This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Ring (mathematics) by Ciro Santilli 40 Updated 2025-07-16
A Ring can be seen as a generalization of a field where:
Addition however has to be commutative and have inverses, i.e. it is an Abelian group.
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.
A polynomial ring is another example with the same properties as the integers.
The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:
Note that is not a ring because you can by addition reach the zero matrix.
Distributive property by Ciro Santilli 40 Updated 2025-07-16
One of the defining properties of algebraic structure with two operations such as ring and field:
This property shows how the two operations interact.
Gram per cubic centimetre (g/cm³) is a unit of density, which measures how much mass of a substance is contained in a given volume. Specifically, it indicates how many grams of a substance are present in one cubic centimetre of that substance. 1 g/cm³ is equivalent to 1,000 kg/m³ in the metric system. The density of a substance can provide important information about its properties and behavior.
"Cotyla" could refer to several things depending on the context, but it is not widely recognized or established in common knowledge as of my last update in October 2023. It might refer to: 1. **Biological Term**: In biological contexts, "cotyla" can refer to a shallow, cup-shaped structure, such as a cavity or socket in anatomical terminology.
The gill is a unit of measurement for volume. It is primarily used to measure liquids, particularly in the context of alcoholic beverages. The size of a gill can vary depending on the country and its specific measurement system: - **In the UK**, a gill is equal to 142.07 milliliters (ml), which is approximately 4.8 fluid ounces. - **In the US**, a gill is defined as 118.
DialAmerica is a telemarketing and call center services company that provides a variety of services, primarily focused on outbound telemarketing and inbound customer service. Founded in 1985, the company works with clients across various industries, including telecommunications, retail, healthcare, and non-profit organizations. DialAmerica's services often include lead generation, customer surveys, market research, appointment setting, and direct response campaigns.
The Do Not Call (DNC) list is a registry established in various countries, including the United States, to help consumers avoid unwanted telemarketing calls. Individuals can add their phone numbers to this list to indicate that they do not wish to receive unsolicited sales calls from telemarketers. In the U.S., the National Do Not Call Registry is managed by the Federal Trade Commission (FTC).
Frequency, in a general sense, refers to the number of occurrences of a repeating event per unit of time. It is commonly used in various fields, including physics, music, and electronics. Here are a few specific contexts where the term "frequency" is relevant: 1. **Physics**: In wave mechanics, frequency is the number of cycles of a wave that pass a given point in one second.
NOC, which stands for "Norwegian orca," is a term associated with a specific case of an orca (also known as a killer whale) that gained attention due to its unusual vocalizations. In 1984, a captive orca named NOC at the National Marine Aquarium in San Diego was observed to have mimicked human speech patterns. Researchers recorded sounds that resembled human voices, leading to discussions about the cognitive capabilities of marine mammals, particularly orcas.

Pinned article: 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 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  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