NP-complete problems are a class of problems in computational complexity theory. To understand NP-complete problems, we need to break down the concepts of "problem classes" and the related terminology. 1. **P (Polynomial time)**: This class contains decision problems (problems with a yes/no answer) for which a solution can be found in polynomial time.
NP-hard problems are a class of problems in computational complexity theory that are at least as hard as the hardest problems in NP (nondeterministic polynomial time). The key properties of NP-hard problems include: 1. **Definition**: A problem is considered NP-hard if every problem in NP can be reduced to it in polynomial time. This means that if you could solve an NP-hard problem quickly (in polynomial time), you could also solve all NP problems quickly.
The Circuit Satisfiability Problem (also known as Circuit-SAT) is a problem in computer science and computational complexity theory that involves determining whether there exists an input assignment to the variables of a given Boolean circuit that produces a specified output (usually True). ### Detailed Explanation: 1. **Boolean Circuit**: A Boolean circuit is a mathematical model for digital logic circuits. It consists of a set of wires and logic gates (such as AND, OR, NOT) that compute a Boolean function.
Linear search, also known as sequential search, is a fundamental algorithm used to find a specific value or an element in a list or an array. The linear search problem involves searching through each element of the list one by one until the desired value is found or until all elements have been checked. ### Description of the Linear Search Algorithm: 1. **Initialization**: Start at the first element of the list.
The "Promise Problem" refers to a class of decision problems in computational complexity that involves promises — that is, certain guarantees about the input. Specifically, it's related to a decision problem where the input is guaranteed to satisfy one of several conditions (or "promises"), but not necessarily all. In more formal terms, a promise problem can be defined as a pair of languages \( L_1 \) and \( L_2 \).
Algerian mathematics refers to the contributions to mathematics made by Algerian mathematicians, as well as the mathematical education and developments in Algeria, particularly after its independence in 1962. This field of study encompasses various areas of mathematics, including pure mathematics, applied mathematics, statistics, and mathematical education. Algerian mathematicians have made significant contributions across various disciplines, including algebra, analysis, geometry, and number theory, among others.
Babylonian mathematics refers to the mathematical system developed and utilized by the ancient civilization of Babylon, primarily during the period from approximately 2000 BCE to 300 BCE. This system is notable for several key characteristics: 1. **Base-60 Number System**: Babylonian mathematics primarily employed a sexagesimal (base-60) numeral system, which means that it was based on the number 60 rather than the decimal (base-10) system used in most modern mathematics.
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