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A Concise Introduction To Pure Mathematics Third Edition

Author: Martin Liebeck
Publisher: CRC Press
ISBN: 1439835985
Size: 66.39 MB
Format: PDF, ePub, Mobi
View: 1984
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Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Third 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, the use of Euler’s formula to study the five Platonic solids, the use of prime numbers to encode and decode secret information, and the theory of how to compare the sizes of two infinite sets. New to the Third Edition The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. These new chapters introduce the ideas of limits of sequences and continuous functions as well as several interesting applications, such as the use of the intermediate value theorem to prove the existence of nth roots. This edition also includes solutions to all of the odd-numbered exercises. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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 further courses in abstract algebra and analysis.

Solutions Manual For Lang S Linear Algebra

Author: Rami Shakarchi
Publisher: Springer Science & Business Media
ISBN: 146120755X
Size: 46.37 MB
Format: PDF, Mobi
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This solutions manual for Lang’s Undergraduate Analysis provides worked-out solutions for all problems in the text. They include enough detail so that a student can fill in the intervening details between any pair of steps.

Vector Calculus Linear Algebra And Differential Forms

Author: John H. Hubbard
Publisher:
ISBN: 9780130414083
Size: 60.31 MB
Format: PDF, ePub
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This text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. Appendix material on harder proofs and programs allows the book to be used as a text for a course in analysis. The organization and selection of material present

From Calculus To Analysis

Author: Rinaldo B. Schinazi
Publisher: Springer Science & Business Media
ISBN: 9780817682897
Size: 80.66 MB
Format: PDF, Mobi
View: 7141
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This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.

How To Prove It

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 1139450972
Size: 43.68 MB
Format: PDF, Docs
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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Numbers And Functions

Author: R. P. Burn
Publisher: Cambridge University Press
ISBN: 1316033783
Size: 74.51 MB
Format: PDF, Docs
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The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this third edition of Numbers and Functions, Professor Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of more than 800 problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, of which most are supplied with brief answers, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. Carefully corrected and updated throughout, this new edition also includes extra questions on integration and an introduction to convergence. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.

Calculus For Biology And Medicine

Author: Claudia Neuhauser
Publisher: Pearson Higher Ed
ISBN: 0321999541
Size: 17.64 MB
Format: PDF
View: 5256
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This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. Calculus for Biology and Medicine, Third Edition, addresses the needs of readers in the biological sciences by showing them how to use calculus to analyze natural phenomena—without compromising the rigorous presentation of the mathematics. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides readers with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. This book is suitable for a wide audience, as all examples were chosen so that no formal training in biology is needed.