es

We introduce a wide range of fundamental mathematical concepts and structures in this chapter on foundation of mathematics. Understanding their fundamental opera- tions and attributes, we start with sets and functions. We then delve into the metric space universe, which offers a framework for comprehending distance and conver- gence. Moving on to algebraic structures, we examine the distinctive qualities and illustrative instances of groups, rings, and fields. Polynomial rings and their essential properties are introduced, as are matrices and their rank, trace, and determinant, all of which are highlighted as they have vital roles in the coming chapters. The latter sections of the chapter provide an overview of Euclidean space and demonstrate how to solve systems of linear equations using techniques like Cramer’s rule, LU decom- position, Gauss elimination, etc. These fundamental ideas in mathematics serve as the building blocks for more complex mathematical research and have numerous applications in science and engineering.

 

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