1. From Arithmetic to Algebra

  1. Ulrich L. Rohde1,2,
  2. G. C. Jain3,
  3. Ajay K. Poddar2 and
  4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch1

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) From Arithmetic to Algebra, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch1

Author Information

  1. 1

    BTU Cottbus, Germany

  2. 2

    Synergy Microwave Corporation, Paterson, NJ, USA

  3. 3

    Defense Research & Development Organization, Maharashtra, India

  4. 4

    Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

Publication History

  1. Published Online: 28 DEC 2011
  2. Published Print: 9 DEC 2011

ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

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Keywords:

  • arithmetic to algebra, solution of equations and unknowns;
  • algebra, set of rules, best language for thinking about laws;
  • notation of arithmetic and algebra, an important difference

Summary

This chapter contains sections titled:

  • Introduction

  • The Set of Whole Numbers

  • The Set of Integers

  • The Set of Rational Numbers

  • The Set of Irrational Numbers

  • The Set of Real Numbers

  • Even and Odd Numbers

  • Factors

  • Prime and Composite Numbers

  • Coprime Numbers

  • Highest Common Factor (H.C.F.)

  • Least Common Multiple (L.C.M.)

  • The Language of Algebra

  • Algebra as a Language for Thinking

  • Induction

  • An Important Result: The Number of Primes is Infinite

  • Algebra as the Shorthand of Mathematics

  • Notations in Algebra

  • Expressions and Identities in Algebra

  • Operations Involving Negative Numbers

  • Division by Zero