The "mathematics of music" refers to the relationship between mathematical concepts and musical structures, encompassing various aspects, including harmony, rhythm, scales, and tuning systems. Here are some key points that illustrate this connection: 1. **Frequency and Pitch**: The pitch of a musical note is determined by its frequency, measured in hertz (Hz). For example, the note A4 (the A above middle C) is typically tuned to 440 Hz.
Computational science is a multidisciplinary field that uses computational techniques and simulations to solve complex scientific and engineering problems. It combines elements of computer science, applied mathematics, and domain-specific knowledge from various scientific disciplines, such as physics, chemistry, biology, and engineering. Key aspects of computational science include: 1. **Modeling and Simulation**: Developing mathematical models that describe physical, biological, or social systems and using simulations to study their behavior under various conditions.
Mental calculation refers to the process of performing arithmetic calculations in one’s mind without the use of external tools such as calculators, pen, or paper. It involves using cognitive abilities to manipulate numbers, solve problems, and derive answers based on mental arithmetic techniques. Key aspects of mental calculation include: 1. **Speed**: Mental calculations aim to achieve quick results, allowing individuals to solve problems efficiently. 2. **Accuracy**: While speed is important, maintaining accuracy in calculations is crucial to ensure reliable results.
"Numbers" can refer to several different concepts depending on the context. Here are a few possible interpretations: 1. **Mathematical Concept**: In mathematics, numbers are symbols used to represent quantities and are fundamental to counting, measuring, and performing various calculations. They include various types such as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
Topological dynamics is a branch of mathematics that studies the behavior of dynamical systems through the lens of topology. It focuses on how systems evolve over time while considering the global structure of the space in which they reside. The central objects of study in topological dynamics are often continuous functions on topological spaces that model the evolution of a system.
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