Titlebook: Mathematical Structures; From Linear Algebra Joachim Hilgert Textbook 20241st edition The Editor(s) (if applicable) and The Author(s), und

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Modulesbroad that it can form the framework for the relevant functions of almost all central areas of mathematics. On the other hand, the module structure is also so rich that it allows a significant theory that has extremely interesting applications. A key goal of this chapter is to provide convincing evi

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Pattern Recognition that the presented structure theory of modules would be exemplary for algebraic structures. In particular, we address the parallels mentioned in Section . between the constructions of sub- and quotient structures for vector spaces, rings, and modules, as well as the repeatedly mentioned naturality

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Sheavesd to open subsets, e.g., the set of all continuous functions defined on the open subset. In order for such an assignment to be considered local data, the objects assigned to two open sets should be compatible with each other when the open sets intersect. For continuous functions, this is the case si

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Algebraic Varietiesson with submanifolds of real or complex vector spaces. We have obtained examples of such submanifolds as zero sets of differentiable functions, whose derivative on the zero set is everywhere different from zero. If one considers polynomial functions instead of differentiable functions, one can also

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Specialization, Generalization and Unification of Structureslist of well-motivated structures that have not yet been listed in the first two parts. Otherwise, e.g., the absence of . would be inexcusable. Rather, the aim is to convey a sense that the structural considerations of the first two parts allow us to place a multitude of mathematical terms without m

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Joachim HilgertProvides an introduction to the mathematical structures that are of great importance in modern fields such as algebraic geometry.Shows the interplay of elementary structures and discusses details that

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