Relevant bibliographies by topics / Foundations of mathematics

Contents

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

Academic literature on the topic 'Foundations of mathematics'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 April 2022

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Journal articles on the topic "Foundations of mathematics"

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Mancosu, Paolo. "Between Russell and Hilbert: Behmann on the Foundations of Mathematics." Bulletin of Symbolic Logic 5, no. 3 (September 1999): 303–30. http://dx.doi.org/10.2307/421183.

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AbstractAfter giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition of the solution to the antinomies as found in Principia Mathematica. In the process of explaining the theory of Principia, Behmann also presented an original approach to the foundations of mathematics which saw in sense perception of concrete individuals the Archimedean point for a secure foundation of mathematical knowledge. The last part of the paper points out an important numbers of connections between Behmann's work and Hilbert's foundational thought.
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IANCU, MIHNEA, and FLORIAN RABE. "Formalising foundations of mathematics." Mathematical Structures in Computer Science 21, no. 4 (July 1, 2011): 883–911. http://dx.doi.org/10.1017/s0960129511000144.

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Over recent decades there has been a trend towards formalised mathematics, and a number of sophisticated systems have been developed both to support the formalisation process and to verify the results mechanically. However, each tool is based on a specific foundation of mathematics, and formalisations in different systems are not necessarily compatible. Therefore, the integration of these foundations has received growing interest. We contribute to this goal by using LF as a foundational framework in which the mathematical foundations themselves can be formalised and therefore also the relations between them. We represent three of the most important foundations – Isabelle/HOL, Mizar and ZFC set theory – as well as relations between them. The relations are formalised in such a way that the framework permits the extraction of translation functions, which are guaranteed to be well defined and sound. Our work provides the starting point for a systematic study of formalised foundations in order to compare, relate and integrate them.
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Bagaria, Joan. "On Turing’s legacy in mathematical logic and the foundations of mathematics." Arbor 189, no. 764 (December 30, 2013): a079. http://dx.doi.org/10.3989/arbor.2013.764n6002.

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Wagner, Roi. "Wronski's Foundations of Mathematics." Science in Context 29, no. 3 (August 30, 2016): 241–71. http://dx.doi.org/10.1017/s0269889716000077.

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ArgumentThis paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.
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Melkikh, Alexey V. "The Brain and the New Foundations of Mathematics." Symmetry 13, no. 6 (June 3, 2021): 1002. http://dx.doi.org/10.3390/sym13061002.

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Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain.
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Acerbi, Fabio. "Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus." Science in Context 23, no. 2 (May 4, 2010): 151–86. http://dx.doi.org/10.1017/s0269889710000037.

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ArgumentThis article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.
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Shiu, P., and Paul Taylor. "Practical Foundations of Mathematics." Mathematical Gazette 84, no. 499 (March 2000): 175. http://dx.doi.org/10.2307/3621547.

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Mcavaney, K. L., Albert D. Polimeni, and H. Joseph Straight. "Foundations of Discrete Mathematics." Mathematical Gazette 76, no. 477 (November 1992): 433. http://dx.doi.org/10.2307/3618422.

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Streicher, Thomas. "Practical Foundations of Mathematics." Science of Computer Programming 38, no. 1-3 (August 2000): 155–57. http://dx.doi.org/10.1016/s0167-6423(00)00009-5.

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Bottia, Martha Cecilia, Stephanie Moller, Roslyn Arlin Mickelson, and Elizabeth Stearns. "Foundations of Mathematics Achievement." Elementary School Journal 115, no. 1 (September 2014): 124–50. http://dx.doi.org/10.1086/676950.

