The number systems and operations of arithmetic : an explanation of the fundamental principles of mathematics which underlie the understanding and use of arithmetic, designed for in-service training of elementary school teachers and pre-service training of elementary school teacher candidates /

The Number Systems and Operations of Arithmetic was written for the single purpose of explaining to elementary school teachers (both in-service and in-training) the nature of those basic principles of mathematics which form the foundations and structural framework of arithmetic, and how the familiar...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Klose, Orval M.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford : Pergamon Press, 1966.
Edición:First edition.
Colección:Commonwealth and international library of science and technology, engineering, and liberal studies. Mathematics division.
Temas:
Arithmetic > Foundations.
Arithm�etique > Fondements.
MATHEMATICS > General.
Arithmetic > Foundations
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover; The Number Systems and Operations of Arithmetic; Copyright Page; Table of Contents; PREFACE; PART I: The Number Systems; CHAPTER 1.1. THE ORIGIN OF NUMERICAL THINKING; 1.1.1. The Set Concept in Human Affairs; 1.1.2. The Natural Number Concept; 1.1.3. The Counting Process; CHAPTER 1.2. THE NATURAL OPERATIONS WITH THE NATURAL NUMBERS; 1.2.1. Addition Considered as Extended Counting; 1.2.2. Multiplication Considered as a Special Case of Extended Addition; 1.2.3. Exponentiation Considered as a Special Case of Extended Multiplication; 1.2.4. Binary Operations
  • CHAPTER 1.3. THE NATURAL LAWS FOR THE NATURAL OPERATIONS1.3.1. The Closure Laws; 1.3.2. The Commutative Laws; 1.3.3. The Associative Laws; 1.3.4. The Distributive Law; 1.3.5. Identity Elements; 1.3.6. Use of Sentences in Describing Natural Laws and Other Relations; CHAPTER 1.4. THE INVERSE OPERATIONS AND CONVERGENCE; THE NUMBER SYSTEMS GENERATED BY THESE OPERATIONS; 1.4.1. The Nature of an Inverse Operation; 1.4.2. Subtraction; the Integers; 1.4.3. Division; the Rational Numbers; 1.4.4. Convergence; the Real Numbers; 1.4.5. Root Extraction and the Determination of Logarithms
  • The Complex Numbers1.4.6. Graphical Comparison of the Number Systems; CHAPTER 1.5. CLASSIFICATION OF THE NUMBER SYSTEMS AS ABSTRACT SYSTEMS; 1.5.1. Inverse Elements; 1.5.2. Abstract Systems; 1.5.3. Examples of Groups; 1.5.4. Examples of Fields; CHAPTER 1.6. SUMMARY; 1.6.1. Summary of the Summary; PART II: Computational Algorithms; CHAPTER 2.1. COMPUTATION WITH THE NATURAL NUMBERS; 2.1.1. The Addition Algorithm; 2.1.2. The Multiplication Algorithm; 2.1.3. The Subtraction Algorithm; 2.1.4. The Division Algorithm; 2.1.5. Adaptation from Natural Numbers to Integers
  • 2.1.6. Algorithms for Greatest Common Divisor2.1.7. Algorithm for Least Common Multiple; 2.1.8. Algorithms for Change of Base; CHAPTER 2.2. COMPUTATION WITH RATIONAL NUMBERS; 2.2.1. Multiplication; 2.2.2. Addition; 2.2.3. Subtraction; 2.2.4. Division; CHAPTER 2.3. COMPUTATION WITH REAL NUMBERS; DECIMAL REPRESENTATION; 2.3.1. Addition; 2.3.2. Multiplication; 2.3.3. Subtraction; 2.3.4. Division; 2.3.5. Remarks on Precise Computation with Irrational Numbers; 2.3.6. Square Root Extraction; 2.3.7. Rounding Off; Significant Digits; CHAPTER 2.4. COMPUTATION WITH THE COMPLEX NUMBERS
  • 2.4.1. Numerical Computation2.4.2. Graphical Representation of Complex Sums, Differences, Products, Quotients, Powers and Roots; INDEX; ELEMENTARY VECTORS; MODERN MATHEMATICS IN SECONDARYSCHOOLS

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