Finite character by Wikipedia Bot 0
In the context of mathematics, particularly in the field of representation theory, a **finite character** refers to a homomorphism from a group (often a finite group or a compact group) into the multiplicative group of non-zero complex numbers (or into a field). Characters are used to study the representations of groups, particularly in the context of finite groups and their representations over the complex numbers.
The Finite Intersection Property (FIP) is a concept from topology and set theory. It applies to a collection of sets and states that a family of sets has the finite intersection property if the intersection of every finite subcollection of these sets is non-empty. Formally, let \( \mathcal{A} \) be a collection of sets.
Hypergraph by Wikipedia Bot 0
A hypergraph is a generalization of a graph in which an edge can connect any number of vertices, rather than just two. In a traditional graph, an edge is a connection between exactly two vertices. In contrast, a hypergraph allows an edge (often called a hyperedge) to link multiple vertices simultaneously.
Matroid by Wikipedia Bot 0
A **matroid** is a combinatorial structure that generalizes the notion of linear independence in vector spaces to more abstract settings. It is defined by a pair \((S, I)\), where: - \(S\) is a finite set of elements. - \(I\) is a collection of subsets of \(S\) (called independent sets) that satisfy certain properties.
The Maximum Coverage Problem is a well-known problem in combinatorial optimization and computer science. It can be described as follows: Given a finite set \( U \) (the universe) and a collection of subsets \( S_1, S_2, \ldots, S_m \) of \( U \), the goal is to select a certain number \( k \) of these subsets such that the number of unique elements covered by the selected subsets is maximized.
Near polygon by Wikipedia Bot 0
The term "near polygon" does not have a widely recognized definition in standard geometry or mathematics. However, it may refer to various concepts depending on the context: 1. **Computational Geometry**: In computational geometry, a "near polygon" could indicate a polygon that closely approximates another shape or object, possibly in terms of shape or boundary. This could involve applying algorithms to minimize the difference between two shapes.
Nerve complex by Wikipedia Bot 0
The term "nerve complex" can refer to several related concepts in biology and medical science, though it is not a standard term used universally. Here are a few interpretations that may align with your interest: 1. **Anatomical Structure**: In anatomy, a nerve complex might refer to a network of nerves that work together to control a specific function or region of the body. An example could be the brachial plexus, a network of nerves that innervates the upper limb.
Pi-system by Wikipedia Bot 0
A Pi-system is a concept from measure theory, a branch of mathematics that deals with the formalization of concepts like size and probability. A Pi-system (or π-system) is specifically a collection of sets that has some special properties: 1. **Closure Under Intersection**: If you have two sets \( A \) and \( B \) in the Pi-system, then their intersection \( A \cap B \) is also in the Pi-system.
In the context of mathematical topology, a collection of sets (often subsets of a topological space) is said to be **point-finite** if, for every point in the space, there are only finitely many sets in the collection that contain that point. More formally, let \( \mathcal{A} \) be a collection of subsets of a topological space \( X \).
Property B by Wikipedia Bot 0
"Property B" can refer to various concepts depending on the context. For instance, in real estate, it could denote a specific piece of property or real estate asset. In legal discussions, it might refer to a specific property right or classification.
Ring of sets by Wikipedia Bot 0
In mathematics, particularly in measure theory and set theory, a **ring of sets** is a collection of sets that is closed under certain operations. More formally, a family \( R \) of sets is called a ring if it satisfies the following properties: 1. **Closure under intersection**: If \( A \) and \( B \) are in \( R \), then \( A \cap B \) is also in \( R \).
The Sauer–Shelah lemma is a result in combinatorics and model theory that provides a bound on the size of a family of finite sets that can be shattered by a given number of points. It is named after Sigmund Sauer and Saharon Shelah, who independently discovered it.
JTAG by Ciro Santilli 37 Updated +Created
Sigma-ideal by Wikipedia Bot 0
In the context of set theory and measure theory, a **σ-ideal** (sigma-ideal) is a specific type of collection of sets that satisfies certain properties concerning the operations of countable unions and subsets. More formally, a family \( I \) of subsets of a set \( X \) is called a σ-ideal if it satisfies the following conditions: 1. **Non-empty:** The empty set is an element of \( I \), i.e.
The Social Golfer Problem (SGP) is a classic combinatorial optimization problem that involves grouping players into teams for a golf tournament, where the goal is to maximize socialization (i.e., minimize repeated pairings) over multiple rounds. Here's how it works: 1. **Players and Groups**: You have a fixed number of players, often divided into groups of a specific size.
Sperner family by Wikipedia Bot 0
A Sperner family is a specific type of collection of sets in combinatorics, named after Emanuel Sperner, who studied these structures in the context of set theory. A Sperner family, or Sperner's family, is defined as a family of subsets of a finite set such that no one subset is contained within another.
Sergei Aseev by Wikipedia Bot 0
As of my last update in October 2023, there is no widely known figure or concept specifically named Sergei Aseev. It is possible that this name could refer to a private individual or a lesser-known person in a specific field. If you have more context about who Sergei Aseev is or what area he is associated with (e.g.
The Teichmüller–Tukey lemma is a result in set theory and topology, particularly in the study of families of sets and their combinatorial properties. The lemma states that for certain types of families of sets, there is a particular way to extract a subset with specific properties.
Aephraim M. Steinberg is a physicist known for his work in quantum mechanics and quantum information science. He is notable for contributions to experimental quantum physics, particularly in areas related to quantum optics and the study of quantum entanglement. Steinberg's research has implications for the development of quantum computing and understanding fundamental aspects of quantum theory.
Ainissa Ramirez by Wikipedia Bot 0
Ainissa Ramirez is a prominent materials scientist, author, and speaker known for her work in the field of science communication and materials science. She has contributed significantly to the understanding of the properties and applications of materials, especially in areas such as energy and electronics. In addition to her scientific research, Ramirez is recognized for her efforts to engage the public with science through her writing and talks. She has authored books aimed at making complex scientific topics accessible and interesting to a general audience.

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