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Dissertations / Theses on the topic "Foundations of mathematics"

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Uzquiano, Gabriel 1968. "Ontology and the foundations of mathematics." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9370.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1999.
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"Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more, precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences (whose acceptance plays a crucial role in applications) place serious constraints on the sorts of items to which numerals, as we ordinarily use them, can be taken to refer: Numerals cannot be taken to refer to objects that exist contingently such as people, mountains, or rivers, but rather must be taken to refer to objects that exist necessarily such as abstracta. Chapter 2, "Modern Set Theory and Replacement," takes up a challenge to explain the reasons one should accept the axiom of replacement of Zermelo-Fraenkel set theory, when its applications within ordinary mathematics and the rest of science are often described as rare and recondite. We argue that this is not a question one should be interested in; replacement is required to ensure that the element-set relation is well-founded as well as to ensure that the cumulation of sets described by set theory reaches and proceeds beyond the level w of the cumulative hierarchy. A more interesting question is whether we should accept instances of replacement on uncountable sets, for these are indeed rarely used outside higher set theory. We argue that the best case for (uncountable) replacement comes not from direct, intuitive considerations, but from the role replacement plays in the formulation of transfinite recursion and the theory of ordinals, and from the fact that it permits us to express and assert the (first-order) content of the modern cumulative view of the set theoretic universe as arrayed in a cumulative hierarchy of levels. Chapter 3, "A No-Class Theory of Classes," makes use of the apparatus of plural quantification to construe talk of classes as plural talk about sets, and thus provide an interpretation of both one- and two-sorted versions of first-order Morse-Kelley set theory, an impredicative theory of classes. We argue that the plural interpretation of impredicative theories of classes has a number of advantages over more traditional interpretations of the language of classes as involving singular reference to gigantic set-like entities, only too encompassing to be sets, the most important of these being perhaps that it makes the machinery of classes available for the formalization of much recent and very interesting work in set theory without threatening the universality of the theory as the most comprehensive theory of collections, when these are understood as objects.
by Gabriel Uzquiano.
Ph.D.
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Frovin, Jørgensen Klaus. "Kant's schematism and the foundations of mathematics /." Roskilde : Section Philosophy and Science Studies, Roskilde University, 2005. http://hdl.handle.net/1800/1664.

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Nefdt, Ryan Mark. "The foundations of linguistics : mathematics, models, and structures." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/9584.

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The philosophy of linguistics is a rich philosophical domain which encompasses various disciplines. One of the aims of this thesis is to unite theoretical linguistics, the philosophy of language, the philosophy of science (particularly mathematics and modelling) and the ontology of language. Each part of the research presented here targets separate but related goals with the unified aim of bringing greater clarity to the foundations of linguistics from a philosophical perspective. Part I is devoted to the methodology of linguistics in terms of scientific modelling. I argue against both the Conceptualist and Platonist (as well as Pluralist) interpretations of linguistic theory by means of three grades of mathematical involvement for linguistic grammars. Part II explores the specific models of syntactic and semantics by an analogy with the harder sciences. In Part III, I develop a novel account of linguistic ontology and in the process comment on the type-token distinction, the role and connection with mathematics and the nature of linguistic objects. In this research, I offer a structural realist interpretation of linguistic methodology with a nuanced structuralist picture for its ontology. This proposal is informed by historical and current work in theoretical linguistics as well as philosophical views on ontology, scientific modelling and mathematics.
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Varon, Stephanie Stigers 1939. "The mathematical foundations of classical ballet." Thesis, The University of Arizona, 1997. http://hdl.handle.net/10150/292004.

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This treatise sets out to show how both the mathematical aspect of ballet (and music to a very limited extent) and the associated psychological aspects of both the dancer and the stage space in which he or she operates contribute together to create an entire gestalt that becomes visible on and within the bodies of the dancers as they move through time and space. The recognition of both intention in the role of speaking a language with meaning, along with the existence of energy projection in music, dance and drama, make apparent the existence of this extension of the mental realm into the physical one. Although some people accord the spoken language a privileged status which causes a gap between artists and analytical philosophers, I have attempted, in this work, to show a way in which language may be considered as a concept applying to all languages, including those used in the arts. In this manner, hopefully, this gap between the two sets of theoretical concerns may be shown to be no longer applicable, and a manner of bridging the theoretical split can be forged upon the theory suggested by this treatise.
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Bartocci, C. "Foundations of graded differential geometry." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386972.

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Fennelly, Maxwell. "Geometric foundations of network partitioning." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/375533/.

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Stergianopoulos, Georgios. "Large non-cooperative games : foundations and tools." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/56809/.

