Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Derived C∞C^{\infty}-Geometry I: Foundations

This work is the first in a series laying the foundations of derived geometry in the $C^{\infty}$ setting, and providing tools for the construction and study of moduli spaces of solutions of Partial Differential Equations that arise in differential geometry and mathematical physics. To advertise the advantages of such a theory, we start with a detailed introduction to derived $C^{\infty}$-geometry in the context of symplectic topology and compare and contrast with Kuranishi space theory. In the body of this work, we avail ourselves of Lurie's extensive work on abstract structured spaces to define $\infty$-categories of derived $C^{\infty}$-ring and $C^{\infty}$-schemes and derived $C^{\infty}$-rings and $C^{\infty}$-schemes with corners via a universal property in a suitable $(\infty,2)$-category of $\infty$-categories with respect to the ordinary categories of manifolds and manifolds with corners (with morphisms the $b$-maps of Melrose in the latter case), and prove many basic structural features about them. Along the way, we establish some derived flatness results for derived $C^{\infty}$-rings of independent interest.Comment: 203 pages; comments welcom

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Álgebra y Geometría : Una manera de pensar

El presente material es producto de la experiencia en cátedras del área Álgebra y cursos de ingreso y la previa elaboración de apuntes para Álgebra, Cálculo Numérico y Geometría Analítica, Matemática I. Recopila, unifica, amplía y mejora el material existente. Presenta todos los temas de esas asignaturas, con una base teórica sólida, práctica, aplicaciones y motivaciones, integrando y relacionando contenidos. Algunos temas son comunes y de igual nivel en las tres. Otros difieren en profundidad y hay subtemas abordados solo en alguna de ellas. Por ello, sugerimos al estudiante que utilice el libro con diferente recorrido de acuerdo a su interés. Es texto de las materias mencionadas y puede servir de consulta o referencia para las asignaturas Probabilidades, Estadística e inicio para otras del área Álgebra.Facultad de Ciencias Exacta