Rubik’s Cube: Is there any algebraic function to solve a rubik’s cube? Or which branch of mathematics would help in learning how to solve?
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Rubik's cube is best understood by group theory which is part of abstract algebra. There is no algebraic function but there is a group of transformations on the cube. A group is a set with a binary operation that has a neutral element (doing nothing) and inverse for its elements (reversing an operation) and another property called associativity [imath] a\circ (b\circ c) = (a\circ b) \circ c[/imath]. The group that describes Rubik's cube has [imath] 43,252,003,274,489,856,000 [/imath] many different elements. It is huge and accordingly complex is the mathematics behind it, cp.
en.wikipedia.org
and the links therein.
But before you get frustrated by this specific example, you should figure out the beauty of group theory by investigating simpler examples. Here is a list of smaller groups ...
en.wikipedia.org
... where calculations are easier and the principles and theorems of group theory can be tested.
Group theory plays an important role in crystallography, encryption, and the theory of codes and other fields. They are a basic structure in mathematics. However, it also describes procedures like transforming Rubik's cube, or finding out that there is a group with a mathematically interesting property that has
many elements. But I would start with the observation that the light switch in your room, or the hours on your analog clock build a group before I visited the Monster Group.
Rubik's Cube group - Wikipedia
But before you get frustrated by this specific example, you should figure out the beauty of group theory by investigating simpler examples. Here is a list of smaller groups ...
List of small groups - Wikipedia
Group theory plays an important role in crystallography, encryption, and the theory of codes and other fields. They are a basic structure in mathematics. However, it also describes procedures like transforming Rubik's cube, or finding out that there is a group with a mathematically interesting property that has
808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
many elements. But I would start with the observation that the light switch in your room, or the hours on your analog clock build a group before I visited the Monster Group.