Baker's theorem pertains to the field of complex analysis, specifically dealing with functions that can be expressed through power series. More formally, it relates to the growth of meromorphic functions, which are functions that are holomorphic (complex differentiable) everywhere except for a set of isolated poles.
Serre's modularity conjecture, proposed by Jean-Pierre Serre in the 1980s, is a deep and influential hypothesis in the field of number theory, particularly concerning the relationship between modular forms and elliptic curves.
The Turán–Kubilius inequality is a result in number theory and probabilistic number theory, often related to the distribution of prime numbers. It provides a bound on the probability that certain events, often concerning the sums of random variables, will occur.
Dickson's conjecture is a hypothesis in number theory proposed by the mathematician Leonard Eugene Dickson in 1904. It relates to the distribution of prime numbers and specifically addresses the behavior of prime numbers in arithmetic progressions. The conjecture states that for any given set of integer numbers \(a_1, a_2, ...
Euler's constant, commonly denoted by the symbol \( e \), is a mathematical constant that is approximately equal to 2.71828. It serves as the base of the natural logarithm and is extensively used in various areas of mathematics, particularly in calculus, complex analysis, and number theory.
The Waring–Goldbach problem is a question in number theory that is an extension of Waring's problem. Specifically, it concerns the representation of even integers as sums of prime numbers. The statement of the problem can be framed as follows: For every even integer \( n \), is there a way to express \( n \) as a sum of a bounded number of prime numbers?
A Noetherian topological space is a type of topological space that satisfies a particular property related to its open sets, inspired by Noetherian rings in algebra. Specifically, a topological space \( X \) is called Noetherian if it satisfies the following condition: - **Finite Intersection Property**: Every open cover of \( X \) has a finite subcover.
Non-well-founded set theory is a branch of set theory that allows for sets that can contain themselves as elements, either directly or indirectly, leading to the formation of infinite descending chains. This is in contrast to classical set theory, particularly Zermelo-Fraenkel set theory with the Axiom of Foundation (or Axiom of Regularity), which restricts sets to be well-founded.
The Well-ordering principle is a fundamental concept in set theory and mathematics that states that every non-empty set of non-negative integers (or positive integers) contains a least element.
Dots is a simple yet engaging puzzle game where players aim to connect dots of the same color on a grid to create lines. The main goal is to connect as many dots as possible within a limited number of moves or time. Players can connect dots horizontally or vertically, and the more dots they connect in a single move, the more points they earn.
"Misfit" is a short story by the author and playwright J. D. Salinger, known for exploring themes such as alienation, identity, and the struggles of adolescence. The story often revolves around characters who feel out of place or disconnected from society, reflecting Salinger's recurring exploration of the complexities of human experience.
Sir Cumference is a fictional character often used in educational contexts, particularly in mathematics, to help explain concepts related to circles, geometry, and mathematics in general. The character is typically portrayed as a knight whose adventures revolve around geometric principles. The name "Sir Cumference" is a playful pun on the term "circumference," which refers to the distance around a circle. The character is often featured in a series of children's books that aim to make learning about math fun and engaging.
Rush Hour is a sliding block puzzle game designed by Nob Yoshigahara. The objective of the game is to move a red car out of a grid-like traffic jam of vehicles by sliding them around. The game features a 6x6 grid and includes several vehicles of different lengths, each blocking the way in various configurations. Players need to figure out the correct sequence of moves to free the red car, which is usually located at the center of the grid.
Stave Puzzles is a company known for creating high-quality, handcrafted wooden jigsaw puzzles. Founded in 1974, Stave Puzzles is recognized for its unique designs, intricate pieces, and the use of fine hardwoods such as maple and walnut. Unlike traditional jigsaw puzzles, Stave Puzzles often incorporate imaginative themes and artistic elements, making them appealing to both puzzle enthusiasts and collectors.
A Froebel star, also known as a "Froebel star ornament" or "Froebel star decoration," is a geometric paper star created using a specific folding technique. Named after Friedrich Froebel, the German educator who founded the concept of kindergarten, the Froebel star is often associated with early childhood education and hands-on learning. These stars are typically made from strips of colored paper and involve a folding process that results in a three-dimensional star shape.
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





