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:
    non sort: An
    title: Excursion through Elementary Mathematics, Volume III
    sub title: Discrete Mathematics and Polynomial Algebra
  name:
    name part: Caminha Muniz Neto, Antonio.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 648 p. 24 illus. online resource.
  abstract: This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.
  table of contents: Chapter 01- Elementary Counting Techniques -- Chapter 02- More Counting Techniques -- Chapter 03- Generating Functions -- Chapter 04- Existence of Configurations -- Chapter 05- A Glimpse on Graph Theory -- Chapter 06- Divisibility -- Chapter 07- Diophantine Equations -- Chapter 08- Arithmetic Functions -- Chapter 09- Calculus and Number Theory -- Chapter 10- The Relation of Congruence -- Chapter 11- Congruence Classes -- Chapter 12- Primitive Roots and Quadratic Residues -- Chapter 13- Complex Numbers -- Chapter 14- Polynomials. Chapter 15- Roots of Polynomials -- Cahpter 16- Relations Between Roots and Coefficients -- Chapter 17- Polynomials over R -- Chapter 18- Interpolation of Polynomials -- Chapter 19- On the Factorization of Polynomials -- Chapter 20- Algebraic and Transcendental Numbers -- Chapter 21- Linear Recurrence Relations -- Chapter 22- Hints and Solutions.
  note: by Antonio Caminha Muniz Neto.
  subject:
    topic: Discrete mathematics
  subject:
    topic: Algebra
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Discrete Mathematics
  subject:
    topic: Field Theory and Polynomials
  classification: QA150-272
  classification: 511.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Problem Books in Mathematics
  identifier: 9783319779775
  identifier: https://doi.org/10.1007/978-3-319-77977-5
  record info:
    record creation date: 180417
    record change date: 20191026062243.0
    record identifier: 978-3-319-77977-5