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The strength of this textbook lies in the careful exposition of mathematical thinking, basic set-theoretic notions, and proof techniques combined with contemporary numerical methods used throughout the book. A basic version of computer programs compatible with the widely used program MatLab, and exercises are provided on a disk included with the book.Warmup * Matrix Operations * Invertible Matrices * Subspaces * Rank and Dimension * Geometry * Determinants-I * Diagonalization * Differential Equations * Hermitian Matrices * Triangular Matrices * Unitary Matrices * Block Diagonalization *...

Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds -- including mathematics, philosophy, linguistics, computer science, and engineering. It features numerous exercises of varying levels of difficulty, many with solutions.
A survey of the propositional calculus is followed by chapters on first-order logic and first-order recursive arithmetic. An examination of the arithmetization of syntax follows, along with a review of the incompleteness theorems and other applications of the Liar Paradox....

The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented $2$-manifold without boundary prove that it is invariant under isotopy and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a $2$-manifold.