The Elements of Advanced Mathematics - Couverture rigide

Krantz, Steven G.

 
9781584883036: The Elements of Advanced Mathematics
Couverture rigide
ISBN 10 : 1584883030 ISBN 13 : 9781584883036
Editeur : CRC Press Inc, 2002

Synopsis

The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs.

New in the Second Edition:

  • Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science
  • A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor set
  • Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection
  • Streamlined treatment of non-Euclidean geometry
  • Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations
  • More thorough treatment of the Axiom of Choice and its equivalents
  • Additional material on Russell's paradox and related ideas
  • Expanded treatment of group theory that helps students grasp the axiomatic method
  • A wealth of added exercises

    • Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

    Présentation de l'éditeur

    The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs.

    New in the Second Edition:

  • Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science
  • A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor set
  • Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection
  • Streamlined treatment of non-Euclidean geometry
  • Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations
  • More thorough treatment of the Axiom of Choice and its equivalents
  • Additional material on Russell's paradox and related ideas
  • Expanded treatment of group theory that helps students grasp the axiomatic method
  • A wealth of added exercises

    • Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

    Éditeur
    CRC Press Inc
    Date d'édition
    2002
    Langue
    anglais
    ISBN 10 
    1584883030
    ISBN 13 
    9781584883036
    Reliure
    Relié
    Numéro d'édition
    2
    Nombre de pages
    232
    Coordonnées du fabricant
    non disponible
    Personne responsable
    non disponible