Numbers And Proofs

Author : Reg Allenby
Publisher : Elsevier
ISBN 13 : 0080928773
Total Pages : 288 pages
Book Rating : 4.77/5 ( download)

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Download or read book Numbers and Proofs written by Reg Allenby and published by Elsevier. This book was released on 1997-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow. Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.37/5 ( download)

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Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard H. Hammack
Publisher :
ISBN 13 : 9780989472111
Total Pages : 314 pages
Book Rating : 4.16/5 ( download)

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Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
ISBN 13 : 1461221307
Total Pages : 434 pages
Book Rating : 4.02/5 ( download)

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Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Author : Arthur T. Benjamin
Publisher : American Mathematical Society
ISBN 13 : 1470472597
Total Pages : 210 pages
Book Rating : 4.97/5 ( download)

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Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Author : Joseph J. Rotman
Publisher : Courier Corporation
ISBN 13 : 0486151689
Total Pages : 386 pages
Book Rating : 4.87/5 ( download)

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Download or read book Journey into Mathematics written by Joseph J. Rotman and published by Courier Corporation. This book was released on 2013-01-18 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.

Author : Daniel J. Velleman
Publisher : Cambridge University Press
ISBN 13 : 0521861241
Total Pages : 401 pages
Book Rating : 4.43/5 ( download)

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Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Author : Roger B. Nelsen
Publisher : MAA
ISBN 13 : 9780883857007
Total Pages : 166 pages
Book Rating : 4.06/5 ( download)

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Download or read book Proofs Without Words written by Roger B. Nelsen and published by MAA. This book was released on 1993 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Larry Gerstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468467085
Total Pages : 355 pages
Book Rating : 4.86/5 ( download)

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Download or read book Introduction · to Mathematical Structures and · Proofs written by Larry Gerstein and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

Author : Nicholas A. Loehr
Publisher : CRC Press
ISBN 13 : 1000709809
Total Pages : 483 pages
Book Rating : 4.03/5 ( download)

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Download or read book An Introduction to Mathematical Proofs written by Nicholas A. Loehr and published by CRC Press. This book was released on 2019-11-20 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.