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The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * New chapter on proof by contradiction * New updated proofs * A full range of accessible proofs * Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra * Basic terminology list with definitions at the beginning of the text