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  2. Band diagram - Wikipedia

    en.wikipedia.org/wiki/Band_diagram

    Band diagram for Schottky barrier at equilibrium Band diagram for semiconductor heterojunction at equilibrium. In solid-state physics of semiconductors, a band diagram is a diagram plotting various key electron energy levels (Fermi level and nearby energy band edges) as a function of some spatial dimension, which is often denoted x. [1]

  3. Template:Band structure filling diagram - Wikipedia

    en.wikipedia.org/wiki/Template:Band_structure...

    This template's documentation is missing, inadequate, or does not accurately describe its functionality or the parameters in its code. Please help to expand and improve it . Editors can experiment in this template's sandbox ( create | mirror ) and testcases ( create ) pages.

  4. Representation theory - Wikipedia

    en.wikipedia.org/wiki/Representation_theory

    Representation theory is a useful method because it reduces problems in abstract algebra to problems in linear algebra, a subject that is well understood. [ 5 ] [ 6 ] Representations of more abstract objects in terms of familiar linear algebra can elucidate properties and simplify calculations within more abstract theories.

  5. Free object - Wikipedia

    en.wikipedia.org/wiki/Free_object

    In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.

  6. Abstract algebra - Wikipedia

    en.wikipedia.org/wiki/Abstract_algebra

    In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups , rings , fields , modules , vector spaces , lattices , and algebras over a field .

  7. Lists of mathematics topics - Wikipedia

    en.wikipedia.org/wiki/Lists_of_mathematics_topics

    The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference ...

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  9. Cycle graph (algebra) - Wikipedia

    en.wikipedia.org/wiki/Cycle_graph_(algebra)

    In group theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are particularly useful in visualizing the structure of small finite groups .

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