Proof Patterns
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Proof Patterns
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.
Proof and Knowledge in Mathematics
Distinguished contributors tackle the main problem that arizes when considering an epistemology for mathematics, the nature and sources of mathematical justification.
Fundamentals of Software Engineering
This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Fundamentals of Software Engineering, FSEN 2019, held in Tehran, Iran, in May 2019. The 14 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 47 submissions. The topics of interest in FSEN span over all aspects of formal methods, especially those related to advancing the application of formal methods in the software industry and promoting their integration with practical engineering techniques. The papers are organized in topical sections on agent based systems, theorem proving, learning, verification, distributed algorithms, and program analysis.