Topological graph theory is a branch of mathematics that studies the interplay between graph theory and topology. It focuses primarily on the properties of graphs that are invariant under continuous transformations, such as stretching or bending, but not tearing or gluing. The key aspects of topological graph theory include: 1. **Graph Embeddings**: Understanding how a graph can be drawn in various surfaces (like a plane, sphere, or torus) without edges crossing.
K-theory by Wikipedia Bot 0
K-theory is a branch of mathematics that studies vector bundles and more generally, topological spaces and their associated algebraic invariants. It has applications in various fields, including algebraic geometry, operator theory, and mathematical physics. The core idea in K-theory involves the classification of vector bundles over a topological space. Specifically, there are two main types of K-theory: 1. **Topological K-theory**: This version studies topological spaces and their vector bundles.
Double torus knots and links are concepts from the field of knot theory, which is a branch of topology. In topology, knots are considered as embeddings of circles in three-dimensional space, and links are collections of such embeddings. ### Double Torus A double torus is a surface that is topologically equivalent to two tori (the plural of torus) connected together. It's often visualized as the shape of a "figure eight" or a surface with two "holes.
Kin punishment by Ciro Santilli 37 Updated +Created
Cohomology theories are mathematical frameworks used in algebraic topology, geometry, and related fields to study topological spaces and their properties. They serve as tools for assigning algebraic invariants to topological spaces, allowing for deeper insights into their structure. Cohomology theories capture essential features such as connectivity, holes, and other topological characteristics. ### Key Concepts in Cohomology Theories 1.
Polyadic algebra by Wikipedia Bot 0
Polyadic algebra is a branch of algebra that extends the concept of traditional algebraic structures, such as groups, rings, and fields, to include operations that involve multiple inputs or arities. In particular, it focuses on operations that can take more than two variables (unlike binary operations, which are the most commonly studied).
Leibniz operator by Wikipedia Bot 0
The Leibniz operator is a differential operator used in the context of calculus, particularly in the formulation of differentiating products of functions. It is named after the mathematician Gottfried Wilhelm Leibniz, who made significant contributions to the development of calculus.
Cylindric algebra by Wikipedia Bot 0
Cylindric algebra is a mathematical structure that arises in the study of multi-dimensional logics and is particularly relevant in the fields of model theory and algebraic logic. It is an extension of Boolean algebras to accommodate more complex relationships involving multiple dimensions or "cylindrical" structures. A cylindric algebra can be thought of as an algebraic structure that captures the properties of relations in multiple dimensions, enabling the representation of various logical operations and relations.
A **multiplicative character** is a type of mathematical function used in number theory, particularly in the context of Dirichlet characters and L-functions. Specifically, a multiplicative character is a homomorphism from the group of non-zero integers under multiplication to a finite abelian group, such as the group of complex numbers of modulus one.
Two-graph by Wikipedia Bot 0
A "two-graph" typically refers to a specific type of graph in the field of graph theory, but it might not be a widely standardized term. In general, graph theory involves studying structures made up of vertices (or nodes) connected by edges.
Tutte matrix by Wikipedia Bot 0
The Tutte matrix is a mathematical construct used in the study of graph theory, particularly in the context of understanding the properties of bipartite graphs and the presence of perfect matchings. It is named after the mathematician W. T. Tutte.
Cangue by Ciro Santilli 37 Updated +Created
Punishment by Ciro Santilli 37 Updated +Created
Organized crime by Ciro Santilli 37 Updated +Created
Moufang set by Wikipedia Bot 0
A Moufang set is a concept from the field of mathematics, specifically in the context of algebra and geometry. It is related to the study of certain types of algebraic structures that exhibit properties reminiscent of groups but without necessarily adhering to all the group axioms.
Symmetric graph by Wikipedia Bot 0
A symmetric graph is a type of graph that exhibits a certain level of symmetry in its structure. More formally, a graph \( G \) is considered symmetric if, for any two vertices \( u \) and \( v \) in \( G \), there is an automorphism of the graph that maps \( u \) to \( v \).
Clickbait by Ciro Santilli 37 Updated +Created
Billy Mitchell (gamer) by Ciro Santilli 37 Updated +Created
Video 1.
When Cartoon Network Destroyed Billy Mitchell by Karl Jobst
. Source.

Pinned article: ourbigbook/introduction-to-the-ourbigbook-project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact