Buenas! soy estudiante de matemática, quería preguntar si alguien conoce buenos libros de teoría de computación, pero más orientado a fundamentos de las matemáticas que a aplicaciones como tal. Maquinas de Turing, autómatas, todo eso.
Gracias!
Eso! Mis lecturas desde marzo de 2025, que, además, fue cuando comencé a adentrarme en la literatura. Los leí casi todos en mi celular, salvo Los Demonios y Anna Karénina. Acabo de terminar Guerra y Paz (!!!) y probablemente mi siguiente lectura sea Middlemarch o la Inquilina de Wildfell Hall (o terminar Cumbres Borrascosas)!
Opiniones y recomendaciones?
PS: también leí 1984, me olvidé de ponerlo. Lo leí antes de Vida y Destino, y me sorprendió cómo, en Grossman, aparecen muchos elementos que exhibe Orwell en su distopía.
Hi to everyone! I'm not sure if this is the right place to ask, but I figured that on a books subreddit there probably wouldn't be many people who listen to KC, so maybe the KC's-Readers ratio is a bit better here.
I'm looking for book recommendations that evoke a feeling similar to Starless. I know that's an incredibly vague request, but since I can't really put into words what the song makes me feel, I'm hoping those of you who know it will fill in the gaps.
Thanks!
Hi everyone! I'm a first-year undergraduate student and the other day, when I was in a linear algebra office hour, and category theory happened to come up. The professor asked for examples of categories, and I said "graphs" (thinking of a category where the objects are the graphs and the class of morphisms are the graph morphisms). But another student said that graphs were a category with the vertices as objects and the edges as morphisms, and for some reason I think his answer ended up sounding more convincing to the professor. That doesn't seem like a category, but maybe we could modify it a bit so that it satisfies something similar to the axioms of a category. Anyway, here are my questions:
If we consider G/\\\~ to be the set of directed multigraphs whose edges are induced by equivalence relations, could we form a category with the vertices as objects and the edges as morphisms? And if so, what kind of category would it be? Reflexivity gives the identity morphism, and transitivity means that if there is a morphism from A to B and another from B to C, then there is one from A to C (this is not directly a composition, but we could define the composition of edges as paths, and since there is an edge f from A to B and another edge g from B to C, there is a path (composition) that first goes through f and then g). However, the equivalence relation also imposes symmetry, which makes every morphism an isomorphism.
If the above were really a category, could we then form a category whose objects are the graphs belonging to G/\\\~ and whose morphisms are graph morphisms? And this category may be a 2-category?
I've probably said a lot of mathematically incorrect things throughout this post, but I'd like to organize my ideas a bit.
Hi everyone! The other day I was in a linear algebra office hour, and category theory happened to come up. The professor asked for examples of categories, and I said "graphs" (thinking of a category where the objects are the graphs and the class of morphisms are the graph morphisms). But another student said that graphs were a category with the vertices as objects and the edges as morphisms, and for some reason I think his answer ended up sounding more convincing to the professor. That doesn't seem like a category, but maybe we could modify it a bit so that it satisfies something similar to the axioms of a category. Anyway, here are my questions:
If we consider G/\~ to be the set of directed multigraphs whose edges are induced by equivalence relations, could we form a category with the vertices as objects and the edges as morphisms? And if so, what kind of category would it be? Reflexivity gives the identity morphism, and transitivity means that if there is a morphism from A to B and another from B to C, then there is one from A to C (this is not directly a composition, but we could define the composition of edges as paths, and since there is an edge f from A to B and another edge g from B to C, there is a path (composition) that first goes through f and then g). However, the equivalence relation also imposes symmetry, which makes every morphism an isomorphism.
If the above were really a category, could we then form a category whose objects are the graphs belonging to G/\~ and whose morphisms are graph morphisms? And this category may be a 2-category?
I've probably said a lot of mathematically incorrect things throughout this post, but I'd like to organize my ideas a bit.
Buenas! Soy estudiante de primer semestre de la licenciatura de matemáticas. En mi facultad no hay distinción de "puras" o "aplicadas", simplemente elijes las materias que quieras dentro de una lista muy amplia, algunas impartidas en otras facultades. Pero es cierto que las materias del primer año, prácticamente las únicas obligatorias de la carrera, tienen un enfoque conceptual y demostrativo. También es muy libre en cuanto al ritmo (no sé hasta que punto sea así en todas las universidades), puedes hacer grupos y teoría de galois, anillos o módulos u otras materias de álgebra abstracta apenas en el tercer semestre.
Yo quiero hacer un enfoque de matemáticas puras, sobre todo de fundamentos, categorías y álgebra abstracta. La pregunta es: ¿cuál tendrá que ser mi nivel en un primer año de licenciatura? Es decir, ¿con qué conceptos tendría que pensar con soltura, que técnicas de demostración tendría que tener dominadas, cuánta teoría tendría que saber de analisis/álgebra lineal/matemática discreta?