Relevant bibliographies by topics / Foundations of calculus

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Foundations of calculus'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Foundations of calculus"

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Hansen, Michael R., and Zhou Chaochen. "Duration calculus: Logical foundations." Formal Aspects of Computing 9, no. 3 (1997): 283–330. http://dx.doi.org/10.1007/bf01211086.

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Roslyakov, A. V., A. A. Lysikov, and V. D. Vitevskiy. "Network Calculus. Part 1. Theoretical foundations." Infokommunikacionnye tehnologii 16, no. 1 (2018): 19–33. http://dx.doi.org/10.18469/ikt.2018.16.1.02.

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Budach, Lothar. "On the Combinatorial Foundations of Regge-Calculus." Annalen der Physik 501, no. 1 (1989): 1–14. http://dx.doi.org/10.1002/andp.19895010102.

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COURANT, JUDICAËL. "A module calculus for Pure Type Systems." Journal of Functional Programming 17, no. 3 (2006): 287–352. http://dx.doi.org/10.1017/s0956796806005867.

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AbstractSeveral proof-assistants rely on the very formal basis of Pure Type Systems (PTS) as their foundations. We are concerned with the issues involved in the development of large proofs in these provers such as namespace management, development of reusable proof libraries and separate verification. Although implementations offer many features to address them, few theoretical foundations have been laid for them up to now. This is a problem as features dealing with modularity may have harmful, unsuspected effects on the reliability or usability of an implementation.In this paper, we propose a
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Wagner, Jennifer, and Janet Sharp. "A Calculus Activity with Foundations in Geometric Learning." Mathematics Teacher 110, no. 8 (2017): 618–23. http://dx.doi.org/10.5951/mathteacher.110.8.0618.

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Danielson, Christopher. "They'll Need It for Calculus." Mathematics Teaching in the Middle School 20, no. 5 (2014): 260–65. http://dx.doi.org/10.5951/mathteacmiddscho.20.5.0260.

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A calculus teacher with a middle school background challenges the assumptions that algebraic manipulation skills are the most important foundations for calculus. He suggests the use of a smaller set of big middle school ideas that will be important to later success with the ideas of calculus.
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Khrennikov, A. Yu. "Foundations of analysis on superspace — 1: Differential calculus." P-Adic Numbers, Ultrametric Analysis, and Applications 7, no. 2 (2015): 96–110. http://dx.doi.org/10.1134/s2070046615020028.

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ANDRÉKA, HAJNAL, STEVEN GIVANT, PETER JIPSEN, and ISTVÁN NÉMETI. "ON TARSKI’S AXIOMATIC FOUNDATIONS OF THE CALCULUS OF RELATIONS." Journal of Symbolic Logic 82, no. 3 (2017): 966–94. http://dx.doi.org/10.1017/jsl.2016.32.

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AbstractIt is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left
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Zeilberger, Doron. "Symbolic Moment Calculus I: Foundations and Permutation Pattern Statistics." Annals of Combinatorics 8, no. 3 (2004): 369–78. http://dx.doi.org/10.1007/s00026-004-0226-2.

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HYLAND, J. M. E. "Classical lambda calculus in modern dress." Mathematical Structures in Computer Science 27, no. 5 (2015): 762–81. http://dx.doi.org/10.1017/s0960129515000377.

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Recent developments in the categorical foundations of universal algebra have given an impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's representation theorem is then completely natural and leads to a precise Fundamental Theorem showing the essential equivalence between the categorical and more familiar notions.
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Dissertations / Theses on the topic "Foundations of calculus"

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Smith, Michael M. "PRE-CALCULUS CONCEPTS FUNDAMENTAL TO CALCULUS." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1164048974.

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Ong, C. H. Luke. "The Lazy Lambda Calculus : an investigation into the foundations of functional programming." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47211.

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Smith, Michael Anthony. "Embedding an object calculus in the unifying theories of programming." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:8b5be90d-59c1-42c0-a996-ecd8015097b3.

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Hoare and He's Unifying Theories of Programming (UTP) provides a rich model of programs as relational predicates. This theory is intended to provide a single framework in which any programming paradigms, languages, and features, can be modelled, compared and contrasted. The UTP already has models for several programming formalisms, such as imperative programming, higher-order programming (e.g. programing with procedures), several styles of concurrent programming (or reactive systems), class-based object-orientation, and transaction processing. We believe that the UTP ought to be able to repres
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Atzemoglou, George Philip. "Higher-order semantics for quantum programming languages with classical control." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:9fdc4a26-cce3-48ed-bbab-d54c4917688f.

