Diagonalization in Formal Mathematics

In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.

Advanced undergraduates and graduate students in the natural sciences receive a solid foundation in several fields of mathematics with this text. Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions.

As Computer Science progressively matures as an established discipline, it becomes increasingly important to revisit its theoretical foundations, learn the appropriate techniques for answering theory-based questions, and build one’s confidence in implementing this knowledge when building computer applications. Students well-grounded in theory and abstract models of computation can excel in computing’s many application arenas.