In mathematics, particularly in set theory, a **family of sets** is a collection of sets, often indexed by some set or structure. While the term "family of sets" can be used informally to refer to any group of sets, it has a more formal definition in certain contexts.
Hypercomplex numbers extend the concept of complex numbers to higher dimensions. While complex numbers can be represented in the form \( a + bi \), where \( a \) and \( b \) are real numbers and \( i \) is the imaginary unit satisfying \( i^2 = -1 \), hypercomplex numbers involve additional dimensions and may introduce multiple imaginary units.
In mathematics, an **invariant** is a property or quantity that remains unchanged under certain transformations or operations. The concept of invariance is fundamental in various fields of mathematics, including algebra, geometry, calculus, and topology. Here are some key areas where invariants are commonly discussed: 1. **Geometry**: Invariants under geometric transformations (like translations, rotations, and reflections) could include properties like distances, angles, or areas.
The Kantor double, more formally known as the Kantor double construction or Kantor double group, refers to a specific method in the context of group theory, particularly in the study of semigroups and their representations. It involves constructing a group from a given semigroup or a set of elements, often used in algebraic structures related to geometry or combinatorics.
The field of statistics has a rich history, and many important publications have shaped its development. Here are some key works and publications that are widely regarded as significant in the field of statistics: 1. **"Statistical Methods for Research Workers" by Ronald A. Fisher (1925)** - This book introduced many concepts that are now fundamental in statistics, including the design of experiments and the analysis of variance. 2. **"The Design of Experiments" by Ronald A.
A list of mathematical societies includes organizations that promote the advancement, teaching, and application of mathematics. These societies often support research, publish journals, organize conferences, and provide resources for mathematicians and educators. Here are some notable mathematical societies from around the world: ### International Societies 1. **International Mathematical Union (IMU)** - Promotes international cooperation in mathematics. 2. **European Mathematical Society (EMS)** - Supports the development of mathematics in Europe.
Stochastic processes are mathematical objects that are used to describe systems or phenomena that evolve over time in a probabilistic manner. Here's a list of topics commonly associated with stochastic processes: 1. **Basic Concepts:** - Definition of stochastic processes - Sample space and probability measures - Random variables - Pathwise continuity and discontinuity 2. **Types of Stochastic Processes:** - Discrete-time vs. continuous-time processes - Discrete-state vs.
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