A Concise Introduction to Pure Mathematics Fourth Edition

Author: Martin Liebeck
Publisher: CRC Press
ISBN: 1498722938
Format: PDF, ePub
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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.

Understanding Pure Mathematics

Author: A. J. Sadler
Publisher: Oxford University Press, USA
ISBN: 9780199142439
Format: PDF, Docs
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A classic single-volume textbook, popular for its direct and straightforward approach. Understanding Pure Mathematics starts by filling the gap between GCSE and A Level and builds on this base for candidates taking either single-subject of double-subject A Level.

How to Think Like a Mathematician

Author: Kevin Houston
Publisher: Cambridge University Press
ISBN: 9781139477055
Format: PDF, Kindle
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Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

Introduction to Mathematical Logic Sixth Edition

Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 1482237784
Format: PDF, Docs
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The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing. The sixth edition incorporates recent work on Gödel’s second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

Introduction to Algebra

Author: Peter J. Cameron
Publisher: Oxford University Press on Demand
ISBN: 0198569130
Format: PDF, ePub, Docs
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This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.

Essential Calculus

Author: James Stewart
Publisher: Cengage Learning
ISBN: 1133112293
Format: PDF, Docs
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This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart’s other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book’s website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart’s other books. ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart’s textbooks the best-selling calculus texts in the world. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

A Modern Introduction to Probability and Statistics

Author: F.M. Dekking
Publisher: Springer Science & Business Media
ISBN: 1846281687
Format: PDF, Mobi
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Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Elementary Analysis

Author: Kenneth A. Ross
Publisher: Springer Science & Business Media
ISBN: 1461462711
Format: PDF
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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Guide to Analysis

Author: F. Mary Hart
Publisher: Macmillan International Higher Education
ISBN: 1349093904
Format: PDF
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Guide to Analysis aims to minimise the difficulties which arise from the contrast between analysis and sixth form mathematics. It includes historical notes and anecdotes which will help the reader to appreciate how the subject developed to its present form. Plenty of worked and unworked examples, the latter with hints for solution and answers, are also included.