Relevant bibliographies by topics / Foundations of mathematics

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  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: 17 June 2025

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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 (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 (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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Moldovan, Angelo-Vlad. "Between Pathology and Well-Behaviour – A Possible Foundation for Tame Mathematics." Studia Universitatis Babeș-Bolyai Philosophia 67, Special Issue (2022): 67–81. http://dx.doi.org/10.24193/subbphil.2022.sp.iss.04.

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"An in-depth examination of the foundations of mathematics reveals how its treatment is centered around the topic of “unique foundation vs. no need for a foundation” in a traditional setting. In this paper, I show that by applying Shelah’s stability procedures to mathematics, we confine ourselves to a certain section that manages to escape the Gödel phenomenon and can be classified. We concentrate our attention on this mainly because of its tame nature. This result makes way for a new approach in foundations through model-theoretic methods. We then cover Penelope Maddy’s “foundational virtues” and what it means for a theory to be foundational. Having explored what a tame foundation can amount to, we argue that it can fulfil some of Maddy’s foundational qualities. In the last part, we will examine the consequences of this new paradigm – some philosophical in nature – on topics like philosophy of mathematical practice, the incompleteness theorems and others. Keywords: foundations of mathematics, tame mathematics, clarity-based knowledge, philosophy of mathematical practice, incompleteness theorems "
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Woleński, Jan. "Foundations of Mathematics and Mathematical Practice. The Case of Polish Mathematical School." Studia Historiae Scientiarum 21 (August 26, 2022): 237–57. https://doi.org/10.4467/2543702XSHS.22.007.15973.

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The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, nonconstructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland.
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Bagaria, Joan. "On Turing’s legacy in mathematical logic and the foundations of mathematics." Arbor 189, no. 764 (2013): a079. http://dx.doi.org/10.3989/arbor.2013.764n6002.

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Khudaikulova, Saida, and Shahabbas Ruzikulov. "QUANTUM MATHEMATICS AND PHYSICS: STUDYING MATHEMATICAL FOUNDATIONS AND APPLICATIONS." MEDICINE, PEDAGOGY AND TECHNOLOGY: THEORY AND PRACTICE 2, no. 12 (2024): 293–95. https://doi.org/10.5281/zenodo.14549617.

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Quantum mechanics and quantum physics have revolutionized our understanding of the fundamental nature of reality. At the core of this revolution lies quantum mathematics, which provides the mathematical foundation for describing the motion of particles at microscopic scales. This article explores the fundamental mathematical structures of quantum mechanics, including Hilbert spaces, operators, and wave functions, as well as their applications in modeling physical systems. The research also examines how quantum physics contrasts with classical physics concepts and offers new insights into topics such as quantum entanglement, superposition, and quantum computing. By analyzing the mathematical foundations of quantum theories, the article aims to shed light on the intersection of mathematics and physics, offering a deeper understanding of how mathematical formulas help predict and explain quantum phenomena. Furthermore, it discusses the potential implications of quantum mathematics in emerging fields such as quantum computing and cryptography.
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Mcavaney, K. L., Albert D. Polimeni, and H. Joseph Straight. "Foundations of Discrete Mathematics." Mathematical Gazette 76, no. 477 (1992): 433. http://dx.doi.org/10.2307/3618422.

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Shiu, P., and Paul Taylor. "Practical Foundations of Mathematics." Mathematical Gazette 84, no. 499 (2000): 175. http://dx.doi.org/10.2307/3621547.

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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 (2014): 124–50. http://dx.doi.org/10.1086/676950.

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

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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.<br>Includes bibliographical references.<br>"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.<br>by Gabriel Uzquiano.<br>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. Dover Publications, 2008.

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

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

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

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

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

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

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Kugathasan, Thambyrajah. Foundations of mathematics. Vretta, 2013.

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

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Dempe, Stephan. Foundations of bilevel programming. Springer, 2011.

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Book chapters on the topic "Foundations of mathematics"

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Arlinghaus, Sandra L., Joseph J. Kerski, and William C. Arlinghaus. "Mathematics' Foundations." In Teaching Mathematics Using Interactive Mapping. CRC Press, 2023. http://dx.doi.org/10.1201/9781003305613-7.

