A volume element is a differential quantity used in mathematics and physics, typically in the context of calculus and geometric analysis. It represents an infinitesimally small portion of space, allowing for the integration and measurement of quantities over three-dimensional regions.
Olav Kallenberg is a notable figure in the field of mathematics, particularly known for his contributions to probability theory and stochastic processes. He has authored several influential texts and papers in these areas. His work often focuses on the theoretical foundations of stochastic processes and their applications.
The Ryll-Nardzewski fixed-point theorem is a result in the field of functional analysis, specifically concerning fixed points in nonatomic convex sets in topological vector spaces. It generalizes certain fixed-point results, including the well-known Brouwer fixed-point theorem, to more general settings.
The Stewart–Walker lemma is a result in the field of differential geometry, particularly in the study of Riemannian manifolds. It is specifically related to the curvature of manifolds and provides conditions under which the curvature tensor can be expressed in terms of the metric tensor and its derivatives. The lemma is often invoked in the context of proving properties about space forms and the relationship between curvature and geometric structures on manifolds.
Wiener's lemma is a result in functional analysis and harmonic analysis, particularly related to the theory of Fourier series and the spaces of functions. It is named after Norbert Wiener, who contributed significantly to the field.
The Parrot's Theorem is a humorous and informal mathematical theorem that originated in a cartoon by mathematician and author Paul Erdős. The essence of the theorem is that if a parrot mimics the phrase "I am a math genius," then at least one person in the room will believe it. While not a formal theorem in the traditional sense, it serves to illustrate ideas about belief, perception, and the influence of authority or charisma in discussions, particularly in mathematics and academia.
A wireless mesh network is a type of network topology where multiple wireless devices (nodes) work together to create a flexible and self-organizing network. Unlike traditional networks that rely on a central router or access point, a mesh network allows each node to communicate with one another directly, extending the network's range and reliability.
Guy Henniart is a French mathematician known for his work in the fields of algebraic geometry and mathematical logic. He is particularly recognized for his contributions to model theory and the study of algebraic structures.
The term "difference" can refer to several concepts depending on the context. Here are a few common meanings: 1. **Mathematics**: In mathematics, the difference usually refers to the result of subtracting one number from another. For example, the difference between 8 and 3 is 5 (8 - 3 = 5). 2. **Comparative Analysis**: In a broader sense, difference can refer to the characteristics that distinguish one thing from another.
As of my last update in October 2023, The American Mathematical Monthly is a well-regarded journal published by the Mathematical Association of America (MAA). It features articles on mathematics that are accessible to a broad audience, including undergraduates, teachers, and professional mathematicians. The editorial board typically consists of mathematicians and educators who are experts in various areas of mathematics.
"Topics" is one of Aristotle's works in which he addresses the nature of dialectical reasoning and argumentation. In this text, Aristotle explores how to construct and evaluate arguments, focusing particularly on how to engage in reasoning about likely or probable conclusions rather than certain truths. The main purpose of "Topics" is to provide a systematic method for argumentation, particularly in the context of informal logic and debate.
QWK, short for "Quick Write Kit," is a file format primarily used for offline mail systems in bulletin board systems (BBS). It was developed in the 1980s to facilitate the exchange of messages among users of BBSes. The QWK format allows users to download messages from a BBS to their local computer, read and reply to them offline, and then upload their replies back to the BBS.
Thailand uses a mix of metric and traditional measurement systems. The country officially adopted the metric system in 1923, but some traditional Thai units are still in common use.
"Disneymania" is a series of compilation albums released by Disney featuring popular contemporary artists performing reimagined versions of classic Disney songs. The albums began in the early 2000s and typically include a mix of pop, rock, and R&B interpretations of beloved tracks from Disney movies and theme parks. The first album, "Disneymania," was released in 2002 and featured artists such as Jessica Simpson, Smash Mouth, and Lil' Romeo.
The ARIA Number 1 Hits in Symphony is a concert event that features orchestral renditions of popular songs that have reached number one on the Australian ARIA (Australian Recording Industry Association) chart. This concert typically includes a selection of hit songs from various genres and eras, performed by a live symphony orchestra along with vocalists. The concerts aim to celebrate the iconic music that has topped the charts in Australia, providing a unique experience by combining classical music elements with contemporary hits.
"Animetal Marathon II" is a musical album by the Japanese band Animetal, known for their heavy metal covers of popular anime theme songs and soundtracks. This album is part of a series in which the band performs energetic, metal versions of iconic anime music. Animetal is celebrated for blending the world of anime and heavy metal, appealing to fans of both genres.
"Another Side" is an album by British singer and performer John Barrowman, released in 2010. It features a mix of musical styles, showcasing Barrowman's versatile vocal abilities. The album includes a selection of songs that reflect Barrowman's theatrical background, incorporating both contemporary pop and classic show tunes. Notable tracks often highlight his strengths in emotive vocal performances and engaging interpretations.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. - Infinitely deep tables of contents:
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





