Our experience has led us to believe that the remark above, thugh contradictory, expresses the frustration many students feel as they pass from beginning calculus to a more rigorous level of mathematics. This book developed from a series of lecture nots for a course at Central Michigan University that was designed to address this lament. The text is intended to bridge the gap between calculus and advabced courses in at least three ways. First, it provides a firm foundation in the major ideas needed for continued work. Second, it guides students to think and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Finally, we present introductions to modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics.
Chapter 1. Logic and Proofs
Chapter 2. Set Theory
Chapter 3. Relations
Chapter 4. Functions
Chapter 5. Cardinality
Chapter 6. Concepts of Algebra
Chapter 7. Concepts of Analysis