'The straight line'; 'The circle'; 'General'. Exercises are included at the end of each section. This book will be of value to anyone with an interest in geometry, mathematics and the history of education.

Originally published in 1946, this book was prepared by the Committee for the Calculation of Mathematical Tables. The text contains a series of tables of Legendre polynomials, created to meet the needs of researchers in various branches of mathematics and physics. The tables were largely designed by Leslie John Comrie (1893-1950), an astronomer who was integral to the development of mechanical computation. This book will be of value to anyone with an interest in Legendre polynomials and mathematical tables.

Originally published in 1946, this book was prepared on behalf of the Committee for the Calculation of Mathematical Tables. The text contains a series of tables with data relating to the Airy function. The tables were developed by Jeffrey Charles Percy Miller (1906-81), a British mathematician who was integral to the development of computing. This book will be of value to anyone with an interest in differential equations and the history of mathematics.

Originally published in 1911, this practical textbook of exercises was primarily aimed at school students and was intended to provide an accessible yet challenging 'informal course' on solid geometry for classwork, homework and revision. The book is divided into three principal sections: chapters 1-6 discuss the main properties of lines and planes, chapters 7-13 examine properties of the principal solid figures, including mensuration, whilst chapters 14-16 consider coordinates in three dimensions, plan, elevation and perspective, also known as descriptive geometry. The book covers key theorems, whilst cataloguing useful geometry questions focused on developing a broad understanding of the subject. Intended as educational rather than technical material and a practical, systematic supplement to school lessons, this book will be of great value to scholars of mathematics as well as to anyone with an interest in the history of education.

Originally published in 1916, this book was written to provide readers with a concise account of the leading properties of quartic surfaces possessing nodes or nodal curves. A brief summary of the leading results discussed in the book is included in the form of an introduction. This book will be of value to anyone with an interest in quartic surfaces, algebraic geometry and the history of mathematics.

Originally published in 1938, this book provides a series of exercises in arithmetic intended to take pupils ten minutes to complete. The text was created to train pupils in speed and accuracy in the fundamentals of arithmetic, avoiding unnecessary written work. This book will be of value to anyone with an interest in arithmetic, mathematics and the history of education.

The difficulty of solving the non-linear equations of motion for compressible fluids has caused the linear approximations to these equations to be used extensively in applications to aeronautics. Originally published in 1955, this book is the first permanent work devoted exclusively to the problems involved in this important and rapidly developing subject. The first part of the book gives the derivation and interpretation of the linear equations for steady motion, the solution of these equations and a discussion of the boundary conditions and aerodynamic forces. The remainder examines various specific boundary value problems and the methods, which have been developed for their solution. Vectorial notation is used extensively throughout and an elementary familiarity with the theory and practice of compressible fluid flow is required. This book will be of considerable value to scholars of physics and mathematics as well as to anyone with an interest in the history of education.

Originally published in 1934, this informative textbook was written by renowned mathematician and astronomer Duncan Sommerville (1879-1934). Primarily aimed at undergraduates, the book carefully starts from the very beginning of the subject, but also engages with concepts which are considered profoundly more specialist in the field of geometry. Following on from a renewed and flourishing interest in geometry at the time, this textbook was 'written more in accordance with the tendencies of the present', placing a different emphasis on the subject's cornerstone principles and illuminating new developments in the field. Chapters are detailed and contain material often required for examinations; topics covered include the Cartesian coordinate system and tangential equations. Well planned, with a scholarly treatment of the subject and capturing a unified knowledge of geometry, this book will be a considerably valuable source to scholars of mathematics as well as to anyone with an interest in the history of education.

How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean-particularly in Syracuse, Sicily and Alexandria, Egypt-as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order-integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities-makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

Originally published in 1926, this textbook was aimed at first-year undergraduates studying physics and chemistry, to help them become acquainted with the concepts and processes of differentiation and integration. Notably, a prominence is given to inequalities and more specifically to inequations, as reflected in the syllabus and general practice of the time. The book is divided into four parts: 'Number', 'Logarithms', 'Functions' and 'Differential and integral calculus'. Appendices are included as well as biographical notes on the mathematicians mentioned and an index of symbols. A self-contained and systematic introduction on mathematical analysis, this book provides an excellent overview of the essential mathematical theorems and will be of great value to scholars of the history of education.

Joseph Larmour (1857-1942) was a theoretical physicist who made important discoveries in relation to the electron theory of matter, as espoused in his 1900 work Aether and Matter. Originally published in 1929, this is the first part of a two-volume set containing Larmour's collected papers. The papers are presented in chronological order across the volumes, enabling readers to understand their theoretical development and framing them in an accessible form for 'future historical interests'. Authorial notes and appendices are also included. This book will be of value to anyone with an interest in the word of Larmour, mathematics physics and the history of science.