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Following Schmeidler (1973) and Mas-Colell (1984), economists have typically used aggregative games with a continuum of players to model strategic environments with a large number of participants. In these games a player's payoff depends on her own strategy and on an average of the strategies of everyone in the game. Examples include corporate competition in global markets, welfare maximization in multi-period economies, strategic voting in national elections, network congestion, and environmental models of pollution or, more generally, widespread externalities. This study consists of three chapters. In Chapter 1 we unveil a weakness of the Schmeidler - Mas-Colell framework, and we develop a potential remedy that leaves the framework intact. In Chapter 2 we set the theoretical foundations for an alternative framework that is immune to the above weakness. Finally, in Chapter 3 we demonstrate how our approach accommodates types of players. We provide a number of fully worked-through examples and an appendix at the end of each chapter that includes the proofs to our propositions.
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Beaton, Ryan. "Interpreting Frege's Grundgesetze in an adaptation of Quine's New Foundations." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81592.

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We first give a modern presentation of the formal language of Frege's Grundgesetze. There follows a comparison of the motivations for Frege's "Cumulative Type Theory" and for Russell's Type Theory and of the basic arithmetical definitions in each. Quine's New Foundations and, in particular, extensions of Jensen's modification, NFU, are introduced and consistency results are discussed. Finally, an interpretation is given in an NFU framework of a modified form of the Grundgesetze theory. It is shown that an "Axiom of Counting" necessary for arithmetic in NFU is needed in an analogous way for arithmetic in our interpretation; it is further demonstrated that from the statement of this axiom in NFU, the appropriate analogue is provable for our interpretation. The development of arithmetic in an NFU framework is seen essentially to be that intended by Frege in the Grundgesetze.
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Johnson, Estrella Maria Salas. "Establishing Foundations for Investigating Inquiry-Oriented Teaching." PDXScholar, 2013. http://pdxscholar.library.pdx.edu/open_access_etds/1102.

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The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe the experiences of mathematicians implementing the curriculum from their perspective. Second. I will describe a study that explores the mathematical work done by teachers as they respond to the mathematical activity of their students. Finally, I will discuss a theoretical paper in which I synthesize aspects of the instructional theory underlying the TAAFU curriculum in order to develop an analytic framework for analyzing student learning. This dissertation will serve as a foundation for my future research focused on the relationship between teachers' mathematical work and the learning of their students.
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Szudzik, Matthew P. "Some Applications of Recursive Functionals to the Foundations of Mathematics and Physics." Research Showcase @ CMU, 2010. http://repository.cmu.edu/dissertations/26.

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We consider two applications of recursive functionals. The first application concerns Gödel’s theory T , which provides a rudimentary foundation for the formalization of mathematics. T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0N, the successor function S, and the operator RT for primitive recursion on objects of type T . It is known that the functions from non-negative integers to non-negative integers that can be defined in this theory are exactly the <ε0-recursive functions of non-negative integers. But it is not well-known which functionals of arbitrary type can be defined in T . We show that when the domain and codomain are restricted to pure closed normal forms, the functionals of arbitrary type that are definable in T are exactly those functionals that can be encoded as <ε0-recursive functions of non-negative integers. This result has many interesting consequences, including a new characterization of T . The second application is concerned with the question: “When can a model of a physical system be regarded as computable?” We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel’s notion of a mechanistic theory is discussed, and several examples of computable physical models are given, including models which feature discrete motion, a model which features non-discrete continuous motion, and nondeterministic models such as radioactive decay. We show how computable physical models on effective topological spaces can be formulated with recursive functionals in the theory of type-two effectivity (TTE). Various common operations on computable physical models are described, such as the operation of coarse-graining and the formation of statistical ensembles. The definition of a computable physical model also allows for a precise formalization of the computable universe hypothesis— the claim that all the laws of physics are computable.
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Books on the topic "Foundations of mathematics"

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Belding, David French. Foundations of analysis. 2nd ed. Mineola, N.Y: Dover Publications, 2008.

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Vass, Isobel. Foundations in mathematics. London: Edward Arnold, 1985.

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Vass, Isobel. Foundations in mathematics. London: Edward Arnold, 1985.

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Vass, Isobel. Foundations in mathematics. London: Edward Arnold, 1985.

