An Introduction To Mathematical Proofs

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Introduction To Proof In Abstract Mathematics

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Author : Andrew Wohlgemuth
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17

Introduction To Proof In Abstract Mathematics written by Andrew Wohlgemuth and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.

Originally published: Philadelphia: Saunders College Pub., c1990.

Journey Into Mathematics

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Author : Joseph J. Rotman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18

Journey Into Mathematics written by Joseph J. Rotman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.

This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Book Of Proof

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Author : Richard H. Hammack
language : en
Publisher:
Release Date : 2013-05

Book Of Proof written by Richard H. Hammack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05 with Mathematics categories.

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. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

How To Prove It

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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16

How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

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.

Mathematical Reasoning

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Author : Theodore A. Sundstrom
language : en
Publisher:
Release Date : 2003

Mathematical Reasoning written by Theodore A. Sundstrom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Proof theory categories.

Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.

An Introduction To Mathematical Reasoning

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Author : Peter J. Eccles
language : en
Publisher: Cambridge University Press
Release Date : 1997-12-11

An Introduction To Mathematical Reasoning written by Peter J. Eccles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.

ÍNDICE: Part I. Mathematical Statements and Proofs: 1. The language of mathematics; 2. Implications; 3. Proofs; 4. Proof by contradiction; 5. The induction principle; Part II. Sets and Functions: 6. The language of set theory; 7. Quantifiers; 8. Functions; 9. Injections, surjections and bijections; Part III. Numbers and Counting: 10. Counting; 11. Properties of finite sets; 12. Counting functions and subsets; 13. Number systems; 14. Counting infinite sets; Part IV. Arithmetic: 15. The division theorem; 16. The Euclidean algorithm; 17. Consequences of the Euclidean algorithm; 18. Linear diophantine equations; Part V. Modular Arithmetic: 19. Congruences of integers; 20. Linear congruences; 21. Congruence classes and the arithmetic of remainders; 22. Partitions and equivalence relations; Part VI. Prime Numbers: 23. The sequence of prime numbers; 24. Congruence modulo a prime; Solutions to exercises.

Proofs And Fundamentals

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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Proofs And Fundamentals written by Ethan D. Bloch 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 2013-12-01 with Mathematics categories.

In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se.

An Introduction To Proof Through Real Analysis

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Author : Daniel J. Madden
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-14

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 2017-08-14 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.

Mathematical Proofs

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Author : Gary Chartrand
language : en
Publisher: Pearson
Release Date : 2013

Mathematical Proofs written by Gary Chartrand and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Proof theory categories.

This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.

An Introduction To Writing Mathematical Proofs

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Author : Prof Thomas Bieske
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-05-29

An Introduction To Writing Mathematical Proofs written by Prof Thomas Bieske and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with categories.

This textbook is designed to help students transition from calculus-type courses that focus on computation to upper-level mathematics courses that focus on proof-writing. Using the familiar topics of real numbers, high school geometry and calculus, students are introduced to the methods of proof-writing and pre-proof strategy planning. A supplemental workbook for instructors is available upon request from the author. The workbook includes chapter vocabulary lists, creative writing exercises, group projects, and classroom discussions.