Introductory Concepts for Abstract Mathematics (Relié)

Kenneth-E Hummel

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  • Chapman & Hall/crc

  • Paru le : 28/06/2000
  • 1 million de livres à découvrir
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A gap has long existed between basic calculus studies and abstract algebra and real analysis. Over the years, the focus of calculus instruction has become ever more computational, leaving those interested in higher mathematics somewhat ill prepared for the more advanced, abstract work which requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics will help students bridge the gap between calculus and the more advanced mathematical studies. It teaches how to deal effectively with abstract ideas, comprehend the logical structure of proofs, and write mathematics using conventional terminology in an effective, logical, and comprehensible way. Features • Provides die foundation required for advanced mathematical studies by including a thorough development of sets, relations, and functions. • Imparts other important concepts, such as the development of real numbers, least upper bounds, and concepts related to, transfinite cardinal arithmetic. • Teaches the writing of mathematics and the construction of proofs.
  • LOGIC AND PROOF
    • Logic and Propositional Calculus
    • Tautologies and Validity
    • Quantifiers and Predicates
    • Techniques of Derivation and Rules of Inference
    • Informal Proof and Theorem-Proving Techniques
    • On Theorem Proving and Writing Proofs
    • Mathematical Induction
  • SETS
    • Sets and Set Operations
    • Set Union, Intersection, and Complement
    • Generalized Union and Intersection
  • FUNCTIONS AND RELATIONS
    • Cartesian Products
    • Relations
    • Partitions
    • Functions
    • Composition of Functions
    • Image and Preimage Functions
  • ALGEBRAIC AND ORDER PROPERTIES OF NUMBER SYSTEMS
    • Binary Operations
    • The Systems of Whole and Natural Numbers
    • The System Z of Integers
    • The System Q of Rational Numbers
    • Other Aspects of Order
    • The Real Number System
  • TRANSFINITE CARDINAL NUMBERS
    • Finite and Infinite Sets
    • Denumerable and Countable Sets
    • Uncountable Sets
    • Transfinite Cardinal Numbers
  • AXIOM OF CHOICE AND ORDINAL NUMBERS
    • Partially Ordered Sets
    • Least Upper Bound and Greatest Lower Bound
    • Axiom of Choice
    • Well Ordered Sets.
  • Date de parution : 28/06/2000
  • Editeur : Chapman & Hall/crc
  • ISBN : 1-58488-134-8
  • EAN : 9781584881346
  • Présentation : Relié
  • Nb. de pages : 332 pages
  • Poids : 0.655 Kg
  • Dimensions : 16,0 cm × 24,1 cm × 2,4 cm

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Introductory Concepts for Abstract Mathematics
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