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Relevant bibliographies by topics / Mathematical conjectures

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Academic literature on the topic 'Mathematical conjectures'

Author: Grafiati

Published: 2 November 2024

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Journal articles on the topic "Mathematical conjectures"

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Davies, Alex, Petar Veličković, Lars Buesing, et al. "Advancing mathematics by guiding human intuition with AI." Nature 600, no. 7887 (2021): 70–74. http://dx.doi.org/10.1038/s41586-021-04086-x.

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AbstractThe practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and t

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Zeybek Simsek, Zulfiye. "Constructing-Evaluating-Refining Mathematical Conjectures and Proofs." International Journal for Mathematics Teaching and Learning 21, no. 2 (2020): 197–215. http://dx.doi.org/10.4256/ijmtl.v21i2.263.

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This study focused on investigating the ability of 58 pre-service mathematics teachers' (PSMTs) to construct-evaluate-refine mathematical conjectures and proofs. The PSMTs enrolled in a three-credit mathematics course that offered various opportunities for them to engage with mathematical activities including constructing-evaluating-refining proofs in various topics. The PSMTs' proof constructions were coded in three categories as: Type P1, Type P2 and Type P3 in decreasing levels of sophistication (from a mathematical stand point) and the constructions of conjectures were coded in two categor

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Astawa, I. Wayan Puja. "The Differences in Students’ Cognitive Processes in Constructing Mathematical Conjecture." JPI (Jurnal Pendidikan Indonesia) 9, no. 1 (2020): 49. http://dx.doi.org/10.23887/jpi-undiksha.v9i1.20846.

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Constructing mathematical conjectures involves individuals’ unique and complex cognitive processes in which have not yet fully understood. The cognitive processes refer to any of the mental functions assumed to be involved in the acquisition, storage, interpretation, manipulation, transformation, and the use of knowledge. Understanding of these cognitive processes may assist individuals in constructing mathematical conjectures. This study aimed to describe the differences in students’ cognitive processes in constructing mathematical conjecture which is based on their mathematical ability and g

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Amir, Firana, and Mohammad Faizal Amir. "Action Proof: Analyzing Elementary School Students Informal Proving Stages through Counter-examples." International Journal of Elementary Education 5, no. 2 (2021): 401. http://dx.doi.org/10.23887/ijee.v5i3.35089.

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Both female and male elementary school students have difficulty doing action proof by using manipulative objects to provide conjectures and proof of the truth of a mathematical statement. Counter-examples can help elementary school students build informal proof stages to propose conjectures and proof of the truth of a mathematical statement more precisely. This study analyzes the action proof stages through counter-examples stimulation for male and female students in elementary schools. The action proof stage in this study focuses on three stages: proved their primitive conjecture, confronted

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BARTH, PETER. "IWASAWA THEORY FOR ONE-PARAMETER FAMILIES OF MOTIVES." International Journal of Number Theory 09, no. 02 (2012): 257–319. http://dx.doi.org/10.1142/s1793042112501357.

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In [A formulation of conjectures on p-adic zeta functions in non-commutative Iwasawa theory, in Proc. St. Petersburg Mathematical Society, Vol. 12, American Mathematical Society Translations, Series 2, Vol. 219 (American Mathematical Society, Providence, RI, 2006), pp. 1–85] Fukaya and Kato presented equivariant Tamagawa number conjectures that implied a very general (non-commutative) Iwasawa main conjecture for rather general motives. In this article we apply their methods to the case of one-parameter families of motives to derive a main conjecture for such families. On our way there we get s

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Mollin, R. A., and H. C. Williams. "Proof, Disproof and Advances Concerning Certain Conjectures on Real Quadratic Fields." Canadian Journal of Mathematics 47, no. 5 (1995): 1023–36. http://dx.doi.org/10.4153/cjm-1995-054-7.

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AbstractThe purpose of this paper is to address conjectures raised in [2]. We show that one of the conjectures is false and we advance the proof of another by proving it for an infinite set of cases. Furthermore, we give hard evidence as to why the conjecture is true and show what remains to be done to complete the proof. Finally, we prove a conjecture given by S. Louboutin, for Mathematical Reviews, in his discussion of the aforementioned paper.

