Proof, Logic, and Conjecture

The Mathematician's Toolbox
Author: Robert S. Wolf
Publisher: St. Martin's Press
ISBN: 9780716730507
Category: Mathematics
Page: 421
View: 2266

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This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.

Refocusing education in Nigeria

a book of readings
Author: S. O. Oriaifo,Pius O. E. Nwaokolo,Godson C. Igborgbor
Publisher: N.A
ISBN: N.A
Category: Educational change
Page: 455
View: 3543

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The Nuts and Bolts of Proofs

An Introduction to Mathematical Proofs
Author: Antonella Cupillari
Publisher: Academic Press
ISBN: 0123822181
Category: Mathematics
Page: 296
View: 8436

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The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable. Jumps right in with the needed vocabulary—gets students thinking like mathematicians from the beginning Offers a large variety of examples and problems with solutions for students to work through on their own Includes a collection of exercises without solutions to help instructors prepare assignments Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics

Introduction to Advanced Mathematics: A Guide to Understanding Proofs


Author: Connie M. Campbell
Publisher: Cengage Learning
ISBN: 0547165382
Category: Mathematics
Page: 144
View: 3192

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This text offers a crucial primer on proofs and the language of mathematics. Brief and to the point, it lays out the fundamental ideas of abstract mathematics and proof techniques that students will need to master for other math courses. Campbell presents these concepts in plain English, with a focus on basic terminology and a conversational tone that draws natural parallels between the language of mathematics and the language students communicate in every day. The discussion highlights how symbols and expressions are the building blocks of statements and arguments, the meanings they convey, and why they are meaningful to mathematicians. In-class activities provide opportunities to practice mathematical reasoning in a live setting, and an ample number of homework exercises are included for self-study. This text is appropriate for a course in Foundations of Advanced Mathematics taken by students who've had a semester of calculus, and is designed to be accessible to students with a wide range of mathematical proficiency. It can also be used as a self-study reference, or as a supplement in other math courses where additional proofs practice is needed. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Books in Print


Author: R.R. Bowker Company
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 4510

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Was ist Mathematik?


Author: Richard Courant,Herbert Robbins
Publisher: Springer-Verlag
ISBN: 3662000539
Category: Mathematics
Page: N.A
View: 8958

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47 brauchen nur den Nenner n so groß zu wählen, daß das Intervall [0, IJn] kleiner wird als das fragliche Intervall [A, B], dann muß mindestens einer der Brüche m/n innerhalb des Intervalls liegen. Also kann es kein noch so kleines Intervall auf der Achse geben, das von rationalen Punkten frei wäre. Es folgt weiterhin, daß es in jedem Intervall unendlich viele rationale Punkte geben muß; denn wenn es nur eine endliche Anzahl gäbe, so könnte das Intervall zwischen zwei beliebigen benachbarten Punkten keine rationalen Punkte enthalten, was, wie wir eben sahen, unmöglich ist. § 2. Inkommensurable Strecken, irrationale Zahlen und der Grenzwertbegriff 1. Einleitung Vergleicht man zwei Strecken a und b hinsichtlich ihrer Größe, so kann es vor kommen, daß a in b genau r-mal enthalten ist, wobei r eine ganze Zahl darstellt. In diesem Fall können wir das Maß der Strecke b durch das von a ausdrücken, indem wir sagen, daß die Länge von b das r-fache der Länge von a ist.

Begriffsschrift und andere Aufsätze

Mit E. Husserls und H. Scholz' Anmerkungen herausgegeben von Ignacio Angelelli
Author: Gottlob Frege
Publisher: Georg Olms Verlag
ISBN: 3487006235
Category: Philosophy
Page: 124
View: 5171

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Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively.

Mathematische Edelsteine

der elementaren Kombinatorik, Zahlentheorie und Geometrie
Author: Ross Honsberger
Publisher: Springer-Verlag
ISBN: 3322859304
Category: Mathematics
Page: 179
View: 988

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Proof in mathematics education

research, learning and teaching
Author: David Alexander Reid,Christine Knipping
Publisher: N.A
ISBN: 9789460912443
Category: Education
Page: 251
View: 8929

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Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving. This book is intended to help teachers, researchers and graduate students to overcome the difficulty of getting an overview of research on proof and proving. It reviews the key findings and concepts in research on proof and proving, and embeds them in a contextual frame that allows the reader to make sense of the sometimes contradictory statements found in the literature. It also provides examples from current research that explore how larger patterns in reasoning and argumentation provide insight into teaching and learning.

Naive Mengenlehre


Author: Paul R. Halmos
Publisher: Vandenhoeck & Ruprecht
ISBN: 9783525405277
Category: Arithmetic
Page: 132
View: 6136

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Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit
Author: Edward Frenkel
Publisher: Springer-Verlag
ISBN: 3662434210
Category: Mathematics
Page: 317
View: 8477

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Vorlesungen über Differential- und Integralrechnung

Zweiter Band: Funktionen Mehrerer Veränderlicher
Author: Richard Courant
Publisher: Springer-Verlag
ISBN: 3709158184
Category: Mathematics
Page: 412
View: 2534

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

College Preparatory Mathematics 2

Geometry Version 4.1, Complete
Author: Brian Hoey,Karen Wootton,Tom Sallee,CPM Educational Program,Eric Ettlin,Julien Howe
Publisher: N.A
ISBN: 9781885145703
Category: Mathematics
Page: 555
View: 3844

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