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This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known proble
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Marko, Benjamin David. "Teaching Concepts Foundational to Calculus Using Inquiry and Technology." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1144777991.

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Bologna, Mauro. "The Dynamic Foundation of Fractal Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4235/.

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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and
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Guenot, Nicolas. "Nested Deduction in Logical Foundations for Computation." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/99/08/PDF/thesis.pdf.

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Cette thèse s'intéresse à l'usage des formalismes d'inférence profonde comme fondement des interprétations calculatoires des systèmes de preuve, en suivant les deux approches principales: celle des preuves comme programmes et celle de la recherche de preuve comme calcul. La première contribution est le développement d'une famille de systèmes de preuve pour la logique intuitionniste dans le calcul des structures et dans les séquents imbriqués. Pour lesquels des procédures de normalisation internes sont fournies. L'une de ces procédures est alors interprétée en termes calculatoires, comme un raf
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Giachino, Elena. "Session type : semantic foundations and object-oriented applications." Paris 7, 2009. http://www.theses.fr/2009PA077186.

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Deux processus qui échangent des messages doivent s'accorder sur un protocole à adopter lors de l'interaction, pour avoir la garantie que la communication avance sans discordances. Dans la théorie des types session la spécification du protocole est un type associé au canal et décrit la séquence et la direction des données échangées. Dans cette thèse nous étudions les types session dans une perspective fondatrice et une linguistique. Nous définissons d'abord une sémantique pour les types session. Puisque ces types décrivent le comportement de communication d'un processus, il semble naturel de l
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Milici, Pietro. "A quest for exactness : machines, algebra and geometry for tractional constructions of differential equations." Thesis, Paris 1, 2015. http://www.theses.fr/2015PA010675.

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Dans La Géométrie de 1637, Descartes a trouvé un “équilibre” entre constructions géométriques et manipulation symbolique au moyen de l’introduction d’opportunes machines idéales. En particulier, les instruments de Descartes étaient l’algèbre polynomiale (analyse) et une classe de constructions diagrammatiques (synthèse). Cette approche implique une classification des courbes, suivant laquelle les courbes algébriques peuvent être considérées comme “purement géométriques”. Cette limite a été dépassée à l’aide d’une méthode générale par Newton et Leibniz, en introduisant l’infini dans la partie a
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Abboud, Youssef. "Développement d’un macroélément pour l’étude des fondations superficielles sous charge sismique." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1010/document.

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Cette thèse vise à développer une méthode pour la justification des fondations superficielles sous charge sismique dans le cadre du nouveau zonage sismique de la France, entré en vigueur en 2011 et des justifications post Fukushima. Elle s’inscrit dans le cadre d’un contrat de recherche entre l’IFSTTAR et EDF CEIDRE.Un modèle basé sur le concept de macroélément est développé pour étudier l’interaction sol-structure (ISS) en prenant en compte les différentes non linéarités. Sa formulation se base sur la théorie de l’élastoplasticité et s’inspire des normes en vigueur (Eurocodes 7 et 8) et. Les
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Books on the topic "Foundations of calculus"

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Euler. Foundations of Differential Calculus. Springer New York, 2000. http://dx.doi.org/10.1007/b97699.

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Euler, Leonhard. Foundations of differential calculus. Springer, 2000.

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Kashiwara, Masaki. Foundations of algebraic analysis. Princeton University Press, 1986.

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P, Narayanaswami P., ed. Foundations of analysis: The theory of limits. Harper & Row, 1989.

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Belding, David French. Foundations of analysis. 2nd ed. Dover Publications, 2008.

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M, Buchanan James. The calculus of consent: Logical foundations of constitutional democracy. Liberty Fund, 1999.

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Letnikov, A. V. Osnovy drobnogo ischislenii︠a︡: S prilozhenii︠a︡mi v teorii razrabotki nefti︠a︡nykh i gazovykh zalezheĭ, podzemnoĭ gidrodinamike i dinamike biologicheskikh sistem = Foundations of fractional calculus. Izdatelʹstvo "Neftegaz", 2011.

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Herzberg, Frederik. Stochastic Calculus with Infinitesimals. Springer Berlin Heidelberg, 2013.