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Barahmand, Ali. "On Mathematical Conjectures and Counterexamples." Journal of Humanistic Mathematics 9, no. 1 (2019): 295–303. http://dx.doi.org/10.5642/jhummath.201901.17.

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Barbosa, Lucas De Souza, Cinthya Maria Schneider Meneghetti, and Cristiana Andrade Poffal. "O uso de geometria dinâmica e da investigação matemática na validação de propriedades geométricas." Ciência e Natura 41 (July 16, 2019): 12. http://dx.doi.org/10.5902/2179460x33752.

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This paper presents an activity on Geometry of position using GeoGebra software, based on Mathematical Investigation. The Dynamic Geometry, through software, becomes a tool for the formation of a mental image of abstract objects and motivation to introduce the idea of justifying its properties through arguments external to software. Allied to Dynamic Geometry, Mathematical Investigation guides the possible ways to construct conjectures and justifications and emphasizes that conjecture and looking for properties are as important as demonstrating them, since it shows the Mathematics as a knowled

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Rizos, Ioannis, and Nikolaos Gkrekas. "Is there room for conjectures in mathematics? The role of dynamic geometry environments." European Journal of Science and Mathematics Education 11, no. 4 (2023): 589–98. http://dx.doi.org/10.30935/scimath/13204.

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Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after discussing at a theoretical level the concepts of proof and conjecture, both in a paper-and-pencil environment and in a dynamic geometry environment (DGE) as well as how school practice affects them, we fully explain a task involving various mathematical

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Formanowicz, Piotr, and Krzysztof Tanaś. "The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks." International Journal of Applied Mathematics and Computer Science 22, no. 3 (2012): 765–78. http://dx.doi.org/10.2478/v10006-012-0057-y.

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Abstract It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians worki

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Dissertations / Theses on the topic "Mathematical conjectures"

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Chilstrom, Peter. "Singular Value Inequalities: New Approaches to Conjectures." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/443.

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Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular val

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Bergqvist, Tomas. "To explore and verify in mathematics." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-9345.

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This dissertation consists of four articles and a summary. The main focus of the studies is students' explorations in upper secondary school mathematics. In the first study the central research question was to find out if the students could learn something difficult by using the graphing calculator. The students were working with questions connected to factorisation of quadratic polynomials, and the factor theorem. The results indicate that the students got a better understanding for the factor theorem, and for the connection between graphical and algebraical representations. The second study

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Keliher, Liam. "Results and conjectures related to the sharp form of the Littlewood conjecture." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23402.

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Let $0<n sb1<n sb2< cdots<n sb{N}$ be integers for $N in{ rm I !N},$ and let $ lambda sb1, lambda sb2, ..., lambda sb{N}$ be complex numbers of modulus 1. If $f( theta)= lambda sb1e sp{in sb1 theta}+ lambda sb2 e sp{in sb2 theta}+ cdots+ lambda sb{N}e sp{in sb{N} theta},$ and $g( theta)=e sp{i theta}+e sp{2 theta}+ cdots+e sp{iN theta},$ then a conjecture originally proposed by Hardy and Littlewood states that $ int sbsp{0}{2 pi} vert g( theta) vert sp{p}{d theta over2 pi} leq int sbsp{0}{2 pi} vert f( theta) vert sp{p}{d theta over2 pi}$ for $0<p leq2,$ and that the inequality is reversed for

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Tran, Anh Tuan. "The volume conjecture, the aj conjectures and skein modules." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44811.

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This dissertation studies quantum invariants of knots and links, particularly the colored Jones polynomials, and their relationships with classical invariants like the hyperbolic volume and the A-polynomial. We consider the volume conjecture that relates the Kashaev invariant, a specialization of the colored Jones polynomial at a specific root of unity, and the hyperbolic volume of a link; and the AJ conjecture that relates the colored Jones polynomial and the A-polynomial of a knot. We establish the AJ conjecture for some big classes of two-bridge knots and pretzel knots, and confirm the volu

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Cheukam, Ngouonou Jovial. "Apprentissage automatique de cartes d’invariants d’objets combinatoires avec une application pour la synthèse d’algorithmes de filtrage." Electronic Thesis or Diss., Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2024. http://www.theses.fr/2024IMTA0418.

