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The Tower Of Hanoi – Myths And Maths
''The Tower of Hanoi – Myths and Maths'' is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics Although this book is in recreational mathematics, it takes its subject seriously, and brings in material from automata theory, computational complexity, the design and analysis of algorithms, graph theory, and group theory, topology, fractal geometry, chemical graph theory, and even psychology (where related puzzles have applications in psychological testing). The 1st edition of the book had 10 chapters, and the 2nd edition has 11. In both cases they begin with chapter zero, on the background and history of the Tower of Hanoi puzz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tower Of Hanoi
The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: # Only one disk may be moved at a time. # Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. # No disk may be placed on top of a disk that is smaller than it. With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2''n'' − 1, where ''n'' is the number of disks. Origins The puzzle was introduced to the West ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychological Testing
Psychological testing is the administration of psychological tests. Psychological tests are administered by trained evaluators. A person's responses are evaluated according to carefully prescribed guidelines. Scores are thought to reflect individual or group differences in the construct the test purports to measure. The science behind psychological testing is psychometrics. Psychological tests According to Anastasi and Urbina, psychological tests involve observations made on a "carefully chosen ''sample'' mphasis authorsof an individual's behavior." A psychological test is often designed to measure unobserved constructs, also known as latent variables. Psychological tests can include a series of tasks or problems that the respondent has to solve. Psychological tests can include questionnaires and interviews, which are also designed to measure unobserved constructs. Questionnaire- and interview-based scales typically differ from psychoeducational tests, which ask for a responden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematics Enthusiast
''The Mathematics Enthusiast'' is a triannual peer-reviewed open access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre op ... academic journal covering undergraduate mathematics, mathematics education, including historical, philosophical, and cross-cultural perspectives on mathematics. It is hosted by ScholarWorks at the University of Montana. The journal was established in 2004 and its founding editor-in-chief is Bharath Sriraman. The journal exists as an independent entity in order to give authors full copyright over their articles, and is not affiliated with any commercial publishing companies. Abstracting and indexing The journal is abstracted and indexed in Academic Search Complete, Emerging Sources Citation Index, PsycINFO, and Scopus. References External links * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ACM Computing Reviews
''ACM Computing Reviews'' (''CR'') is a scientific journal that reviews literature in the field of computer science. It is published by the Association for Computing Machinery and the editor-in-chief is Carol Hutchins (New York University). See also * ''ACM Guide to Computing Literature'' * '' ACM Computing Surveys'' * ''Algorithms'' External links * Computing Reviews ''ACM Computing Reviews'' (''CR'') is a scientific journal that reviews literature in the field of computer science. It is published by the Association for Computing Machinery and the editor-in-chief is Carol Hutchins (New York University). See ... Computer science journals Publications established in 1985 English-language journals Review journals 1985 establishments in the United States {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIGACT News
ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science. It was founded in 1968 by Patrick C. Fischer. Publications SIGACT publishes a quarterly print newsletter, ''SIGACT News''. Its online version, ''SIGACT News Online'', is available since 1996 for SIGACT members, with unrestricted access to some features. Conferences SIGACT sponsors or has sponsored several annual conferences. *COLT: Conference on Learning Theory, until 1999 *PODC: ACM Symposium on Principles of Distributed Computing (jointly sponsored by SIGOPS) *PODS: ACM Symposium on Principles of Database Systems *POPL: ACM Symposium on Principles of Programming Languages *SOCG: ACM Symposium on Computational Geometry (jointly sponsored by SIGGRAPH), until 2014 *SODA: ACM/SIAM Symposium on Discrete Algorithms (jointly sponsored by the Society for Industrial and Applied Mathematics). T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of ''Mathematical Reviews'' and additionally contains citation information for over 3.5 million items as of 2018. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal ''Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Mathematical Society
The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current president is Volker Mehrmann, professor at the Institute for Mathematics at the Technical University of Berlin. Goals The Society seeks to serve all kinds of mathematicians in universities, research institutes and other forms of higher education. Its aims are to #Promote mathematical research, both pure and applied, #Assist and advise on problems of mathematical education, #Concern itself with the broader relations of mathematics to society, #Foster interaction between mathematicians of different countries, #Establish a sense of identity amongst European mathematicians, #Represent the mathematical community in supra-national institutions. The EMS is itself an Affiliate Member of the International Mathematical Union and an Associate Membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński Triangle
The Sierpiński triangle (sometimes spelled ''Sierpinski''), also called the Sierpiński gasket or Sierpiński sieve, is a fractal curve, fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursion, recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similarity, self-similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Poland, Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński. Constructions There are many different ways of constructing the Sierpinski triangle. Removing triangles The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets: # Start with an equilateral triangle. # Subdivide it into four smaller congruent equilateral triangles and re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanoi Graph
In graph theory and recreational mathematics, the Hanoi graphs are undirected graphs whose vertices represent the possible states of the Tower of Hanoi puzzle, and whose edges represent allowable moves between pairs of states. Construction The puzzle consists of a set of disks of different sizes, placed in increasing order of size on a fixed set of towers. The Hanoi graph for a puzzle with n disks on k towers is denoted H^n_k. Each state of the puzzle is determined by the choice of one tower for each disk, so the graph has k^n vertices. In the moves of the puzzle, the smallest disk on one tower is moved either to an unoccupied tower or to a tower whose smallest disk is larger. If there are u unoccupied towers, the number of allowable moves is :\binom-\binom, which ranges from a maximum of \tbinom (when u is zero or one and \tbinom is zero) to k-1 (when all disks are on one tower and u is k-1). Therefore, the degree (graph theory), degrees of the vertices in the Hanoi graph range ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics". The exponential function satisfies the exponentiation identity e^ = e^x e^y \text x,y\in\mathbb, which, along with the definition e = \exp(1), shows that e^n=\underbrace_ for positive i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
