Originally published in 1962, as the second edition of a 1930 original, 'the main purpose of the book is to give a logical connected account of the subject, by starting with the definition of 'Number' and proceeding in what appears ... to be a natural sequence of steps'. The chapters cover all of the cornerstones of complex mathematical analyses; chapters include, 'Bounds and limits of sequences', 'Integral calculus' and 'Functions of more than one variable'. Multiple examples are included at the end of every chapter to support and illustrate the fundamental concepts; 'I have aimed at presenting the subject in such a way as to make every important concept clearly understood'. Primarily aimed at undergraduates with a background in advanced calculus for study and practice, this comprehensive and dynamic textbook will be of considerable value to scholars of mathematics as well as to anyone with an interest in 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 1926, this book was written to provide mathematical and scientific students with an introduction to the subject of integral calculus. The text was largely planned around the syllabus for the Higher Certificate Examination. A short historical survey is included. This book will be of value to anyone with an interest in integral calculus, 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.

I.M. Gelfand (1913 - 2009), one of the world's leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. In this three-volume Collected Papers Gelfand presents a representative sample of his work. Gelfand's research led to the development of remarkable mathematical theories - most of which are now classics - in the field of Banach algebras, infinite-dimensional representations of Lie groups, the inverse Sturm-Liouville problem, cohomology of infinite-dimensional Lie algebras, integral geometry, generalized functions and general hypergeometric functions. The corresponding papers form the major part of the collection. Some articles on numerical methods and cybernetics as well as a few on biology are also included. A substantial number of the papers have been translated into English especially for this edition. The collection is rounded off by an extensive bibliography with almost 500 references. Gelfand's Collected Papers will be a great stimulus, especially for the younger generation, and will provide a strong incentive to researchers.

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.

This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

Originally published in 1927, as the first of a two-part set, this informative and systematically organised textbook, primarily aimed at university students, contains a vectorial treatment of geometry, reasoning that by the use of such vector methods, geometry is able to be 'both simplified and condensed'. Chapters I-XI discuss the more elementary parts of the subject, whilst the remainder is devoted to an exploration of the more complex differential invariants for a surface and their applications. Chapter titles include, 'Curves with torsion', 'Geodesics and geodesic parallels' and 'Triply orthogonal systems of surfaces'. Diagrams are included to supplement the text. Providing a detailed overview of the subject and forming a solid foundation for study of multidimensional differential geometry and the tensor calculus, this book will prove an invaluable reference work to scholars of mathematics as well as to anyone with an interest in the history of education.

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 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 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.

This is the first comprehensive monograph on the mathematical theory of the solitaire game "The Tower of Hanoi" which was invented in the 19th century by the French number theorist Edouard Lucas. The book comprises a survey of the historical development from the game's predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpinski graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the "Tower of London", are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

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.

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.

In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

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.