Journey Into Mathematics An Introduction With Proofs
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Journey Into Mathematics An Introduction With Proofs
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Author : Joseph J. Rotman
language : en
Publisher:
Release Date :
Journey Into Mathematics An Introduction With Proofs written by Joseph J. Rotman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Proof theory categories.
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.
The Nuts And Bolts Of Proofs
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Author : Antonella Cupillari
language : en
Publisher: Academic Press
Release Date : 2001
The Nuts And Bolts Of Proofs written by Antonella Cupillari and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
Journey Into Discrete Mathematics
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Author : Owen D. Byer
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-11-13
Journey Into Discrete Mathematics written by Owen D. Byer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-13 with Mathematics categories.
Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.
Introduction To Proofs And Proof Strategies
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Author : Shay Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-22
Introduction To Proofs And Proof Strategies written by Shay Fuchs 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 2023-06-22 with Mathematics categories.
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
Proofs And Logic A Comprehensive Guide To Mathematical Reasoning
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-15
Proofs And Logic A Comprehensive Guide To Mathematical Reasoning written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-15 with Mathematics categories.
In the realm of mathematics, proofs stand as the gatekeepers of truth, ensuring that mathematical statements are not mere assertions but logical consequences of established axioms and definitions. "Proofs and Logic: A Comprehensive Guide to Mathematical Reasoning" is your gateway to mastering the art of mathematical proof construction. This comprehensive book is meticulously crafted to empower you with the skills and techniques necessary to navigate the intricate world of mathematical arguments. Whether you are a student seeking to excel in your studies, a teacher aiming to inspire your students, or a professional mathematician seeking to expand your knowledge, this book is your essential companion. With crystal-clear explanations, engaging examples, and thought-provoking exercises, this book takes you on a journey through the diverse landscape of proofs. From direct proofs that establish the truth of a statement through a sequence of logical steps to proofs by contradiction that reveal the absurdity of a statement's negation, you will gain a deep understanding of the various methods of proof construction. Beyond the realm of proofs, this book delves into the foundations of logic, set theory, propositional logic, and predicate logic, providing you with a solid grasp of the formal structure of mathematical statements. With this knowledge, you will be able to analyze and evaluate mathematical arguments with precision and rigor. As you progress through this book, you will not only develop a profound appreciation for the beauty and elegance of mathematical proofs but also cultivate a valuable skill set that will serve you well in your academic and professional endeavors. Whether you aspire to pursue a career in mathematics, science, engineering, or any field that values logical reasoning, this book is your indispensable guide. Join us on this intellectual adventure as we unlock the power of logical reasoning and embark on a journey into the fascinating world of mathematical proofs. "Proofs and Logic" is more than just a book; it is an invitation to embark on a transformative learning experience that will reshape your understanding of mathematics and empower you to tackle complex problems with confidence. If you like this book, write a review!
Math Made Visual
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Author : Claudi Alsina
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-12-31
Math Made Visual written by Claudi Alsina and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-31 with Mathematics categories.
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.
Cliffstestprep Cset Mathematics
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Author : Janet B Andreasen
language : en
Publisher: Houghton Mifflin Harcourt
Release Date : 2007-10-16
Cliffstestprep Cset Mathematics written by Janet B Andreasen and has been published by Houghton Mifflin Harcourt this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-16 with Study Aids categories.
Your complete guide to a higher score on the CSET: Mathematics. Features information about certification requirements, an overview of the test - with a scoring scale, description of the test structure and format and proven test-taking strategies Approaches for answering the three types of questions: multiple-choice enhanced multiple-choice constructed-response. Reviews and Practice Focused reviews of all areas tested: algebra, number theory, geometry, probability, calculus, and history of mathematics Practice problems for selected difficult areas and domains 2 Full-Length Practice Tests are structured like the actual exam and are complete with answers and explanations The Glossary of Terms has description of Key Formulas and Properties Test-Prep Essentials from the Experts at CliffsNotes
Elementary Analysis
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Author : Kenneth A. Ross
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Elementary Analysis written by Kenneth A. Ross 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 2013-04-17 with Mathematics categories.
Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.