|
Induction Puzzles
Induction puzzles are logic puzzles, which are examples of Dynamic epistemic logic, multi-agent reasoning, where the solution evolves along with the principle of mathematical induction, induction. A puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps. According to the principle of induction, a solution to the simplest case makes the solution of the next complicated case obvious. Once the simplest case of the induction puzzle is solved, the whole puzzle is solved subsequently. Typical tell-tale features of these puzzles include any puzzle in which each participant has a given piece of information (usually as Common knowledge (logic), common knowledge) about all other participants but not themselves. Also, usually, some kind of hint is given to suggest that the participants can trust each other's intelligence — they are capable of theory of mind (that "every participant knows modus ponens" is common knowl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Three Hats Puzzle
3 (three) is a number, numeral (linguistics), numeral and numerical digit, digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic numerals, Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Non-cooperative Game Theory
In game theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in various accounts most prominent being John Nash's 1951 paper in the journal ''Annals of Mathematics''. Counterintuitively, non-cooperative game models can be used to model cooperation as well, and vice versa, cooperative game theory can be used to model competition. Some examples of this would be the use of non-cooperative game models in determining the stability and sustainability of cartels and coalitions. The difference between cooperative and non-cooperative game theory According to Nash, the difference between cooperative game theory and non-cooperative game theory is that “(cooperative game) theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game. Our (no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algebraic Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error detection and correction, Error control (or ''channel coding'') # Cryptography, Cryptographic coding # Line code, Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, DEFLATE data compression makes files small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is a game with groups of players who form binding “coalitions” with external enforcement of cooperative behavior (e.g. through contract law). This is different from non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are analysed by focusing on coalitions that can be formed, and the joint actions that groups can take and the resulting collective payoffs. Mathematical definition A cooperative game is given by specifying a value for every coalition. Formally, the coalitional game consists of a finite set of players N , called the ''grand coalition'', and a ''characteristic function'' v : 2^N \to \mathbb from the set of all possible coalitions of players to a set of payments that satisfies v( \emptyset ) = 0 . The function describes how much collective payoff a set of players can gain by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
University Of California, Santa Barbara
The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an independent teachers college, UCSB joined the University of California system in 1944. It is the third-oldest undergraduate campus in the system, after University of California, Berkeley, UC Berkeley and University of California, Los Angeles, UCLA. UCSB's campus sits on the oceanfront site of a converted WWII-era United States Marine Corps, Marine Corps air station. UCSB is organized into three undergraduate colleges (UCSB College of Letters and Science, Letters and Science, UCSB College of Engineering, Engineering, College of Creative Studies, Creative Studies) and two graduate schools (Gevirtz Graduate School of Education, Education and Bren School of Environmental Science & Management, Environmental Science & Management), offering more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Thesis
A thesis (: theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: DocumentationPresentation of theses and similar documents International Organization for Standardization, Geneva, 1986. In some contexts, the word ''thesis'' or a cognate is used for part of a bachelor's or master's course, while ''dissertation'' is normally applied to a doctorate. This is the typical arrangement in American English. In other contexts, such as within most institutions of the United Kingdom, South Africa, the Commonwealth Countries, and Brazil, the reverse is true. The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, and the required minimum study period ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original research. The name of the degree is most often abbreviated PhD (or, at times, as Ph.D. in North American English, North America), pronounced as three separate letters ( ). The University of Oxford uses the alternative abbreviation "DPhil". PhDs are awarded for programs across the whole breadth of academic fields. Since it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and, in some cases, defend their work before a panel of other experts in the field. In many fields, the completion of a PhD is typically required for employment as a university professor, researcher, or scientist. Definition In the context o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Missouri University Of Science And Technology
Missouri University of Science and Technology (Missouri S&T or S&T) is a public research university in Rolla, Missouri. It is a member institution of the University of Missouri System. Most of its 6,456 students (2023) study engineering, business, sciences, and mathematics. Known primarily for its engineering school, Missouri S&T offers degree programs in business and management systems, information science and technology, sciences, social sciences, humanities, and arts. It is classified as a "STEM-dominant", R1 university with "very high research spending and doctorate production". History Engineering and agricultural education was a rarity in American higher education in 1860, but that changed dramatically in 1862, when the Morrill Land-Grant Acts passed Congress. The law gave generous deeds of public land to states that created schools with programs in engineering and scientific agriculture. Debates over the Civil War and reconstruction slowed progress in Missouri, but fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Common Knowledge (logic)
Common knowledge is a special kind of knowledge for a group of agents. There is ''common knowledge'' of ''p'' in a group of agents ''G'' when all the agents in ''G'' know ''p'', they all know that they know ''p'', they all know that they all know that they know ''p'', and so on ''ad infinitum''.Osborne, Martin J., and Ariel Rubinstein. ''A Course in Game Theory''. Cambridge, MA: MIT, 1994. Print. It can be denoted as C_G p. The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study ''Convention'' (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cambridge
Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 United Kingdom census, the population of the City of Cambridge was 145,700; the population of the wider built-up area (which extends outside the city council area) was 181,137. (2021 census) There is archaeological evidence of settlement in the area as early as the Bronze Age, and Cambridge became an important trading centre during the Roman Britain, Roman and Viking eras. The first Town charter#Municipal charters, town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is well known as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