Originally published in 1921, this book was intended as a textbook of dynamics for the use of students who have some acquaintance with the methods of the differential and integral calculus. The chapters cover a vast range of topics and include the existing well-known key theorems of the day; chapters include, 'Displacement, velocity, acceleration', 'Forces acting on a particle' and 'The rotation of the Earth'. Notably, difficult and challenging topics are marked with an asterisk to indicate the advanced nature of the subject and a collection of miscellaneous examples are appended to most of the chapters to assist with classes and revision, most of which have been sourced from previous examination papers. Linear equations and diagrams are included throughout to support the text. This book will be a valuable resource to scholars of physics and engineering as well as to anyone with an interest in the history of education.

First published in 1927, as the second edition of a 1915 original, this book presents exercises in arithmetic aimed at school students. The text is divided into three main sections: Part I mainly covers integers; Part II covers fractions; Part III covers miscellaneous areas. Each section ends with revision papers and more exercises. This book will be of value to anyone with an interest in mathematics and the history of education.

Joseph Larmour (1857-1942) was a theoretical physicist who made important discoveries in relation to the electron theory of matter, as espoused in his 1900 work Aether and Matter. Originally published in 1929, this is the second part of a two-volume set containing Larmour's collected papers. The papers are presented in chronological order across the volumes, enabling readers to understand their theoretical development and framing them in an accessible form for 'future historical interests'. Authorial notes and appendices are also included. This book will be of value to anyone with an interest in the word of Larmour, mathematics physics and the history of science.

Abraham Adrian Albert (1905-72) was an American mathematician primarily known for his groundbreaking work on algebra. In this book, which was originally published in 1938, Albert provides a detailed exposition of 'modern abstract algebra', taking into account numerous discoveries in the field during the preceding ten years. A glossary is included. This is a highly informative book that will be of value to anyone with an interest in the development of algebra and the history of mathematics.

The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley Alan Turing was the mathematician whose cipher-cracking transformed the Second World War. Taken on by British Intelligence in 1938, as a shy young Cambridge don, he combined brilliant logic with a flair for engineering. In 1940 his machines were breaking the Enigma-enciphered messages of Nazi Germany's air force. He then headed the penetration of the super-secure U-boat communications. But his vision went far beyond this achievement. Before the war he had invented the concept of the universal machine, and in 1945 he turned this into the first design for a digital computer. Turing's far-sighted plans for the digital era forged ahead into a vision for Artificial Intelligence. However, in 1952 his homosexuality rendered him a criminal and he was subjected to humiliating treatment. In 1954, aged 41, Alan Turing took his own life.

An important figure in the development of modern mathematical logic and abstract algebra, Augustus De Morgan (1806-71) was also a witty writer who made a hobby of collecting evidence of paradoxical and illogical thinking from historical sources as well as contemporary pamphlets and periodicals. Based on articles that had appeared in The Athenaeum during his lifetime, this work was edited by his widow and published in book form in 1872. It parades all varieties of crackpot, from circle-squarers to inventors of perpetual motion machines, all for the reader's entertainment and education. Filled with anecdotes, personal opinions and 'squibs' of every kind, the book remains enjoyable reading for those who are amused rather than appalled by the human condition. Also reissued in the Cambridge Library Collection are the Memoir of Augustus De Morgan (1882), prepared by his wife, and his ambitious Formal Logic (1847).

Newton's Principia paints a picture of the earth as a spinning, gravitating ball. However, the earth is not completely rigid and the interplay of forces will modify its shape in subtle ways. Newton predicted a flattening at the poles, yet others disagreed. Plenty of books have described the expeditions which sought to measure the shape of the earth, but very little has appeared on the mathematics of a problem which remains of enduring interest even in an age of satellites. Published in 1874, this two-volume work by Isaac Todhunter (1820-84), perhaps the greatest Victorian historian of mathematics, takes the mathematical story from Newton, through the expeditions which settled the matter in Newton's favour, to the investigations of Laplace which opened a new era in mathematical physics. Volume 1 traces developments from Newton up to 1780, including coverage of the work of Maupertuis, Clairaut and d'Alembert.

Newton's Principia paints a picture of the earth as a spinning, gravitating ball. However, the earth is not completely rigid and the interplay of forces will modify its shape in subtle ways. Newton predicted a flattening at the poles, yet others disagreed. Plenty of books have described the expeditions which sought to measure the shape of the earth, but very little has appeared on the mathematics of a problem, which remains of enduring interest even in an age of satellites. Published in 1874, this two-volume work by Isaac Todhunter (1820-84), perhaps the greatest Victorian historian of mathematics, takes the mathematical story from Newton, through the expeditions which settled the matter in Newton's favour, to the investigations of Laplace which opened a new era in mathematical physics. Volume 2 is largely devoted to the work of Laplace, tracing developments up to 1825.