Riemannian geometry is a branch of differential geometry concerning Riemannian manifolds, which are smooth manifolds equipped with a Riemannian metric. Here are some important formulas and concepts commonly used in Riemannian geometry: ### Key Formulas and Concepts 1.
Mathematical jargon refers to specialized terminology used in mathematics. Below is a list of common mathematical terms and phrases that are frequently encountered in various fields of mathematics: 1. **Abstraction** - The process of extracting the underlying essence of a concept, often involved in moving from concrete to general ideas. 2. **Algorithm** - A step-by-step procedure or formula for solving a problem or accomplishing a task.
Mnemonics in physics can help students remember complex concepts, formulas, and principles. Here is a list of some commonly used physics mnemonics: ### Mechanics 1. **Kinematic Equations**: - **SUVAT** for remembering the variables: - S = Displacement - U = Initial Velocity - V = Final Velocity - A = Acceleration - T = Time 2.
A mathematical instrument is a tool or device used to aid in the measurement, calculation, visualization, or analysis of mathematical concepts or problems. These instruments can range from simple hand-held tools to complex electronic devices. Here are a few categories and examples of mathematical instruments: 1. **Measuring Tools**: Instruments used for measuring lengths, angles, areas, or volumes.
Mathematics organizations are professional or academic groups that bring together individuals who are interested in various fields of mathematics. These organizations typically focus on promoting the advancement of mathematical knowledge, fostering collaboration among researchers and educators, providing resources for teaching and learning, and disseminating research through publications and conferences. They can vary in scope, size, and mission, and may serve professionals in pure mathematics, applied mathematics, statistics, mathematical education, and interdisciplinary fields.
Mathematics papers typically refer to scholarly articles or research papers that explore various topics within the field of mathematics. These papers are usually written by mathematicians, researchers, or students and are published in academic journals, conference proceedings, or as preprints. Mathematics papers can cover a wide range of topics, including, but not limited to: 1. **Pure Mathematics**: This includes areas such as algebra, geometry, topology, analysis, number theory, and mathematical logic.
Elementary algebra is a branch of mathematics that deals with the basic concepts and operations of algebra. It involves the study of variables, constants, expressions, equations, and inequalities. The foundational principles of elementary algebra include: 1. **Variables**: Symbols (often letters) used to represent unknown quantities. For example, in the equation \(x + 2 = 5\), \(x\) is a variable.
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