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Arlinghaus, Sandra L., Joseph J. Kerski, and William C. Arlinghaus. "Mathematics' Foundations." In Teaching Mathematics Using Interactive Mapping. CRC Press, 2023. http://dx.doi.org/10.1201/9781003305613-6.

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

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Schroeder, Severin. "Foundations of Mathematics." In Wittgenstein on Mathematics. Routledge, 2020. http://dx.doi.org/10.4324/9781003056904-2.

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Hoffmann, Dirk W. "Foundations of Mathematics." In Gödel's Incompleteness Theorems. Springer Berlin Heidelberg, 2024. http://dx.doi.org/10.1007/978-3-662-69550-0_2.

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

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

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

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

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

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Conference papers on the topic "Foundations of mathematics"

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Naraharisetti, Pavan Kumar. "Laying the foundations of Machine Learning in Undergraduate Education through Engineering Mathematics." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.121271.

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Some educators place an emphasis on the commonalities between engineering mathematics with process control, among others and this helps students see the bigger picture of what is being taught. Traditionally, some of the concepts such as diffusion and heat transfer are taught with a mathematical point of view. Now-a-days, Machine Learning (ML) has emerged as topic of greater interest to both educators and learners and new and disparate modules are sometimes introduced to teach the same. With the emergence of these new topics, some students (falsely) believe that ML is a new field that is somehow different and not linked to engineering mathematics. In this work, we show the link between the different topics from engineering mathematics, that are traditionally taught in UG education, with ML. We hope that educators and learners will appreciate the treatise and think differently, and we further hope that this will further increase the interest to improve ML models.
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Chen, Lijie, Jiatu Li, and Igor C. Oliveira. "Reverse Mathematics of Complexity Lower Bounds." In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2024. http://dx.doi.org/10.1109/focs61266.2024.00040.

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Ford Versypt, Ashlee N. "Design Education Across the Curriculum for the Future of Design." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.181858.

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The future of computer-aided process design hinges on continued recruitment, training, and retention of the next generations of engineers. Many elementary and secondary school programs focused on engineering have made substantial impacts in informing children about careers in science, technology, engineering, and mathematics (STEM). A report by the National Academies established three general principles for pre-college engineering education, the first of which is that elementary and secondary engineering education should emphasize engineering design. Curricula focused on teaching the engineering design process have been developed for K-12 students and educators... (ABSTRACT ABBREVIATED)
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Zavala, Victor M. "From Process to Systems Design: A Perspective on the Future of Design Education." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.184659.

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Chemical engineers are natural �systems-thinkers�; this is a skill that allows us to analyze highly complex processes that involve heterogeneous components, phenomena, and scales. Systems-thinking skills are fostered in the chemical engineering curriculum via integrative and project-based courses, such as process/product design and laboratories. However, existing curricula tends to focus scope to product/process boundaries, offering limited opportunities to capture connections to behavior occurring at small scales (e.g., atomistic and molecular) and at large scales (e.g., supply chains, policy, markets, and infrastructures). This limit in scope can hinder our ability to appreciate how products/processes that we develop impact society, markets, and the environment (e.g., the opioid addiction crisis, environmental impacts of forever chemicals and chemical fertilizers, and electricity markets). This limit in scope can also hinder our ability to appreciate how emerging tools from the molecular sciences can help us design better products/processes. Expanding the boundaries of our thinking is essential in overcoming these limitations. In this perspective, I discuss how emerging concepts and technologies from machine learning, data science, environmental sciences, molecular simulations, and mathematics provide powerful tools to help foster systems-thinking over a broad set of scales and to help establish connections with non-traditional disciplines (e.g., social sciences). In addition, I discuss the need to create new conceptual frameworks, case studies, and software that can help foster systems-thinking.
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Fan, Jia, Mingyang Li, Yueen Li, Lei Zhang, and Zhen Wang. "Leveraging foundational mathematics for advancements in artificial intelligence." In International Conference on Mechatronics and Intelligent Control (ICMIC 2024), edited by Kun Zhang and Pascal Lorenz. SPIE, 2025. https://doi.org/10.1117/12.3054753.

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Santhamoorthy, Pooja Zen, and Selen Cremaschi. "Mathematical Optimization of Separator Network Design for Sand Management." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.154881.

