LEADER 06075nam 2200637 a 450 001 9910814944103321 005 20200520144314.0 010 $a1-283-29461-3 010 $a9786613294616 010 $a1-118-06176-4 010 $a1-118-06177-2 010 $a1-118-06171-3 035 $a(CKB)3520000000000179 035 $a(EBL)697632 035 $a(OCoLC)751969641 035 $a(SSID)ssj0000538404 035 $a(PQKBManifestationID)11360775 035 $a(PQKBTitleCode)TC0000538404 035 $a(PQKBWorkID)10560016 035 $a(PQKB)10348895 035 $a(MiAaPQ)EBC697632 035 $a(PPN)157873943 035 $a(EXLCZ)993520000000000179 100 $a20110128d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe language of mathematics $eutilizing math in practice /$fRobert L. Baber 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$d2011 215 $a1 online resource (438 p.) 300 $aIncludes index. 311 $a0-470-87889-4 327 $aTHE LANGUAGE OF MATHEMATICS; CONTENTS; LIST OF TABLES; PREFACE; PART A INTRODUCTORY OVERVIEW; 1 Introduction; 1.1 What Is Language?; 1.2 What Is Mathematics?; 1.3 Why Use Mathematics?; 1.4 Mathematics and Its Language; 1.5 The Role of Translating English to Mathematics in Applying Mathematics; 1.6 The Language of Mathematics vs. Mathematics vs. Mathematical Models; 1.7 Goals and Intended Readership; 1.8 Structure of the Book; 1.9 Guidelines for the Reader; 2 Preview: Some Statements in English and the Language of Mathematics; 2.1 An Ancient Problem: Planning the Digging of a Canal 327 $a2.2 The Wall Around the Ancient City of Uruk2.3 A Numerical Thought Puzzle; 2.4 A Nursery Rhyme; 2.5 Making a Pot of Tea; 2.6 Combining Data Files; 2.7 Selecting a Telephone Tariff; 2.8 Interest on Savings Accounts, Bonds, etc.; 2.9 Sales and Value-Added Tax on Sales of Goods and Services; 2.10 A Hand of Cards; 2.11 Shear and Moment in a Beam; 2.12 Forming Abbreviations of Names; 2.13 The Energy in Earth's Reflected Sunlight vs. That in Extracted Crude Oil; PART B MATHEMATICS AND ITS LANGUAGE; 3 Elements of the Language of Mathematics; 3.1 Values; 3.2 Variables; 3.3 Functions; 3.4 Expressions 327 $a3.4.1 Standard Functional Notation3.4.2 Infix Notation; 3.4.3 Tree Notation; 3.4.4 Prefix and Postfix Notation; 3.4.5 Tabular Notation; 3.4.6 Graphical Notation; 3.4.7 Figures, Drawings, and Diagrams; 3.4.8 Notation for Series and Quantification; 3.4.9 Specialized Notational Forms for Certain Expressions; 3.4.10 Advantages and Disadvantages of the Different Notational Forms; 3.5 Evaluating Variables, Functions, and Expressions; 3.5.1 Complete (Total) Evaluation; 3.5.2 Partial Evaluation; 3.5.3 Undefined Values of Functions and Expressions; 3.6 Representations of Values vs. Names of Variables 327 $a4 Important Structures and Concepts in the Language of Mathematics4.1 Common Structures of Values; 4.1.1 Sets; 4.1.2 Arrays (Indexed Variables), Subscripted Variables, and Matrices; 4.1.3 Sequences; 4.1.4 The Equivalence of Array Variables, Functions, Sequences, and Variables; 4.1.5 Direct Correspondence of Other Mathematical Objects and Structures; 4.1.6 Relations; 4.1.7 Finite State Machines; 4.2 Infinity; 4.3 Iterative Definitions and Recursion; 4.4 Convergence, Limits, and Bounds; 4.5 Calculus; 4.6 Probability Theory; 4.6.1 Mathematical Model of a Probabilistic Process 327 $a4.6.2 Mean, Median, Variance, and Deviation4.6.3 Independent Probabilistic Processes; 4.6.4 Dependent Probabilistic Processes and Conditional Probabilities; 4.7 Theorems; 4.8 Symbols and Notation; 5 Solving Problems Mathematically; 5.1 Manipulating Expressions; 5.2 Proving Theorems; 5.2.1 Techniques and Guidelines for Proving Theorems; 5.2.2 Notation for Proofs; 5.2.3 Lemmata and Examples of Proofs; 5.2.4 Additional Useful Identities; 5.3 Solving Equations and Other Boolean Expressions; 5.4 Solving Optimization Problems 327 $aPART C ENGLISH, THE LANGUAGE OF MATHEMATICS, AND TRANSLATING BETWEEN THEM 330 $a"The subject of this book is how to formulate a mathematical model from an English description of a problem. This book views mathematical notation as a language and develops the implications of this view for translating English text into mathematical expressions and mathematical models, i.e. for applying mathematics to problems described in English. In order to apply mathematics to a practical problem, one must first transform an English statement of the problem and the requirements for its solution into mathematical expressions. This book examines this process in detail, presents new insight into it, and develops explicit guidelines for this important step. This book identifies the basic elements (values, variables, and functions) of the language of mathematics and presents the grammatical rules for combining them into expressions and other structures. Different notational forms for expressions are described and defined. Correspondences between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics are identified. These lead to useful guidelines for translating English into the language of mathematics. In addition, the book contains many examples of translating English into mathematics. The approach presented in this book makes mathematics accessible to many people who have been turned off from mathematics by their early exposure to it"--$cProvided by publisher. 606 $aMathematical notation 606 $aEnglish language$xMachine translating 615 0$aMathematical notation. 615 0$aEnglish language$xMachine translating. 676 $a510.1/4 686 $aMAT025000$2bisacsh 700 $aBaber$b Robert Laurence$0322853 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814944103321 996 $aThe language of mathematics$94093567 997 $aUNINA