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A Chinese abacus.
Wiskunde word algemeen gedefinieer as die studie van patrone in strukture, verandering en ruimte; meer informeel gestel, kan 'n mens sê dat dit die studie van 'getalle en syfers’ is. Uit die formele oogpunt gesien is dit die ondersoek van aksiomaties gedefinieerde abstrakte strukture deur gebruik te maak van simboliese logika en wiskundige notasie; ander uitgangspunte word in die Filosofie van wiskunde bespreek. Wiskunde kan gesien word as 'n eenvoudige uitbreiding van gesproke en geskrewe tale, met 'n uiters presies gedefinieerde woordeskat en taalstruktuur met die doelwit om fisiese en konsepsuele vergelykings te ondersoek.

Alhoewel wiskunde self nie gewoonlik beskou word as 'n natuurwetenskap nie, het die spesifieke strukture wat deur wiskundiges ondersoek word dikwels hulle oorsprong in die natuurwetenskappe en meer algemeen in fisika. Wiskundiges definieer en ondersoek egter ook strukture wat suiwer van interne belang tot wiskunde as vakgebied is, omdat die strukture sodoende verkry, 'n verenigde veralgemening vir verskeie vertakkinge kan verskaf of 'n nuttige gereedskap kan wees vir algemene berekeninge. Laastens bestudeer baie wiskundiges gebiede vir suiwer estetiese redes en beskou hulle wiskunde as 'n kunsvorm eerder as 'n praktiese of toegepaste wetenskap. Gauss het na die vak verwys as die `Koningin van die Wetenskappe’. Einstein het opgemerk dat "hoeveel die wette van wiskunde na die werklikheid verwys is onseker, en sover hulle seker is verwys hulle nie na die werklikheid nie".

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Formal sciences – Branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules.

  • Mathematics – The study of quantity, structure, space, and change. Mathematicians seek out patterns,[1][2] and formulate new conjectures.
    • Arithmetic – The study of quantity, especially as the result of combining numbers.
    • Algebra – The study of the rules of operations and relations, and the constructions and concepts arising from them.
    • Calculus – Calculus is the study of change,[3] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
    • Combinatorics – The study of finite or countable discrete structures.
    • Discrete mathematics – The study of mathematical structures that are fundamentally discrete rather than continuous.
    • Geometry – The study of shape, size, relative position of figures, and the properties of space.
    • Trigonometry – The study of triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.
  • Logic – The study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science.
  • Mathematical sciences – academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.
    • Statistics – The study of the collection, organization, and interpretation of data.[4][5]
      • Probability – way of expressing knowledge or belief that an event will occur or has occurred. The concept has an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
      • Regression analysis – Any technique for learning about the relationship between one or more dependent variables Y and one or more independent variables X.
References
  1. Steen, L.A. (April 29, 1988). The Science of Patterns Science, 240: 611–616. and summarized at Association for Supervision and Curriculum Development, ascd.org
  2. Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN 978-0-7167-5047-5
  3. Latorre, Donald R.; Kenelly, John W.; Reed, Iris B.; Biggers, Sherry (2007), Calculus Concepts: An Applied Approach to the Mathematics of Change, Cengage Learning, p. 2, ISBN 0-618-78981-2, http://books.google.com/books?id=bQhX-3k0LS8C , Chapter 1, p 2
  4. Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
  5. The Free Online Dictionary

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