How to Prove It: A Structured Approach - Daniel J. Velleman
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Are you struggling with understanding mathematical proofs? The latest edition of Velleman's renowned text is designed to help students transition from problem-solving to theorem-proving. This comprehensive guide equips students with the necessary techniques to comprehend and construct proofs.
The book commences with fundamental concepts of logic and set theory, providing students with a solid foundation in the language of mathematics and its interpretation. It then systematically breaks down the essential techniques for proof construction, demonstrating how intricate proofs are developed from smaller steps. Detailed 'scratch work' sections unveil the inner workings of proofs related to natural numbers, relations, functions, and infinite sets.
This new edition features over 200 additional exercises, selected solutions, and an introduction to Proof Designer software, allowing students to practice constructing their own proofs. No prior knowledge beyond standard high school mathematics is required, making this book accessible to a wide audience interested in logic and proofs, including computer scientists, philosophers, linguists, and mathematicians.
