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Every physicist and engineer, and certainly every mathematician, would undoubtedly agree that vector algebra is one of the basic mathematical instruments in their toolbox.
Classical Vector Algebra should be viewed as a prerequisite for, and an intro¬duction to, other mathematical courses dealing with vectors, and it follows the typical form and appropriate rigor of more advanced mathematics texts.
The vector algebra discussed in this book briefly addresses vectors in gen¬eral 3- dimensional Euclidean space, and then, in more detail, looks at vectors in Cartesian 𝐑3 space. These vectors are easier to visualize and their oper¬ational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this book could serve as a good way to build up intuitive knowledge for more abstract structures of 𝑛- dimensional vector spaces.
Definitions, theorems, proofs, corollaries, examples, and so on are not useless formalism, even in an introductory treatise – they are the way mathematical thinking has to be structured. In other words, an “introduction” and “rigor” are not mutually exclusive.
The material in this book is neither difficult nor easy. The text is a serious exposition of a part of mathematics that students need to master in order to be proficient in the field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples and exercises.