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J, Wellenzohn Henry, ed. Foundations of mathematics. Clearwater, FL: H&H Pub. Co., 1997.

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Kugathasan, Thambyrajah. Foundations of mathematics. [Canada?]: Vretta, 2013.

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

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Caicedo, Andrés, James Cummings, Peter Koellner, and Paul Larson, eds. Foundations of Mathematics. Providence, Rhode Island: American Mathematical Society, 2017. http://dx.doi.org/10.1090/conm/690.

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Foundations of bilevel programming. Dordrecht: Kluwer Academic, 2002.

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Kurtz, David C. Foundations of abstract mathematics. New York: McGraw-Hill, 1992.

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Book chapters on the topic "Foundations of mathematics"

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Schroeder, Severin. "Foundations of Mathematics." In Wittgenstein on Mathematics, 3–8. New York, NY : Routledge, 2021. | Series: Wittgenstein’s thought and legacy: Routledge, 2020. http://dx.doi.org/10.4324/9781003056904-2.

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Scholz, Erhard. "Foundations of Mathematics." In DMV Seminar, 315–72. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8278-1_10.

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Crabb, Michael Charles, and Ioan Mackenzie James. "Foundations." In Springer Monographs in Mathematics, 141–85. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-1265-5_4.

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Schneider, Peter. "Foundations." In Springer Monographs in Mathematics, 1–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04728-6_1.

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Lam, Tsit Yuen. "Foundations." In Springer Monographs in Mathematics, 9–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-34575-6_2.

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Rodríguez, Rubí E., Irwin Kra, and Jane P. Gilman. "Foundations." In Graduate Texts in Mathematics, 15–38. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4419-7323-8_2.

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Knarr, Norbert. "Foundations." In Lecture Notes in Mathematics, 5–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0096312.

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Bobenko, Alexander, and Yuri Suris. "Foundations." In Graduate Studies in Mathematics, 331–68. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/098/09.

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Lam, T. Y. "Foundations." In Graduate Studies in Mathematics, 1–25. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/067/01.

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Gilman, Jane P., Irwin Kra, and Rubí E. Rodríguez. "Foundations." In Graduate Texts in Mathematics, 7–21. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-74715-6_2.

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Conference papers on the topic "Foundations of mathematics"

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Schumann, Andrew, and Alexander V. Kuznetsov. "Talmudic Foundations of Mathematics." In 10th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS). EAI, 2017. http://dx.doi.org/10.4108/eai.22-3-2017.152404.

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Hildenbrand, Dietmar. "Foundations of Geometric Algebra computing." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756054.

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Khots, Dmitriy, Boris Khots, Luigi Accardi, Guillaume Adenier, Christopher Fuchs, Gregg Jaeger, Andrei Yu Khrennikov, Jan-Åke Larsson, and Stig Stenholm. "Physical Aspects of Observer’s Mathematics." In FOUNDATIONS OF PROBABILITY AND PHYSICS—5. AIP, 2009. http://dx.doi.org/10.1063/1.3109955.

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Chashechkin, Yuli D. "Foundations of Engineering Mathematics for Fluid Flows." In Topical Problems of Fluid Mechanics 2022. Institute of Thermomechanics of the Czech Academy of Sciences, 2022. http://dx.doi.org/10.14311/tpfm.2022.002.

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Based on a definition of engineering mathematics, following from Aristotle and Leibniz's philosophical principles for science, the system of fundamental equations was selected to describe fluid flow dynamics and structure. Complete solutions of the linearized system in total and abridge versions, constructed with the condition of compatibility, describe different waves and ligaments. Weak non-linear approximation describes the effect of flow components interactions and boundary conditions impact. In experiments, ligaments are manifested as sharp interfaces and fibrous. Numerical patterns of stratified flows are analyzed and compared with schlieren visualization of flow fields.
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Muktibodh, A. S. "Foundations of isomathematics." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825589.

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Khots, Boris, and Dmitriy Khots. "The foundations of quantum mechanics in Observer's Mathematics." In QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS 6. AIP, 2012. http://dx.doi.org/10.1063/1.4773156.