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Koroli͡uk, V. S. Mathematical foundations of the state lumping of large systems. Kluwer Academic Publishers, 1993.

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(Victor), Vinnikov V., ed. Foundations of free noncommutative function theory. American Mathematical Society, 2014.

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Book chapters on the topic "Foundations of calculus"

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Güler, Osman. "Differential Calculus." In Foundations of Optimization. Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-68407-9_1.

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Engeler, Erwin. "Lambda Calculus." In Foundations of Mathematics. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-78052-3_13.

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Kallenberg, Olav. "Malliavin Calculus." In Foundations of Modern Probability. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61871-1_22.

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Hehl, Friedrich W., and Yuri N. Obukhov. "Mathematics:Some Exterior Calculus." In Foundations of Classical Electrodynamics. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0051-2_2.

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Zund, Joseph. "The Ricci Calculus." In Foundations of Differential Geodesy. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-79187-1_2.

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Zund, Joseph. "The Cartan Calculus." In Foundations of Differential Geodesy. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-79187-1_3.

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Zund, Joseph. "The General Leg Calculus." In Foundations of Differential Geodesy. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-79187-1_4.

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Sobczyk, Garret. "Calculus on m-Surfaces." In New Foundations in Mathematics. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8385-6_13.

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Kurzhanski, Alexander B., and István Vályi. "The Ellipsoidal Calculus." In Systems & Control: Foundations & Applications. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0277-6_2.

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Cignoli, Roberto L. O., Itala M. L. D’Ottaviano, and Daniele Mundici. "Łukasiewicz ∞-valued calculus." In Algebraic Foundations of Many-Valued Reasoning. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9480-6_5.

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Conference papers on the topic "Foundations of calculus"

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Pykacz, Jarosław, Luigi Accardi, Guillaume Adenier, et al. "Quantum Probability Calculus as Fuzzy-Kolmogorovian Probability Calculus." In FOUNDATIONS OF PROBABILITY AND PHYSICS—5. AIP, 2009. http://dx.doi.org/10.1063/1.3109936.

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Bruni, Alessandro, Sebastian Modersheim, Flemming Nielson, and Hanne Riis Nielson. "Set-Pi: Set Membership p-Calculus." In 2015 IEEE 28th Computer Security Foundations Symposium (CSF). IEEE, 2015. http://dx.doi.org/10.1109/csf.2015.20.

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Arden, Owen, and Andrew C. Myers. "A Calculus for Flow-Limited Authorization." In 2016 IEEE 29th Computer Security Foundations Symposium (CSF). IEEE, 2016. http://dx.doi.org/10.1109/csf.2016.17.

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Pitassi, T., and A. Urquhart. "The complexity of the Hajos calculus." In Proceedings., 33rd Annual Symposium on Foundations of Computer Science. IEEE, 1992. http://dx.doi.org/10.1109/sfcs.1992.267773.

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Tiu, Alwen, and Jeremy Dawson. "Automating Open Bisimulation Checking for the Spi Calculus." In 2010 IEEE 23rd Computer Security Foundations Symposium (CSF). IEEE, 2010. http://dx.doi.org/10.1109/csf.2010.28.

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Galesi, Nicola, Leszek Kolodziejczyk, and Neil Thapen. "Polynomial Calculus Space and Resolution Width." In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2019. http://dx.doi.org/10.1109/focs.2019.00081.

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Alekhnovich, M., and A. A. Razborov. "Lower bounds for polynomial calculus: non-binomial case." In Proceedings 42nd IEEE Symposium on Foundations of Computer Science. IEEE, 2001. http://dx.doi.org/10.1109/sfcs.2001.959893.

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Arapinis, Myrto, Tom Chothia, Eike Ritter, and Mark Ryan. "Analysing Unlinkability and Anonymity Using the Applied Pi Calculus." In 2010 IEEE 23rd Computer Security Foundations Symposium (CSF). IEEE, 2010. http://dx.doi.org/10.1109/csf.2010.15.

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de Gosson, Maurice. "Weyl Calculus in Phase Space and the Torres-Vega and Frederick Equation." In QUANTUM THEORY: Reconsideration of Foundations - 3. AIP, 2006. http://dx.doi.org/10.1063/1.2158732.

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Ong, C. H. L. "Fully abstract models of the lazy lambda calculus." In [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science. IEEE, 1988. http://dx.doi.org/10.1109/sfcs.1988.21953.

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