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Introduction To Mathematical Thinking & Writing
The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis.
Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.
Notation and Assumptions; Section I: Foundations of Logic and Proof Writing; Ch 1. Logic; Ch 2. Beginner-Level Proofs; Ch. 3 Functions; Section II: Basic Principles of Analysis; Ch 4. The Real Numbers; Ch 5. Functions of a Real Variable; Section III: Basic Principles of Aglebra; Ch 6. Groups; Ch 7. Rings; Index