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Pour améliorer l’efficacité des méthodes de résolution de nombreux problèmes d’optimisation combinatoires de notre vie quotidienne, nous utilisons la programmation par contraintes pour générer automatiquement des conjectures. Ces conjectures caractérisent des objets combinatoires utilisés pour modéliser ces problèmes d’optimisation. Ce sont notamment les graphes, les arbres, les forêts, les partitions et les séquences. Contrairement à l’état de l’art, le système, dénommé Bound Seeker, que nous avons élaboré ne génère pas seulement de manière indépendante les conjectures, mais il explicite auss

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Mostert, Pieter. "Stark's conjectures." Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/18998.

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Includes bibliographical references.<br>We give a slightly more general version of the Rubin-Stark conjecture, but show that in most cases it follows from the standard version. After covering the necessary background, we state the principal Stark conjecture and show that although the conjecture depends on a choice of a set of places and a certain isomorphism of Q[GJ-modules, it is independent of these choices. The conjecture is shown to satisfy certain 'functoriality' properties, and we give proofs of the conjecture in some simple cases. The main body of this dissertation concerns a slightly m

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Puente, Philip C. "Crystallographic Complex Reflection Groups and the Braid Conjecture." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011877/.

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Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the space with reflecting hyperplanes removed has a presentation mimicking that of the Coxeter presentation;

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Narayanan, Sridhar. "Selberg's conjectures on Dirichlet series." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55517.

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In this thesis we introduce the Rankin-Selberg hypothesis in the Selberg Class to obtain a non-vanishing theorem on line $ Re(s)=1$ for a certain sub-class of functions in this class. We also prove that the Selberg's Conjectures imply the $S sb{K}$-primitivity of $ zeta sb{K}.$

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Jost, Thomas. "On Donovan's conjecture." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318785.

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Khoury, Joseph. "La conjecture de Serre." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/9554.

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Une des grandes reussites de l'algebre commutatif des annees soixante-dix etait la preuve de la "conjecture de Serre". Dans ces papiers, j'expose deux solutions differentes de cette conjecture. Les deux solutions sont exposees avec beaucoup de details de facon qu'un lecteur qui n'a pas une connaissance profonde en algebre commutatif puisse les comprendre sans beaucoup de difficultes.

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Books on the topic "Mathematical conjectures"

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Nickerson, Raymond S. Mathematical reasoning: Patterns, problems, conjectures, and proofs. Psychology Press, 2010.

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Nickerson, Raymond S. Mathematical reasoning: Patterns, problems, conjectures, and proofs. Psychology Press, 2010.

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E, Ladas G., ed. Dynamics of second order rational difference equations: With open problems and conjectures. Chapman & Hall/CRC, 2002.

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Graczyk, Jacek. The real Fatou conjecture. Princeton University Press, 1998.

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Schwartz, Diane Driscoll. Conjecture & proof: An introduction to mathematical thinking. Saunders College Pub., 1997.

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Charles, Figuieres, ed. Theory of conjectural variations. World Scientific, 2004.

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Salamon, Peter. Facts, conjectures, and improvements for simulated annealing. Society for Industrial and Applied Mathematics, 2003.

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Gessen, Masha. Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime. Icon Books, 2011.

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Ecalle, Jean. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Hermann, 1992.

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Gul, Faruk. Foundation of dynamic monopoly and the Coase conjecture. Institute for Mathematical Studies in the Social Sciences, Stanford University, 1985.

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Book chapters on the topic "Mathematical conjectures"

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Tenenbaum, Gérald, and Michel Mendès France. "The major conjectures." In The Student Mathematical Library. American Mathematical Society, 2000. http://dx.doi.org/10.1090/stml/006/05.

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Leuschke, Graham, and Roger Wiegand. "The Brauer-Thrall conjectures." In Mathematical Surveys and Monographs. American Mathematical Society, 2012. http://dx.doi.org/10.1090/surv/181/15.

