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For students reading Mathematics, either as part of a general degree or as an ancilliary course for an Honours degree, the subject should be presented in as straightforward a manners as is consistent with a moderate standard of rigour. This course in algebra, co-ordinate geometry and calculus is designed to fulfil these requirements for students at Universities, Polytechnics and Colleges of Technology. The book contains 350 worked examples and 1550 practice examples selected mainly from university examination papers. The practice examples have been carefully graded and some hints are given with the answers so that the book may be used for private study as well as for class work.
Outline Course of Pure Mathematics presents a unified treatment of the algebra, geometry, and calculus that are considered fundamental for the foundation of undergraduate mathematics. This book discusses several topics, including elementary treatments of the real number system, simple harmonic motion, Hooke's law, parabolic motion under gravity, sequences and series, polynomials, binomial theorem, and theory of probability. Organized into 23 chapters, this book begins with an overview of the fundamental concepts of differential and integral calculus, which are complementary processes for solving problems of the physical world. This text then explains the concept of the inverse of a function that is a natural complement of the function concept and introduces a convenient notation. Other chapters illustrate the concepts of continuity and discontinuity at the origin. This book discusses as well the significance of logarithm and exponential functions in scientific and technological contexts. This book is a valuable resource for undergraduates and advanced secondary school students.
This classic calculus text remains a must-read for all students of introductory mathematical analysis. Clear, rigorous explanations of the mathematics of analytical number theory and calculus cover single-variable calculus, sequences, number series, more. 1921 edition.
A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. For years, it remains one of the most popular books on pure mathematics. The book contains a large number of descriptive and study materials together with a number of difficult problems with regards to number theory analysis. The book is organized into the following chapters, with each chapter further divided. Real Variables Functions Of Real Variables Complex Numbers Limits Of Functions Of A Positive Integral Variable Limits Of Functions Of A Continuous Variable. Continuous And Discontinuous Functions Derivatives And Integrals Additional Theorems In The Differential And Integral Calculus The Convergence Of Infinite Series And Infinite Integrals The Logarithmic, Exponential And Circular Functions Of A Real Variable The General Theory Of The Logarithmic, Exponential And Circular Functions The book was intended to help reform mathematics teaching in the world, from the University of Cambridge and in schools preparing to study higher mathematics. It was aimed directly at "scholarship level" students - the top 10% to 20% by ability. Hardy himself did not originally find a passion for mathematics, only seeing it as a way to beat other students, which he did decisively, and gain scholarships.[1] However, his book excels in effectively explaining analytical number theory and calculus following the rigor of mathematics. Whilst his book changed the way the subject was taught at university, the content reflects the era in which the book was written. The whole book explores number theory and the author constructs real numbers theoretically. It adequately deals with single-variable calculus, sequences, number series, properties of cos, sin, log, etc. but does not refer to mathematical groups, multi-variable functions or vector calculus. Each section includes some demanding problems. Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.[2] Despite its limitations, it is considered a classic in its field. It is probably of most use to 1st year university students of pure mathematics.
Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician. The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables. Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.
Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Euler’s formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered ones Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher-level mathematics, enabling students to study more advanced courses in abstract algebra and analysis.
A Course of Pure Mathematics by G. H. Hardy: Dive into the world of mathematical analysis with "A Course of Pure Mathematics" by G. H. Hardy. This classic textbook serves as an introductory guide to the principles and concepts of mathematical analysis, offering a rigorous and comprehensive exploration of the subject. With its clear explanations, illustrative examples, and problem-solving techniques, Hardy's book provides a solid foundation for understanding the fundamental principles of mathematics. Key Aspects of the Book "A Course of Pure Mathematics": Comprehensive Coverage: Delve into the various branches of mathematical analysis, including calculus, functions, series, complex numbers, and more. Hardy's comprehensive approach ensures that readers gain a broad understanding of the subject. Rigorous Approach: Experience the rigor and precision of mathematical analysis through Hardy's clear and concise explanations. His logical and systematic approach helps readers develop a strong grasp of mathematical principles. Problem-Solving Techniques: Engage in problem-solving exercises that enhance your mathematical skills and reinforce your understanding of the concepts. Hardy's emphasis on problem-solving cultivates critical thinking and analytical abilities. H. Hardy, a renowned British mathematician, authored "A Course of Pure Mathematics" as a seminal work in the field. Recognized for his contributions to number theory and mathematical analysis, Hardy's book continues to be highly regarded as a foundational text for students and enthusiasts of mathematics. Through his passion for the subject and his commitment to clarity and rigor, Hardy inspires readers to explore the beauty and elegance of mathematical reasoning.
G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.
Written to match the contents of the Cambridge syllabus. Pure Mathematics 1 corresponds to unit P1. It covers quadratics, functions, coordinate geometry, circular measure, trigonometry, vectors, series, differentiation and integration.