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This textbook covers in one volume all topics required in the pure mathematics section of single subject A-Level Mathematics syllabuses in the UK, as well as a significant part of the work required by those studying for Further Mathematics and for A-Level
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.
This textbook covers the requirements of students taking pure mathematics as part of a single-maths A-level exam. It assumes a starting point of the equivalent of Level 7 in the National Curriculum or GCSE Grade B/C.
Includes a section on matrices and transformations, this book features worked examples and exercises to illustrate concepts at every stage of its development. It caters for the "Pure Mathematics" content of various courses in Further Mathematics and also for preparation for the Advanced Extension Award.
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.
Following on from Introducing Pure Mathematics by Smedley and Wiseman, Further Pure Mathematics covers in one volume all the pure mathematics required by students taking further mathematics. It also provides the basics for mathematics encountered in Higher Education. A clear text is supported by worked examples, exercises, and examination questions. The two books will cover the requirements of Pure Mathematics as part of double-certification Mathematics for any examinations board. · Clearly written explanations and graded worked examples to help students when they are studying alone · Wide variety of exercises · Comprehensive selection of recent exam questions from all the major examination boards
Pure Mathematics for Advanced Level, Second Edition is written to meet the needs of the student studying for the General Certificate of Education at Advanced Level. The text is organized into 22 chapters. Chapters 1-5 cover topics in algebra such as operations with real numbers, the binomial theorem, and the quadratic function and the quadratic equation. The principles, methods and techniques in calculus, trigonometry, and co-ordinate geometry are provided as well. Two new chapters have been added: Numerical Methods and Vectors. Mathematics students will find this book extremely useful.
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.
