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: From counting to computing
    sub title: ideas for mathematics education in information age
  name:
    name part: Abramovich, Sergei
    role:
      role term: creator
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  genre: elektronické knihy
  genre: electronic books
  origin info:
    place:
      place term: enk
    date issued: 2025
    copyright date: 2025
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (276 pages)
  abstract: From Counting to Computing demonstrates the powerful integration of formal mathematical reasoning, hands-on educational experiments, and digital computation to solve problems. It focuses on numeric tables shaped as squares, equilateral and isosceles triangles, offering ample opportunities for algebraic generalization in the digital age. Activities are grounded in addition and multiplication tables, polygonal numbers, and Pascal's triangle. Based on the idea that counting objects arranged in geometric shapes leads to the development of numeric patterns, this book extends this concept to digital computing. Using technology-immune/technology-enabled didactical framework, it blends formal reasoning with digital computation in problem solving and provides a conceptual shortcut to achieving mathematically significant computational outcomes. From Counting to Computing covers classic topics from arithmetic, number theory, combinatorics, and probability theory. Many historical and cultural origins of mathematical concepts are highlighted, featuring figures like Pythagoras, Aristotle, Heron of Alexandria, Theon, Fibonacci, Gersonides, Pacioli, Cardano, Galilei, Kepler, Descartes, Fermat, Pascal, Spinoza, Leibniz, Jacob Bernoulli, Binet, de Moivre, Lamé, and Lucas. The final chapter includes problems on the proof of divisibility of integer variable polynomials, motivated by digital computations. Ideal for mathematics teacher education programs and discrete mathematics courses, this book showcases the use of simple algorithms and tools like spreadsheets, Wolfram Alpha, Maple, and Graphing Calculator to achieve sophisticated computational results.
  table of contents: Chapter 1. From concepts to conceptual shortcuts to the use of technology -- Chapter 2. Exploring the addition and the multiplication tables -- Chapter 3. Exploring equilateral triangles filled with integers -- Chapter 4. Exploring isosceles triangles filled with integers -- Chapter 5. Exploring squares filled with integers -- Chapter 6. Pascal's triangle as a bridge from combinatorics to probability -- Chapter 7. From pascal's triangle to fibonacci-like polynomials -- Chapter 8. Problems motivated by digital computing.
  note: Sergei Abramovich.
  note: Includes index.
  note: Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty
  note: Includes bibliographical references.
  subject:
    topic: Mathematics
    topic: Study and teaching
  subject:
    topic: Education
    topic: Teaching
    topic: Subjects
    topic: Mathematics
  subject:
    topic: Teaching of a specific subject
  subject:
    topic: Teaching of reading, writing and numeracy
  subject:
    topic: Educational: Mathematics and numeracy
  classification: 510.71
  classification: 510
  identifier: 9781837089000
  identifier: https://proxy.k.utb.cz/login
  access condition: Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty
  record info:
    record content source: UtOrBLW
    record creation date: 250903
    record change date: 20250903182045.0
    record identifier: em-9781837089000
    language of cataloging:
      language term: eng