Understanding Mathematical Proof
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Understanding Mathematical Proof
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Author : John Taylor
language : en
Publisher: CRC Press
Release Date : 2014-03-21
Understanding Mathematical Proof written by John Taylor and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-21 with Mathematics categories.
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples.
Understanding Mathematical Proof
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Author : John Taylor
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Understanding Mathematical Proof written by John Taylor and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techn
Understanding Proof
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Author : Tom Bennison
language : en
Publisher: Tarquin Group
Release Date : 2018-03-31
Understanding Proof written by Tom Bennison and has been published by Tarquin Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-31 with Mathematics categories.
Proof is central to ny mathematics curriculum and indeed, all mathematical thinking. Now we are delighted to enhance the core texts with a guide to proof for students... and for their teachers too. Content from the core text has been significantly revised and updated and supplemented with new content. Contents: 1. Introduction to proof 2. Exploring Methods of Proof 3. Mathematical Language 4. Direct Proof 5. Indirect Proof 6. Proof by Induction 7. Proof and Applications of Pythagoras' Theorem 8. Proof in Calculus 9. Proving Trigonometric Identities 10. Proof in Statistics and Probability 11. Worked Solutions Expertly written and edited by Tom Bennison and Ed Hall, this book is an essential teaching, learning and revision guide.
Understanding Proof
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Author : Tom Bennison
language : en
Publisher: Tarquin Group
Release Date : 2021-06-11
Understanding Proof written by Tom Bennison and has been published by Tarquin Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-11 with Mathematics categories.
Proof is central to any mathematics curriculum and indeed, all mathematical thinking. Now we are delighted to provide an International Edition of our guide to proof for students...and for their teachers too. Contents: 1. Introduction to proof 2. Exploring Methods of Proof 3. Mathematical Language 4. Direct Proof 5. Indirect Proof 6. Proof by Induction 7. Proof and Applications of Pythagoras' Theorem 8. Proof in Calculus 9. Proving Trigonometric Identities 10. Proof in Statistics and Probability 11. Worked Solutions
Profunedu 2019
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Author : Naufal Ishartono
language : en
Publisher: European Alliance for Innovation
Release Date : 2019-08-06
Profunedu 2019 written by Naufal Ishartono and has been published by European Alliance for Innovation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Education categories.
The 4th Progressive and Fun Education (The 4th Profunedu) International Conference is a forum for researchers and lecturers within the ALPTK Muhammadiyah College to disseminate their best research results. This conference aims to provide a platform for researchers and academics to share their research findings with others and meet lecturers and researchers from other institutions and to strengthen the collaboration and networking amongs the participants. The 4th Profunedu was held on 6-8 August 2019 in Makassar, Indonesia. It is hoped that this proceeding can help improve the quality of education, especially the quality of education in Indonesia.
Explanation And Proof In Mathematics
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-04
Explanation And Proof In Mathematics written by Gila Hanna 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 2009-12-04 with Education categories.
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Shape Understanding System
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Author : Zbigniew Les
language : en
Publisher: Springer
Release Date : 2015-02-06
Shape Understanding System written by Zbigniew Les and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Technology & Engineering categories.
This is the third book presenting selected results of research on the further development of the shape understanding system (SUS) carried out by authors in the newly founded Queen Jadwiga Research Institute of Understanding. In this book the new term Machine Understanding is introduced referring to a new area of research aiming to investigate the possibility of building machines with the ability to understand. It is presented that SUS needs to some extent mimic human understanding and for this reason machines are evaluated according to the rules applied for the evaluation of human understanding. The book shows how to formulate problems and how it can be tested if the machine is able to solve these problems.
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12
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Author : Amy B. Ellis
language : en
Publisher: National
Release Date : 2012
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12 written by Amy B. Ellis and has been published by National this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Education categories.
Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.
Intelligent Computer Mathematics
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Author : Jacques Carette
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-06
Intelligent Computer Mathematics written by Jacques Carette 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 2009-07-06 with Computers categories.
As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.
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