Book of Proof

Author: Richard H. Hammack
Publisher:
ISBN: 9780989472111
Category : Mathematics
Languages : en
Pages : 314

Book Description
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Proofs from THE BOOK

Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194

Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Introduction to Probability

Author: Joseph K. Blitzstein
Publisher: CRC Press
ISBN: 1466575573
Category : Mathematics
Languages : en
Pages : 599

Book Description
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

How to Prove It

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401

Book Description
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.

A Book of Abstract Algebra

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486474178
Category : Mathematics
Languages : en
Pages : 402

Book Description
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Formula One Maths Euro Edition Practice Book A2

Author: Roger Porkess
Publisher: Hodder Education
ISBN: 9780340928660
Category :
Languages : en
Pages : 96

Book Description
Formula One Maths Euro Edition is a unique and carefully structured course designed to fully cover all areas of junior secondary mathematics. The course incorporates a new, exciting and interactive approach to maths at this level. This Practice Book is designed to complement the Formula One Maths textbook. It provides a set of new exercises that will help reinforce the ideas and concepts already taught within each lesson in the Pupil's Book. Formula One Maths Euro Edition Practice Book A2 provides: * A parallel exercise for each lesson in the Pupil's Book * Sets of graded questions written by experienced authors * Prepared homework for pupils * Additional material for those pupils who need extra practice on a certain topic

An Introduction to Measure Theory

Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206

Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

The Crest of the Peacock

Author: George Gheverghese Joseph
Publisher: Penguin Group
ISBN:
Category : Mathematics
Languages : en
Pages : 408

Book Description

Formula One Maths

Author: Catherine Berry
Publisher: Hodder Murray
ISBN: 9780340803066
Category : Education
Languages : en
Pages : 256

Book Description
Forumla One Maths is a structured course designed to cover all programmes of study in the National Curriculum for Maths at Key Stage 3. It also gives coverage of the National Curriculum for Maths at Key Stage 3 and the Nathional Strategy Framework for teaching mathematics: Years 7, 8 and 9. Incorporating the idealogy behind the National strategy, Formula One Maths give a interactive approach to maths at this level.

The Probability Tutoring Book

Author: Carol Ash
Publisher: Wiley-IEEE Press
ISBN: 9780780310513
Category : Mathematics
Languages : en
Pages : 0

Book Description
A self-study guide for practicing engineers, scientists, and students, this book offers practical, worked-out examples on continuous and discrete probability for problem-solving courses. It is filled with handy diagrams, examples, and solutions that greatly aid in the comprehension of a variety of probability problems.