Other Mathematics Commons^™

Proof With Words: 2 + 11 - 1 = 12, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof with words: 2 + 11 – 1 = 12

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Joachim Castella: Studien Zur Thematik "Kalkül Und Kreativität", Rudolf Kaehr

Rudolf Kaehr

Utopie der Zeichen – Zeichen der Utopie Vilém Flusser und Gotthard Günther als Komplement einer neuen Medienphilosophie Medientheorie als Theoriemedium Prolegomena einer allgemeinenMedientheorie Philosophie des LMR Joachim Castella 2000/2001

Rush Hour® And Dijkstra’S Algorithm, Mark Stamp, Brad Engel, Mcintosh Ewell, Victor Morrow

Faculty Publications, Computer Science

The game of Rush Hour® includes a 6 × 6 grid and game pieces representing cars and trucks. The object of the puzzle is to move a special car out of a gridlocked “traffic jam.” In this note we apply Dijkstra’s algorithm and a breadth-first search to solve any Rush Hour configuration.

A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar

Doctoral Dissertations

Traditional iterative methods are stalling numerical processes, in which the error has relatively small changes from one iteration to the next. Multigrid methods overcome the limitations of iterative methods and are computationally efficient. Convergence of iterative methods for elliptic partial differential equations is extremely slow. In particular, the convergence of the non-linear elliptic Poisson grid generation equations used for elliptic grid generation is very slow. Multigrid methods are fast converging methods when applied to elliptic partial differential equations. In this dissertation, a non-linear multigrid algorithm is used to accelerate the convergence of the non-linear elliptic Poisson grid generation method. The …

Modal Rules Are Co-Implications, Alexander Kurz

Engineering Faculty Articles and Research

In [13], it was shown that modal logic for coalgebras dualises—concerning definability— equational logic for algebras. This paper establishes that, similarly, modal rules dualise implications:It is shown that a class of coalgebras is definable by modal rules iff it is closed under H (images) and Σ (disjoint unions). As a corollary the expressive power of rules of infinitary modal logic on Kripke frames is characterised.

La Révolution Scientifique, Les Révolutions, Et L'Histoire Des Sciences. Comment Ernest Coumet Nous A Libérés De L'Héritage D'Alexandre Koyré, Marco Panza

MPP Published Research

Dans son intervention au colloque Koyré (Paris, 1986), Ernest Coumet a suggéré que le terme «révolution scientifique» ne désigne pas chez Koyré un événement historique, mais un idéaltype, au sens de Max Weber. L'auteur discute d'abord cette thèse de Coumet et expose les arguments que ce dermier apporte pour la soutenir. Dans la deuxième partie de l'article, il critique l'usage de la notion de révolution en histoire des sciences, en s'opposant en particulier à la possibilité de distinguer dans les productions des savants une «pensée scientifique» qui serait influencée par la «pensée philosophique» et dont les bouleversements marqueraient l'avènement d'une …

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Dialectics And The Dao: On Both, A And Non-A In Neutrosophy And Chinese Philosophy, Feng Liu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces readers to a new approach to dialectical logic: neutrosophy. Specifically it proposes a multi-valued logic in which the statement “both A and Non-A,” historically rejected as logically incoherent, is treated as meaningful. This unity of opposites constitutes both the objective world and the subjective world –a view with deep roots in Buddhism and Daoism, including the I-Ching. This leads in turn to the presentation of a framework for the development of a contradiction oriented learning philosophy inspired by the Later Trigrams of King Wen in the I-Ching. We show that although A and Non-A are logically inconsistent, …