Bond and Keane explicate the weather of logical, mathematical argument to clarify the that means and significance of mathematical rigor. With definitions of options at their disposal, scholars research the foundations of logical inference, learn and comprehend proofs of theorems, and write their very own proofs—all whereas changing into conversant in the grammar of arithmetic and its type. additionally, they're going to advance an appreciation of different tools of evidence (contradiction, induction), the worth of an evidence, and the wonderful thing about a sublime argument. The authors emphasize that arithmetic is an ongoing, vivid discipline—its lengthy, interesting background constantly intersects with territory nonetheless uncharted and questions nonetheless short of solutions. The authors’ large history in instructing arithmetic shines via during this balanced, specific, and interesting textual content, designed as a primer for higher-level arithmetic classes. They elegantly reveal strategy and alertness and realize the byproducts of either the achievements and the missteps of prior thinkers. Chapters 1–5 introduce the basics of summary arithmetic and chapters 6–8 follow the guidelines and strategies, putting the sooner fabric in a true context. Readers’ curiosity is constantly piqued by way of transparent reasons, useful examples, dialogue and discovery workouts, and old comments.