This text helps the student complete the transition from purely manipulative to rigorous mathematics. It spells out in all detail what is often treated too briefly or vaguely because of lack of time or space. It can be used either for supplementary reading or as a half-year course. It is self-contained, though usually the student will have had elementary calculus before starting it. Without the “starred” sections and problems, it can be (and was) taught even to freshmen. The three chapters are fairly independent and, with small adjustments, may be taught in arbitrary order. The chapter on n-space “imitates” the geometry of lines and planes in 3-space, and ensures a thorough review of the latter, for students who may not have had it. A wealth of problems, some simple, some challenging, follow almost every section.

Contents

• Chapter 1. Some Set Theoretical Notions
• Chapter 2. The Real Number System
• Chapter 3. The Geometry of n Dimensions. Vector Spaces

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