Mathematical proofs are logical arguments that demonstrate the truth or validity of a mathematical statement or theorem. A proof provides an explanation of why a particular statement is true based on axioms (fundamental truths accepted without proof), previously established theorems, and logical reasoning. Key features of mathematical proofs include: 1. **Logical Structure**: A proof is constructed using a clear logical framework, often consisting of statements and arguments that follow a structured approach.
Mathematical terminology refers to the specific language, symbols, and vocabulary used in the field of mathematics. This terminology helps convey concepts, methods, and relationships in a precise and standardized way. Here are some key aspects of mathematical terminology: 1. **Definitions**: Precise descriptions of mathematical concepts, such as "a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Mathematical constants are specific, well-defined numbers that arise in mathematics and have conventional values. These constants are not variable or dependent on a particular circumstance; instead, they are fixed values that are often encountered in various mathematical contexts and disciplines. Here are some of the most notable mathematical constants: 1. **π (Pi)**: Approximately equal to 3.14159, π is the ratio of a circle's circumference to its diameter.
Carreau fluid is a type of non-Newtonian fluid characterized by its shear-thinning behavior, which means its viscosity decreases with an increase in shear rate. This behavior is typically described by the Carreau model, which is a mathematical representation used to describe the flow behavior of such fluids. The Carreau model is especially useful for fluids that exhibit a transition between a more viscous state at low shear rates and a less viscous state at high shear rates.
Analytic philosophers are thinkers who engage in the analytic tradition of philosophy, which emphasizes clarity, logical analysis, and the use of formal techniques. This tradition emerged in the early 20th century, particularly in the Anglo-American philosophical context, and is associated with figures such as Bertrand Russell, Ludwig Wittgenstein, G.E. Moore, and later philosophers like W.V.O. Quine, Daniel Dennett, and Saul Kripke.
Mathematics has evolved through various historical periods, each characterized by different developments, techniques, and areas of focus. Here's a brief overview of key periods in the history of mathematics: ### 1. **Ancient Mathematics (c. 3000 BC - 500 AD)** - **Civilizations:** Early contributions from the Egyptians (geometry and basic arithmetic), Babylonians (base-60 system), and Greeks (geometry and formal proofs).
"Works" about the history of mathematics can refer to a variety of texts, including books, articles, and papers that explore the development of mathematical concepts, theories, and practices over time.
A glossary of calculus typically includes key terms and definitions that are fundamental to understanding the concepts and techniques in this branch of mathematics. Here is a list of common terms and their meanings: 1. **Limit**: A value that a function approaches as the input approaches a certain point. 2. **Derivative**: A measure of how a function changes as its input changes; it represents the slope of the tangent line to the graph of the function at a given point.
The Canadian Society for History and Philosophy of Mathematics (CSHPM) is an academic organization dedicated to promoting scholarly research and discourse in the fields of history and philosophy of mathematics. Founded in Canada, its primary goals include facilitating communication and collaboration among researchers, organizing conferences, and publishing research findings related to the history and philosophy of mathematics.
In mathematics, the term **order** can refer to several different concepts depending on the context. Here are a few key interpretations: 1. **Order of an Element**: In group theory, the order of an element \( g \) in a finite group is the smallest positive integer \( n \) such that \( g^n = e \), where \( e \) is the identity element of the group.
The Kraków School of Mathematics refers to a significant historical network of mathematicians centered in Kraków, Poland, particularly during the interwar period (1918-1939). This group was notable for its contributions to various fields of mathematics, including functional analysis, set theory, and topology.
Mathematical principles refer to fundamental concepts, theories, and rules that govern the field of mathematics. These principles serve as the foundation for mathematical reasoning and problem-solving. Here are some key aspects of mathematical principles: 1. **Axioms and Postulates**: These are basic statements or assumptions that are accepted without proof. They form the foundation from which other statements are derived.
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