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Algebra is not just about numbers. It can be about diagrams or knots or whatever: sets where the elements have operations that fit certain axioms.
by theaeolist 13y ago
Algebra is not just about numbers. It can be about diagrams or knots or whatever: sets where the elements have operations that fit certain axioms.
- cpa 13y agoWell, he only talks about school algebra. I'm not familiar with the US high school curriculum but I doubt it goes much beyond polynomials… FTA (3rd paragraph): > (I should stress that in this article I’m focusing on school arithmetic and school algebra. Professional mathematicians use both terms to mean something far more general.)
- Someone 13y agoThat's almost clear from the question. If this was about higher math, the question would likely have been "What is an algebra?", as "What is algebra?" has the simple but almost content-free answer "The study of algebras." (http://mathworld.wolfram.com/Algebra.html http://mathworld.wolfram.com/Algebra.html)
- dominotw 13y agoHe is not talking about abstract algebra.
- agumonkey 13y agoIt should be said that way, as a choice and not an arbitrary concept tied to numbers. For pupils so many why's can rise from coupling the properties of what we call algebra to a projection on numbers.
- gizmo686 13y agoTake a knot k, and call it a number. To that point, does anyone know if there is a formal definition of what it means to be a number? I know we have number systems in which the Integer-like numbers do not behave the same as the Integers, where the numbers of that system are defined completely independently of the Reals.
- ds9 13y agoOh yes, some outstanding thinkers have gone into mind boggling depth on the meanings of fundamental maths concepts. This started getting a proper treatment in the early 20c. (see https://en.wikipedia.org/wiki/Principia_Mathematica https://en.wikipedia.org/wiki/Principia_Mathematica ) and presumably has come a long way since then. Edit: Of course one has to take a different approach for pedagogical purposes.
- mturmon 13y agoThe author, a fellow of the AMS, is of course aware of this. He's talking about high school algebra, to a general audience, and says so in the OP.