Mathematics can be defined in several ways, reflecting its diverse nature and applications. Here are some common definitions: 1. **Formal Definition**: Mathematics is the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics).
The Degree-Diameter Problem (DDP) is a classic problem in the field of graph theory and combinatorics. It focuses on the trade-off between the degree of vertices in a graph and its diameter. Specifically, the problem seeks to determine the maximum number of vertices \( N \) in a graph given two constraints: the maximum degree \( D \) of any vertex and the maximum diameter \( h \) of the graph.
The De Morgan Medal is an award presented by the London Mathematical Society (LMS) to recognize outstanding achievements in mathematics. Named after the British mathematician August De Morgan, the award is intended to honor individuals for their significant contributions to the field of mathematics, particularly those related to the contributions that are consistent with De Morgan's own work and philosophy. The medal is typically awarded every two years and is one of the highest honors given by the LMS.
Glassy carbon is a type of carbon material that is characterized by its glass-like structure and properties. It is a non-graphitizing carbon, meaning that it does not have a crystalline structure typical of graphite. Instead, it consists of a network of carbon atoms that are bonded in a way that gives it unique physical and chemical properties.
An **automorphism** is a special type of isomorphism in the context of mathematical structures. More specifically, it is a bijective (one-to-one and onto) mapping from a mathematical object to itself that preserves the structure of that object. ### Key Points: 1. **Mathematical Structures**: Automorphisms can exist in various mathematical contexts, such as groups, rings, vector spaces, graphs, and more.
The Awards of Optica (formerly known as the Optical Society of America, or OSA) are prestigious recognitions given by the Optica organization to individuals who have made significant contributions to the field of optics and photonics. These awards celebrate achievements in research, innovation, and leadership within the optics community. The various awards include: 1. **The OSA Frederick Ives Medal**: The highest honor awarded by Optica, recognizing outstanding contributions to optics.
The Mathematical Association of America (MAA) awards several honors to recognize outstanding achievements and contributions in the field of mathematics. Some of the prominent awards include: 1. **Sewell Prize**: Awarded to recognize outstanding teaching in mathematics at the undergraduate level. 2. **Carl B. Allendoerfer Award**: Given for an outstanding mathematical exposition that is accessible to undergraduate students. 3. **G. Dale Meyer Award**: Recognizes outstanding contributions to mathematics education.
Axel Hägerström (1868–1939) was a Swedish philosopher and a prominent figure in the field of legal philosophy and ethics. He is best known for his work in developing a naturalistic approach to ethics and for his contributions to the philosophy of law. Hägerström is often associated with the philosophical tradition known as "Uppsala School," which emphasized a scientific and empirical perspective on human behavior and social institutions.
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!
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
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. 
- 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