An Introduction To The Language Of Mathematics PDF Download
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| Author | : Frédéric Mynard |
| Publisher | : Springer |
| Total Pages | : 185 |
| Release | : 2018-11-24 |
| Genre | : Mathematics |
| ISBN | : 3030006417 |
Download An Introduction to the Language of Mathematics Book in PDF, ePub and Kindle
This is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study.
| Author | : Robert L. Baber |
| Publisher | : John Wiley & Sons |
| Total Pages | : 350 |
| Release | : 2011-09-09 |
| Genre | : Mathematics |
| ISBN | : 1118061764 |
Download The Language of Mathematics Book in PDF, ePub and Kindle
A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
| Author | : György E. Révész |
| Publisher | : Courier Corporation |
| Total Pages | : 208 |
| Release | : 2015-03-17 |
| Genre | : Mathematics |
| ISBN | : 0486169375 |
Download Introduction to Formal Languages Book in PDF, ePub and Kindle
Covers all areas, including operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Numerous worked examples, problem exercises, and elegant mathematical proofs. 1983 edition.
| Author | : Alfred North Whitehead |
| Publisher | : Courier Dover Publications |
| Total Pages | : 176 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486821382 |
Download An Introduction to Mathematics Book in PDF, ePub and Kindle
Concise volume for general students by prominent philosopher and mathematician explains what math is and does, and how mathematicians do it. "Lucid and cogent ... should delight you." — The New York Times. 1911 edition.
| Author | : Mohan Ganesalingam |
| Publisher | : Springer |
| Total Pages | : 273 |
| Release | : 2013-03-14 |
| Genre | : Computers |
| ISBN | : 3642370128 |
Download The Language of Mathematics Book in PDF, ePub and Kindle
The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers
| Author | : Juan Jorge Schäffer |
| Publisher | : World Scientific |
| Total Pages | : 320 |
| Release | : 2014-05-16 |
| Genre | : Mathematics |
| ISBN | : 9814596116 |
Download Basic Language of Mathematics Book in PDF, ePub and Kindle
This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements. Contents:SetsMappingsProperties of MappingsFamiliesRelationsOrdered SetsCompletely Ordered SetsInduction and RecursionThe Natural NumbersFinite SetsFinite SumsCountable SetsSome Algebraic StructuresThe Real Numbers: Complete Ordered FieldsThe Real Number SystemThe Real Numbers: ExistenceInfinite Sets Readership: Undergraduate and graduate students in mathematics; Mathematicians. Key Features:Comprehensive and rigorous in its coverageProvides alternative insights on concepts and definitionsProvides a list of sections with some unusual but insightful approachesKeywords:Sets;Mappings;Families;Order;Natural Numbers;Inductive Proofs;Recursive Definitions;Real Numbers
| Author | : Richard E. Hodel |
| Publisher | : Courier Corporation |
| Total Pages | : 514 |
| Release | : 2013-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486497852 |
Download An Introduction to Mathematical Logic Book in PDF, ePub and Kindle
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
| Author | : Steven Roman |
| Publisher | : Birkhäuser |
| Total Pages | : 169 |
| Release | : 2017-01-05 |
| Genre | : Mathematics |
| ISBN | : 331941917X |
Download An Introduction to the Language of Category Theory Book in PDF, ePub and Kindle
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
| Author | : Judit N. Moschkovich |
| Publisher | : Information Age Pub Incorporated |
| Total Pages | : 180 |
| Release | : 2010 |
| Genre | : Education |
| ISBN | : 9781617351594 |
Download Language and Mathematics Education Book in PDF, ePub and Kindle
A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, Iowa State University Marketing description: Issues of language in mathematics learning and teaching are important for both practical and theoretical reasons. Addressing issues of language is crucial for improving mathematics learning and teaching for students who are bilingual, multilingual, or learning English. These issues are also relevant to theory: studies that make language visible provide a complex perspective of the role of language in reasoning and learning mathematics. What is the relevant knowledge base to consider when designing research studies that address issues of language in the learning and teaching of mathematics? What scholarly literature is relevant and can contribute to research? In order to address issues of language in mathematics education, researchers need to use theoretical perspectives that integrate current views of mathematics learning and teaching with current views on language, discourse, bilingualism, and second language acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematics education by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designing research studies. The volume provides interdisciplinary reviews of the research literature from four very different perspectives: mathematics education (Moschkovich), Cultural-Historical-Activity Theory (Gutierrez, Sengupta-Irving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (Solano-Flores). This volume offers graduate students and researchers new to the study of language in mathematics education an introduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, the volume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volume provides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues.
| Author | : Marcus Kracht |
| Publisher | : Walter de Gruyter |
| Total Pages | : 616 |
| Release | : 2003 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9783110176209 |
Download The Mathematics of Language Book in PDF, ePub and Kindle
Table of contents