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Yingxu Wang. "On abstract intelligence and its denotational mathematics foundations." In 2008 7th IEEE International Conference on Cognitive Informatics (ICCI). IEEE, 2008. http://dx.doi.org/10.1109/coginf.2008.4639146.

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Khots, Dmitriy, Boris Khots, and Andrei Yu Khrennikov. "Quantum Theory from Observer’s Mathematics Point of View." In QUANTUM THEORY: Reconsideration of Foundations—5. AIP, 2010. http://dx.doi.org/10.1063/1.3431504.

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Petrov, I., Al Cheremensky, George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "On Foundations of Newtonian Mechanics." In 35TH INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS”: AMEE-2009. AIP, 2009. http://dx.doi.org/10.1063/1.3271606.

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Khots, Boris, and Dmitriy Khots. "Probability in quantum theory from observer's mathematics point of view." In FOUNDATIONS OF PROBABILITY AND PHYSICS - 6. AIP, 2012. http://dx.doi.org/10.1063/1.3688966.

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Reports on the topic "Foundations of mathematics"

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Awodey, Steven. New Mathematics of Information: Homotopical and Higher Categorical Foundations of Information and Computation. Fort Belvoir, VA: Defense Technical Information Center, September 2014. http://dx.doi.org/10.21236/ada610334.

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Lewis, Alain A. Some Aspects of Constructive Mathematics That Are Relevant to the Foundations of Neoclassical Mathematical Economics and the Theory of Games. Fort Belvoir, VA: Defense Technical Information Center, April 1988. http://dx.doi.org/10.21236/ada198446.

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Frantseva, Anastasiya. The video lectures course "Elements of Mathematical Logic" for students enrolled in the Pedagogical education direction, profile Primary education. Frantseva Anastasiya Sergeevna, April 2021. http://dx.doi.org/10.12731/frantseva.0411.14042021.

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The video lectures course is intended for full-time and part-time students enrolled in "Pedagogical education" direction, profile "Primary education" or "Primary education - Additional education". The course consists of four lectures on the section "Elements of Mathematical Logic" of the discipline "Theoretical Foundations of the Elementary Course in Mathematics" on the profile "Primary Education". The main lecture materials source is a textbook on mathematics for students of higher pedagogical educational institutions Stoilova L.P. (M.: Academy, 2014.464 p.). The content of the considered mathematics section is adapted to the professional needs of future primary school teachers. It is accompanied by examples of practice exercises from elementary school mathematics textbooks. The course assumes students productive learning activities, which they should carry out during the viewing. The logic’s studying contributes to the formation of the specified profile students of such professional skills as "the ability to carry out pedagogical activities for the implementation of primary general education programs", "the ability to develop methodological support for programs of primary general education." In addition, this section contributes to the formation of such universal and general professional skills as "the ability to perform searching, critical analysis and synthesis of information, to apply a systematic approach to solving the assigned tasks", "the ability to participate in the development of basic and additional educational programs, to design their individual components". The video lectures course was recorded at Irkutsk State University.
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Seldin, Jonathan. Mathesis: The Mathematical Foundation of Ulysses. Fort Belvoir, VA: Defense Technical Information Center, November 1987. http://dx.doi.org/10.21236/ada195379.

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Geman, Stuart. Mathematical Foundations for Object Recognition and Image Analysis. Fort Belvoir, VA: Defense Technical Information Center, December 2000. http://dx.doi.org/10.21236/ada389508.

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Beidler, John. Ada Support for the Mathematical Foundations of Software Engineering. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada278031.

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Katsoulakis, Markos A., and Luc Rey-Bellet. Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report. Office of Scientific and Technical Information (OSTI), November 2018. http://dx.doi.org/10.2172/1483471.

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Raychev, Nikolay. Mathematical foundations of neural networks. Implementing a perceptron from scratch. Web of Open Science, August 2020. http://dx.doi.org/10.37686/nsr.v1i1.74.

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Daro, Phil, Frederic Mosher, and Tom Corcoran. Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. Consortium for Policy Research in Education, January 2011. http://dx.doi.org/10.12698/cpre.2011.rr68.

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Plechac, Petr, and Dionisios G. Vlachos. Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design. Office of Scientific and Technical Information (OSTI), January 2018. http://dx.doi.org/10.2172/1417749.

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