Eduardo Sáenz-de-Cabezón – författare

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

"¿Quién leería un libro sobre matemáticas sin que le obliguen?", se preguntará el lector de este libro. Porque al leer sobre ellas se corren varios riesgos… Tal vez cambiemos nuestra idea sobre las matemáticas, con las que hemos vivido tan cómodamente todo este tiempo, y es posible que terminen por gustarnos. Este libro te mostrará que las matemáticas no son tan odiosas como aparentan; en ellas interviene la creatividad, la intuición, el cálculo, la imaginación, la técnica. Son una oportunidad de disfrutar de la realidad de una forma distinta. Porque, lo queramos o no, todos llevamos un matemático en nuestro interior, que tal vez se asustó en la escuela y permanece oculto en un rincón. Inteligencia matemática es la oportunidad perfecta de experimentar por nosotros mismos las formas de razonar de los matemáticos. Tomemos lápiz y papel, garabateemos soluciones, dibujemos y emborronemos, y encontraremos la forma perfecta de leer este libro.

Emmy Noether es la matemática más importante de la historia y una de las científicas más destacadas de todos los tiempos. A pesar de ello, continúa siendo una desconocida para casi todos. Mujer, judía y matemática en la Alemania del primer tercio del siglo XX, superó todas las barreras que la vida y la sociedad le impusieron.A partir de una aproximación cercana, pero rigurosa, El árbol de Emmy nos descubre la vida de una personalidad excepcional, a la que Albert Einstein consideraba un genio, y nos introduce en la historia de muchas otras mujeres matemáticas, en un ámbito que fue y sigue siendo en gran medida masculino.Cada capítulo se cierra con hilos de Twitter que amplían la lectura y enriquecen la mirada de los lectores. Han corrido a cargo de Enrique Borja (@Cuent_Cuanticos), Clara Grima (@ClaraGrima) y Alberto Márquez (@twalmar).