Introduction To Mathematical Structures And Proofs
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Introduction To Mathematical Structures And Proofs
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Author : Larry J. Gerstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-05
Introduction To Mathematical Structures And Proofs written by Larry J. Gerstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-05 with Mathematics categories.
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.
Introduction To Mathematical Structures And Proofs
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Author : Larry Gerstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Introduction To Mathematical Structures And Proofs written by Larry Gerstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Science categories.
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.
Introduction To Mathematical Structures And Proofs
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Author : Springer
language : en
Publisher:
Release Date : 2012-08-01
Introduction To Mathematical Structures And Proofs written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with categories.
Introduction To Mathematical Structures And Proofs
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Author : Larry Gerstein
language : en
Publisher:
Release Date : 2014-09-01
Introduction To Mathematical Structures And Proofs written by Larry Gerstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Discrete Mathematics Proof Techniques And Mathematical Structures
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Author : Robert Clark Penner
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-10-19
Discrete Mathematics Proof Techniques And Mathematical Structures written by Robert Clark Penner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-19 with Mathematics categories.
This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.
Introduction To Mathematics
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Author : Scott A. Taylor
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-13
Introduction To Mathematics written by Scott A. Taylor and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-13 with Mathematics categories.
This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge.
Discrete Mathematics
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Author : R. C. Penner
language : en
Publisher:
Release Date : 1999
Discrete Mathematics written by R. C. Penner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
A Logical Introduction To Proof
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Author : Daniel W. Cunningham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-19
A Logical Introduction To Proof written by Daniel W. Cunningham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-19 with Mathematics categories.
The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.
An Introduction To Mathematical Proofs
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2019-11-20
An Introduction To Mathematical Proofs written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.
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.
Discrete Mathematics
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Author : Rowan Garnier
language : en
Publisher: Taylor & Francis
Release Date : 2009-11-09
Discrete Mathematics written by Rowan Garnier and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-09 with Computers categories.
Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow prog