Classical Vector Algebra

Every physicist, engineer, and certainly a mathematician, would undoubtedly agree that vector algebra is a part of basic mathematical instruments packed in their toolbox.

Classic Vector Algebra should be viewed as a prerequisite, an introduction, for other mathematical courses dealing with vectors, following typical form and appropriate rigor of more advanced mathematics texts.

Vector algebra discussed in this book briefly addresses vectors in general 3-dimensional Euclidian space, and then, in more detail, vectors in Cartesian □□3 space. These vectors are easier to visualize, their operational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this could also serve as a good intuition build up for more abstract structures of □□-dimensional vector spaces.

Definition, theorem, proof, corollary, example, etc. is not useless formalism, even in an introductory treatise -- it is the way mathematical thinking has to be structured. In other words, introduction and rigor should not exclude one another.

The material in this book is not difficult nor easy. The text is a serious exposition of a part of mathematics students need to master in order to be proficient in their field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples/exercises.

每一位物理學家、工程師，當然還有數學家，都毫無疑問地同意向量代數是他們工具箱中的基本數學工具之一。

經典向量代數應該被視為其他與向量相關的數學課程的先修課程，遵循更高級數學教材的典型形式和適當嚴謹性的介紹。

本書中討論的向量代數簡要涉及一般三維歐幾里得空間中的向量，然後更詳細地討論笛卡爾三維空間中的向量。這些向量更容易視覺化，它們的操作技巧相對簡單，但對於向量分析的研究是必要的。此外，這也可以作為對更抽象的n維向量空間結構建立良好直覺的基礎。

定義、定理、證明、推論、例子等等在入門論文中並不是無用的形式主義，這是數學思維必須被結構化的方式。換句話說，介紹和嚴謹性不應互相排斥。

本書的內容既不難也不易。這本書是對學生在其領域中熟練掌握所需的數學部分的嚴肅闡述。除了詳細的理論大綱外，本書還包含了數百個相應的例子/練習題。

Vladimir Lepetic is Professor in the Department of Mathematical Sciences, DePaul University. Research interests include mathematical physics, set theory, foundation and philosophy of mathematics.

Vladimir Lepetic 是德保羅大學數學科學系的教授。他的研究興趣包括數學物理、集合論、數學基礎和哲學。