Conceptual Mathematics
Book (italiano):
Emerging originally from the study of the relationship between geometry and algebra, the concept of category has been increasingly employed in all branches of mathematics, especially in studies where the relationship between different branches is important. While the categorical concepts are latent in elementary mathematics and making them more explicit helps in going beyond elementary algebra into more advanced mathematics, they are generally accessible only through graduate-level textbooks because the available examples involved topics such as modules and topological spaces. In order to make the categorical concepts accessible to any interested high-school student, the authors (both of the state U. of New York at Buffalo) here develop the categorical concepts from the concepts of directed graph and of discrete dynamical system, showing how their features are shared by other categories that are more continuous, such as those whose maps are described by partial differential equations. For this second edition they have provided a more detailed discussion of the links between the elementary categorical material and more advanced applications, introducing the notion of connected component, which is fundamental to the qualitative leaps studied in elementary graph theory and advanced topology. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)
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