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This text helps bridge computationally oriented mathematics with more theoretically oriented mathematics, preparing readers for more advanced courses that require understanding proofs. It covers logic, set theory, axiomatics, number systems, and reading, evaluating, and creating proofs. This third edition includes some of the more modern topics from theoretical computer science, such as the P/NP problem, Boolean algebra, and Church's thesis. Along with new problems and examples, it also illustrates logic in action and discusses topics from the real number system and topology.