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Granpa Granpa 11 June 2019
0

Advanced mathematics

This article is a continuation of Intermediate mathematics

  • 1 Equivalence relation
    • 1.1 Modular arithmetic
  • 2 See also
  • 3 References

From Wikipedia:Equivalence relation:

An Equivalence relation is a generalization of the concept of "is equal to". It has the following properites:

  • a}} (reflexive property),
  • if b}} then a}} (symmetric property), and
  • if b}} and c}} then c}} (transitive property).

As a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.

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From Wikipedia:Modular arithmetic :

Modular arithmetic can be handled mathe…




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Granpa Granpa 11 June 2019
0

Elementary mathematics


  • 1 Positive numbers
    • 1.1 Addition
  • 2 Further reading
  • 3 References


See



  • Introductory mathematics
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Granpa Granpa 11 June 2019
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Introductory mathematics


This article is a continuation of Elementary mathematics


Believe it or not the basis of all of mathematics is nothing more than the simple function.

Next(0)=1
Next(1)=2
Next(2)=3
Next(3)=4

This defines the . Natural numbers are those used for counting.

These have the very convenient property of being . That means that if a
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Granpa Granpa 11 September 2018
0

Clifford algebra

  • 1 Rules

Clifford algebra is a type of algebra characterized by the geometric product of scalars, vectors, bivectors, trivectors...etc.

Just as a vector has length so a bivector has area and a trivector has volume.

Just as a vector has direction so a bivector has orientation. In three dimensions a trivector has only one possible orientation and is therefore a pseudoscalar. But in four dimensions a trivector becomes a pseudovector and the quadvector becomes the pseudoscalar.


All the properties of Clifford algebra derive from a few simple rules.

Let

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Granpa Granpa 21 October 2017
1

Intermediate mathematics

  • 1 See also
  • 2 External links
  • 3 References

Science is a wonderful thing if one does not have to earn one's living at it. One should earn one's living by work of which one is sure one is capable. Only when we do not have to be accountable to anybody can we find joy in scientific endeavor. -Albert Einstein

This article is a continuation of Introductory mathematics

It has been known since the time of that all of geometry can be derived from a handful of objects (points, lines...), a few actions on those objects, and a small number of . Every field of science likewise can be reduced to a small set of objects, actions, and rules. Math itself is not a single field but rather a constellation of related fields. One way in which new fields are created is by …

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