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Dutta, S. P. "Syzygies and Homological Conjectures." In Mathematical Sciences Research Institute Publications. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3660-3_7.

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Rabe, Markus N., and Christian Szegedy. "Towards the Automatic Mathematician." In Automated Deduction – CADE 28. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_2.

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AbstractOver the recent years deep learning has found successful applications in mathematical reasoning. Today, we can predict fine-grained proof steps, relevant premises, and even useful conjectures using neural networks. This extended abstract summarizes recent developments of machine learning in mathematical reasoning and the vision of the N2Formal group at Google Research to create an automatic mathematician. The second part discusses the key challenges on the road ahead.

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Baldwin, John T. "Vaught and Morley Conjectures for ω-Stable Countable Theories." In Perspectives in Mathematical Logic. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-662-07330-8_18.

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Jahnel, Jörg. "Conjectures on the asymptotics of points of bounded height." In Mathematical Surveys and Monographs. American Mathematical Society, 2014. http://dx.doi.org/10.1090/surv/198/03.

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Shekhar, Sudhanshu, and R. Sujatha. "Introduction to the Conjectures of Birch and Swinnerton-Dyer." In Mathematical Lectures from Peking University. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6664-2_1.

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Carmona, Rene, and Frederic Cerou. "Transport by Incompressible random velocity fields: Simula- tions & Mathematical Conjectures." In Mathematical Surveys and Monographs. American Mathematical Society, 1999. http://dx.doi.org/10.1090/surv/064/04.

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Mitchell, Stephen A. "On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint." In Mathematical Sciences Research Institute Publications. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4613-9526-3_7.

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Dinneen, Michael J. "A Program-Size Complexity Measure for Mathematical Problems and Conjectures." In Computation, Physics and Beyond. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27654-5_7.

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Conference papers on the topic "Mathematical conjectures"

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Herlina, Dina, Ely Susanti, Elika Kurniadi, and Novita Sari. "Ability to prove mathematical conjectures through ICT-assisted creative problem solving learning for class VIII students." In THE 2ND NATIONAL CONFERENCE ON MATHEMATICS EDUCATION (NACOME) 2021: Mathematical Proof as a Tool for Learning Mathematics. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0142729.

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Castle, Sarah D. "Embracing Mathematical Conjecture Through Coding and Computational Thinking." In SIGCSE 2024: The 55th ACM Technical Symposium on Computer Science Education. ACM, 2024. http://dx.doi.org/10.1145/3626253.3635561.

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Gurevich, Shagmar. "Proof of the Kurlberg-Rudnick Rate Conjecture." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193112.

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Burqan, Aliaa. "New algebraic insights to the Goldbach conjecture." In 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS5). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0228106.

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Wang, Yu. "The Mathematical Modeling and Proof of the Goldbach Conjecture." In 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018). Atlantis Press, 2018. http://dx.doi.org/10.2991/msam-18.2018.6.

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Chen, Gen-Fang. "Generalization of Steinhaus conjecture." In International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), edited by Zhen Wang and Dunhui Xiao. SPIE, 2023. http://dx.doi.org/10.1117/12.2678950.

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Cruz-Uribe, David, José María Martell, and Carlos Pérez. "A note on the off-diagonal Muckenhoupt-Wheeden conjecture." In V International Course of Mathematical Analysis in Andalusia. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789814699693_0006.

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CHIA, G. L., and SIEW-HUI ONG. "ON BARNETTE'S CONJECTURE AND CBP GRAPHS WITH GIVEN NUMBER OF HAMILTON CYCLES." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0012.

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Huang, Junjie, Ying Xiao, and Chenglian Liu. "A study of android calculator based on Lemoine’s conjecture." In MATHEMATICAL METHODS AND COMPUTATIONAL TECHNIQUES IN SCIENCE AND ENGINEERING II. Author(s), 2018. http://dx.doi.org/10.1063/1.5045419.

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Jansirani, N., R. Rama, and V. R. Dare. "A counter example to Steinberg conjecture." In INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN MATHEMATICS AND COMPUTATIONAL ENGINEERING: ICRAMCE 2022. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0156823.

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