Elementary Mathematics

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The term elementary mathematics (also called elementary mathematics ), in its counterpart to higher mathematics, summarizes those sub-areas of mathematics that deal with so-called elementary mathematical terms and structures, although there is no uniform definition of terms. From a historical perspective, elementary mathematics has a long tradition, can partly be assigned to the area of school mathematics and the elementary area and continues to play a role in individual teacher training courses .

term

Elementary mathematics is characterized by the relatively high level of clarity of the individual contents, whereby experiences from everyday life or physics can also be incorporated. In the second half of the 19th century, the predicate “elementary” was used synonymously for terms such as “basic”, “free of border crossings”, “simple”, “elegant” or “primitive”. Today those contents of elementary mathematics are counted, which deal with "simple basic terms using special methods". It essentially contains basic sentences , statements and axioms as well as trains of thought based on them, some of which are not based on strict, axiomatic proofs , but can be derived with simple logical aids. On the other hand, the elements defined in this way are at the same time quite abstract, as they have the character of structural models such as the representation of vectors by arrows. However, there is no precise definition of the term.

The content of elementary mathematics is dealt with in particular in the context of mathematics lessons, which is why the term is sometimes associated with "school mathematics". Elementary mathematics is also occasionally offered as a university course in connection with a teacher training course for elementary, secondary and secondary schools, in which mathematical content as well as didactic aspects are incorporated, and forms the basis for technical courses, among other things.

history

The history of elementary mathematics is closely linked to the history of mathematics . It includes the writings of the Rhind Papyrus as well as the knowledge of well-known mathematicians and philosophers such as Plato , Aristotle and Euclid . The elements of Euclid, Arithmetica by Diophantos and the arithmetic books of the Middle Ages are considered to be historical writings . Hanfried Lenz also counts the Éléments de mathématique by Nicolas Bourbaki from the 20th century.

Areas

Relevant literature lists the following areas under elementary mathematics, whereby the sorting is sometimes inconsistent:

Fundamental mathematical relationships such as numbers , basic arithmetic operations , fractions , powers and roots , logarithms , series , symmetry , elementary functions and the like are discussed. Furthermore, there are also applied approaches to modeling such as problems from everyday life, for example " compound interest calculation " and entertainment mathematics as well as considerations on combinatorics and probability calculations .

Individual evidence

  1. ↑ Christine Lehmann, Bertram Maurer: Karl Culmann and the graphic statics: Drawing, the language of the engineer . Wilhelm Ernst & Sohn Verlag, Berlin 2006, ISBN 978-3-433-01815-6 , p. 178 .
  2. ↑ Lucienne Félix: Elementary Mathematics in Modern Representation . Volume 2. In: Dieter Rödding (Hrsg.): Logic and basics of mathematics . 2nd Edition. Vieweg Verlag, Braunschweig, ISBN 3-528-08174-0 , p. V-VI .
  3. ↑ Hanfried Lenz: Fundamentals of elementary mathematics . 3. Edition. Deutscher Verlag der Wissenschaften, Berlin 1975, p. 15 .
  4. ^ School mathematics from a higher point of view. (PDF; 27 kB) Accessed August 3, 2013 .
  5. ↑ Elementary Mathematics. (PDF; 182 kB) Retrieved July 11, 2013 .
  6. ↑ Master of Education Elementary Mathematics. (No longer available online.) Archived from the original on June 10, 2013 ; Retrieved August 3, 2013 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.uni-oldenburg.de
  7. ↑ Compact course elementary mathematics. (PDF; 2.3 MB) Retrieved August 3, 2013 .
  8. ↑ Johannes Tropfke: History of Elementary Mathematics . 4th edition. tape 1 . Walter de Gruyter, Berlin 1980, ISBN 3-11-004893-0 , p. 513-660 .
  9. ↑ Hanfried Lenz: Fundamentals of elementary mathematics . 3. Edition. Deutscher Verlag der Wissenschaften, Berlin 1975, p. 15 .

literature

  • Pawel Sergejewitsch Alexandrow , Aleksej I. Markusevic , Helmut Limberg, Karl-Heinz Rupp: Encyclopedia of Elementary Mathematics . Deutscher Verlag der Wissenschaft, Berlin 1954 (work in three volumes).
  • Naturforschende Gesellschaft in Basel (ed.): The collected works of the mathematician and physicist of the Bernoulli family : Volume 2: Elementary mathematics . Birkhäuser Verlag, Basel 1989, ISBN 3-7643-1891-0 (Italian, with English translation).
  • Felix Klein : Elementary Mathematics from a Higher Point of View . Julius Springer Verlag, Berlin 1928 (work in three volumes).
  • Johannes Tropfke : History of elementary mathematics in a systematic representation . Walter de Gruyter , Berlin (first two volumes available online 1902 and 1903 , then seven volumes 1921-24, 3rd edition in four volumes 1930 to 1940, 3rd edition 1980 in three volumes, edited by Kurt Vogel , Helmuth Gericke , Karin Reich among others).

Web links

Wikibooks: Math for Non-Freaks: Fundamentals of Math  - Learning and Teaching Materials