Introduction to Modern Mathematics
eBook - PDF

Introduction to Modern Mathematics

  1. 352 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Introduction to Modern Mathematics

Book details
Table of contents
Citations

About This Book

Introduction to Modern Mathematics focuses on the operations, principles, and methodologies involved in modern mathematics. The monograph first tackles the algebra of sets, natural numbers, and functions. Discussions focus on groups of transformations, composition of functions, an axiomatic approach to natural numbers, intersection of sets, axioms of the algebra of sets, fields of sets, prepositional functions of one variable, and difference of sets. The text then takes a look at generalized unions and intersections of sets, Cartesian products of sets, and equivalence relations. The book ponders on powers of sets, ordered sets, and linearly ordered sets. Topics include isomorphism of linearly ordered sets, dense linear ordering, maximal and minimal elements, quasi-ordering relations, inequalities for cardinal numbers, sets of the power of the continuum, and Cantor's theorem. The manuscript then examines elementary concepts of abstract algebras, functional calculus and its applications in mathematical proofs, and propositional calculus and its applications in mathematical proofs. The publication is a valuable reference for mathematicians and researchers interested in modern mathematics.

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Yes, you can access Introduction to Modern Mathematics by Helena Rasiowa in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
North Holland
Year
2014
ISBN
9781483274720
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. Introduction to Modern Mathematics
  3. Copyright Page
  4. Table of Contents
  5. FOREWORD
  6. CHAPTER I. THE ALGEBRA OF SETS
  7. CHAPTER II: NATURAL NUMBERS. PROOFS BY INDUCTION
  8. CHAPTER III. FUNCTIONS
  9. CHAPTER IV. GENERALIZED UNIONS AND INTERSECTIONS OF SETS
  10. CHAPTER V. CARTESIAN PRODUCTS OF SETS. RELATIONS. FUNCTIONS AS RELATIONS
  11. CHAPTER VI. GENERALIZED PRODUCTS. m-ARY RELATIONS. FUNCTIONS OF SEVERAL VARIABLES. IMAGES AND INVERSE IMAGES UNDER A FUNCTION
  12. CHAPTER VII. EQUIVALENCE RELATIONS
  13. CHAPTER VIII. POWERS OF SETS
  14. CHAPTER IX. ORDERED SETS
  15. CHAPTER X. LINEARLY ORDERED SETS
  16. CHAPTER XI. WELL-ORDERED SETS
  17. CHAPTER XII. THE PROPOSITIONAL CALCULUS AND ITS APPLICATIONS IN MATHEMATICAL PROOFS
  18. CHAPTER XIII. THE FUNCTIONAL CALCULUS AND ITS APPLICATIONS IN MATHEMATICAL PROOFS
  19. CHAPTER XIV. ELEMENTARY CONCEPTS OF ABSTRACT ALGEBRAS
  20. LIST OF IMPORTANT SYMBOLS
  21. AUTHOR INDEX
  22. SUBJECT INDEX