rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Theorems, corollaries, lemmas, and methods of proof
  title info: title
  name:
    name part: Rossi, Richard J.
    role:
      role term: creator
  type of resource: text
  origin info:
    place:
      place term: xx
    place:
      place term: Hoboken, N.J
    publisher: Wiley
    date issued: 2006
    date issued: 9999
    issuance: monographic
  language:
    language term: und
  physical description:
    form: print
  abstract: A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning. Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics. This essential book: * Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs * Reinforces the foundations of calculus and algebra * Explores how to use both a direct and indirect proof to prove a theorem * Presents the basic properties of real numbers * Discusses how to use mathematical induction to prove a theorem * Identifies the different types of theorems * Explains how to write a clear and understandable proof * Covers the basic structure of modern mathematics and the key components of modern mathematics A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs. Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty. Intended as a main text for mathematics courses such as Methods o…
  note: Richard J. Rossi.
  subject:
    topic: Proof theory,Mathematical analysis,Logic, Symbolic and mathematical,Bằng chứng lý thuyết,Phân tích toán học,Logic, tượng trưng và toán học
  subject:
    topic: Foundations,Cơ sở
  classification: 511.36
  classification: R831
  record info:
    record creation date: 210402
    record identifier: CTU_165661