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kathrynag
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What are some applications of abstarct algebra? I have to write a paper and present on a application of abstract algebra and am looking for topic ideas.
VKint said:You could do something like an enumeration of the allowed configurations of the Rubik's cube. The problem is actually quite nice, in that the solution isn't overly complicated and the answer, which characterizes allowed configurations in terms of the signatures of various permutations of sub-cubes, is fairly easy to state.
If you're looking specifically for interesting applications to combinatorics, you could also try starting with Burnside's Lemma or the Redfield-Polya theorem, both of which are truly beautiful (and powerful) results in enumerative combinatorics that tell you how to count states of things modulo some symmetry group. (For example, using R-P, you can answer questions like "In how many distinguishable ways can I paint the faces of an icosahedron using six different colors, such that exactly 4 of the faces are red?")
kathrynag said:What are some applications of abstarct algebra? I have to write a paper and present on a application of abstract algebra and am looking for topic ideas.
Abstract Algebra is a branch of mathematics that studies algebraic structures and their properties. It focuses on abstract concepts and generalizations rather than specific numerical calculations.
Abstract Algebra has numerous applications in fields such as computer science, physics, engineering, and cryptography. It is used to develop efficient algorithms, model physical systems, design error-correcting codes, and secure communication systems.
The basic algebraic structures studied in Abstract Algebra are groups, rings, and fields. These structures have operations defined on them, such as addition, multiplication, and composition, and satisfy certain axioms and properties.
Traditional algebra focuses on solving equations and manipulating specific numbers, while Abstract Algebra deals with abstract concepts and structures. It also studies more general algebraic properties and theorems that apply to multiple algebraic systems.
Some key theorems and concepts in Abstract Algebra include the fundamental theorem of algebra, Lagrange's theorem, isomorphism, subgroups, and homomorphisms. These concepts provide a deeper understanding of the structures and properties of algebraic systems.