Introduction To Mathematical Proofs
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An Introduction To Mathematical Proofs
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Author : Nicholas A. Loehr
language : en
Publisher:
Release Date : 2020
An Introduction To Mathematical Proofs written by Nicholas A. Loehr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
"This book contains an introduction to mathematical proofs, including fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The book is divided into approximately fifty brief lectures. Each lecture corresponds rather closely to a single class meeting"--
Introduction To Mathematical Proofs
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Author : Charles E. Roberts
language : en
Publisher:
Release Date : 2010
Introduction To Mathematical Proofs written by Charles E. Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Logic, Symbolic and mathematical categories.
Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics CoursesIntroduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and t.
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.
Introduction To Mathematical Proofs
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Author : Charles Roberts
language : en
Publisher: CRC Press
Release Date : 2014-12-17
Introduction To Mathematical Proofs written by Charles Roberts and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-17 with Mathematics categories.
Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural num
How To Read And Do Proofs
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Author : Daniel Solow
language : en
Publisher: John Wiley & Sons
Release Date : 1982
How To Read And Do Proofs written by Daniel Solow and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Language Arts & Disciplines categories.
This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra.
An Introduction To Proof Through Real Analysis
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Author : Daniel J. Madden
language : en
Publisher: John Wiley & Sons
Release Date : 2017-09-12
An Introduction To Proof Through Real Analysis written by Daniel J. Madden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Education categories.
An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.
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 Social 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 Proofs In Mathematics
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Author : James Franklin
language : en
Publisher:
Release Date : 1988
Introduction To Proofs In Mathematics written by James Franklin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
How To Read And Do Proofs
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Author : Daniel Solow
language : en
Publisher:
Release Date : 2002
How To Read And Do Proofs written by Daniel Solow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated with step-by-step examples.
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 forinstructors adopting the text for a course.