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Sand produced along with well-production fluids accumulates in the surface facilities over time, taking valuable space, while the sand carried with the fluids damages downstream equipment. Thus, sand is separated from the fluid in the sand traps and separators and removed during periodic clean-ups. But at high sand productions, the probability of unscheduled facilities shutdowns increases. Such extreme production conditions can be handled by strategic planning and optimal design of the separator network to enable maximum sand separation at minimal equipment cost while ensuring the accumulation extent is within tolerable limits. This paper develops a mathematical model to optimize the separator network design to maximize sand separation while the sand accumulation extent and total equipment cost are minimal. The optimization model is formulated using multi-objective mixed-integer nonlinear programming (MINLP). The capabilities of the developed model to assist sand management in the separator network are demonstrated with a case study of optimizing the network for two wells producing sand particles of different sizes. A residence time distribution-based model is used to predict sand settling behavior. The developed Pareto Front shows the trade-off between the increase in total sand accumulation rate and total equipment cost for an increase in the fraction of sand settled.
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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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Chashechkin, Yu D. "ENGINEERING MATHEMATICS FOUNDATIONS IN AEROHYDRODYNAMICS." In ХХI International Conference on the Methods of Aerophysical Research (ICMAR 2022). Федеральное государственное бюджетное учреждение «Сибирское отделение Российской академии наук», 2022. http://dx.doi.org/10.53954/9785604788967_38.

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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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НИКОЛАУ, Лидия. "Теоретические основы обучения математике младших школьников как средство повышения качества математического образования". У Materialele Conferinţei Ştiinţifice Internaţionale "Abordări inter/transdisciplinare în predarea ştiinţelor reale, (concept STEAM)". Ion Creangă Pedagogical State University, 2024. https://doi.org/10.46727/c.steam-2024.p217-223.

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The article considers the question of the theoretical foundations of primary mathematical education. The interpretation of the concepts is given: "theoretical foundations of mathematics teaching methods", "methodological and mathematical foundations of the initial course of mathematics", "methodological and procedural foundations of mathematics teaching methods". Mathematical theories, which are the basis of primary mathematical education, are presented. Didactic principles, technologies and psychological concepts are highlighted, the application of which contributes to improving the quality of mathematical education.
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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. Defense Technical Information Center, 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. Defense Technical Information Center, 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, 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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Markova, Oksana, Serhiy Semerikov та Maiia Popel. СoCalc as a Learning Tool for Neural Network Simulation in the Special Course “Foundations of Mathematic Informatics”. Sun SITE Central Europe, 2018. http://dx.doi.org/10.31812/0564/2250.

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The role of neural network modeling in the learning сontent of special course “Foundations of Mathematic Informatics” was discussed. The course was developed for the students of technical universities – future IT-specialists and directed to breaking the gap between theoretic computer science and it’s applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic “Neural network and pattern recognition” of the special course “Foundations of Mathematic Informatics” are shown. The program code was presented in a CofeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network`s weights, etc. The features of the Kolmogorov–Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed.
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Seldin, Jonathan. Mathesis: The Mathematical Foundation of Ulysses. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada195379.

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

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Sitabkhan, Yasmin, Aida Alikova, Nurgul Toktogulova, Adema Zholdoshbekova, Wendi Ralaingita, and Jonathan Stern. Understanding Primary School Teachers’ Mathematical Knowledge for Teaching. RTI Press, 2024. http://dx.doi.org/10.3768/rtipress.2024.rr.0052.2409.

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We present the results from an exploratory study that aimed to measure teachers’ specialized knowledge in early mathematics during a pilot of an educational intervention using the Foundational Mathematical Knowledge for Teaching (FMKT) survey. The survey was administered to 323 teachers in the Kyrgyz Republic in 2021. We delve into survey results at two timepoints (pre- and post-intervention) to showcase the areas in which the intervention was successful and identify ongoing challenges in teacher knowledge. We found that the FMKT provided detailed, specific information on teacher learning and is an example of one way to center teacher knowledge in an instructional intervention.
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Beidler, John. Ada Support for the Mathematical Foundations of Software Engineering. Defense Technical Information Center, 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), 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, 2020. http://dx.doi.org/10.37686/nsr.v1i1.74.

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