Journal articles: 'Mathematical discovery and justification'

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Harris, Michael, and Mary Beth Ruskai. "Between discovery and justification." Mathematical Intelligencer 23, no. 1 (December 2001): 16–29. http://dx.doi.org/10.1007/bf03024513.

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Venukapalli, Sudhakar. "The Problematics of Scientific Discovery." European Journal of Theology and Philosophy 1, no. 3 (June 16, 2021): 1–8. http://dx.doi.org/10.24018/theology.2021.1.3.15.

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Historically, the problem of discovery or the problem of the genesis of scientific ideas has been taken seriously by the historians, psychologists, sociologists and philosophers who analyzed the creative thinking and formation of ideas and attempted to provide a meaningful account of them. In fact, the philosophical concern with scientific discovery is as old as science and philosophy of science themselves. However, almost throughout the first half of 20th century, philosophical reflection on the phenomenon of scientific discovery remained in a state of suspended animation. This is because the dominant trend in philosophy of science in this period outlawed it. The dominant view in philosophy of science maintained that the phenomenon of scientific discovery is philosophically irrelevant, and an adequate philosophical understanding of science should confine itself to the way in which scientific theories are justified; it was assumed that the process of justification is a neat, spick-and-span phenomenon eminently suited to be described in terms which are, logically speaking, cut and dry. The process of justification or evaluation according to this orthodox view constitutes the essence of science. Obviously, justification was demarcated from discovery. Justification, because of its supposed epistemic transparency, became the exclusive focus of philosophical attention to the detriment of discovery. The invidious distinction between discovery of scientific ideas and justification of finished ideas of science remained the catchword for a long time. This paper is an attempt to critically examine the nihilistic attitude of the dominant philosophies of science and to arrive at a philosophical theory of scientific discovery.

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Chick, Linda, Andrea S. Holmes, Nicole McClymonds, Steve Musick, Patti Reynolds, and Gilda Shultz. "Math by the Month: Read a Story, Discover the Math." Teaching Children Mathematics 14, no. 4 (November 2007): 224–25. http://dx.doi.org/10.5951/tcm.14.4.0224.

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“Math by the Month” activities are designed to engage students to think as mathematicians do. Students may work on the activities individually or in small groups, or the whole class may use these as problems of the week. Because no solutions are suggested, students will look to themselves for mathematical justification, thereby developing the confidence to validate their work.

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Morawski, Roman Z. "Measurement in the context of technoscientific research methodology." tm - Technisches Messen 87, no. 4 (April 26, 2020): 294–301. http://dx.doi.org/10.1515/teme-2019-0109.

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AbstractTechnoscience is a result of integration of technology with empirical sciences, including not only physical sciences, but also life sciences, social sciences and cognitive sciences. Further development of technoscience is unthinkable without extensive use of measurement and mathematical modelling, being two interrelated operations used for acquisition and representation of knowledge. Measurement fundamentals must, therefore, belong to the core of methodological instruction of young researchers in the domain of technoscience. This paper provides an outline of a sought-for discipline-independent programme of such formation, including a conceptual analysis of the key elements of the scientific method, with particular emphasis on the dialectical relationship between measurement and mathematical modelling, on the role of measurement in scientific prediction and explanation, on the role of measurement in the context of discovery and in the context of justification, as well as on the role of measurement in mitigating uncertainty of scientific knowledge.

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Kalish, Mia. "Multisensory mathematical gaming with the Energizer Bunny®." On the Horizon 25, no. 4 (September 11, 2017): 260–66. http://dx.doi.org/10.1108/oth-01-2017-0001.

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Purpose Educational mathematics game models tend to be simplistic because they are target-oriented. This paper aims to show how game models that facilitate discovery and analysis can be derived from successful implementations already existing in the popular culture. Design/methodology/approach Based loosely on Rivera’s Toward a visually-oriented school mathematics curriculum, the analysis combines perspectives from psychology, the graphic arts and object-oriented technology to illustrate the depth and breadth of mathematics in a popular commercial. Findings This paper offers an cross-disciplinary justification for expanding curricular resources beyond traditional alphanumeric metonymies. Illustrations show the mathematical concepts underlying the commercial structure as well as the multimodal, sensuous, semiotic aspects. Research limitations/implications This analytical approach is intended to precede development of game mechanics. It is focused on expanding the psychology of mathematics beyond the metonymic, canned problem approach and toward more dynamic examples. Practical implications Games based on real examples from popular culture can provide learners with an answer to the following question: When will I ever use this in real life? Social implications The philosophy here is that learners will be excited and challenged by engaging real-life mathematics. The issue has always been that people cannot imagine what they have never seen, and this approach gives them a way to see the math in action, answering Rivera’s question, “Can we make a game based on visualizing the mathematics” with a resounding “Yes!” Originality/value This paper offers a fresh approach to designing games for learning mathematics.

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Al-Faqih, Khaled M. S. "A Mathematical Phenomenon in the Quran of Earth-Shattering Proportions: A Quranic Theory Based On Gematria Determining Quran Primary Statistics (Words, Verses, Chapters) and Revealing Its Fascinating Connection with the Golden Ratio." Journal of Arts and Humanities 6, no. 6 (June 22, 2017): 52. http://dx.doi.org/10.18533/journal.v6i6.1192.

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As Almighty God has promised to protect the Quran from alteration, corruption or distortion. Historically, the scripture of the Quran has been subjected to various intense mathematically-based studies to reveal the protection mechanisms embedded in the composition of the Quran and to provide evidence of its credibility, authenticity and divinity. Indeed, this study has discovered a mathematical framework in the Quran based on gematria (Abjad numerals) that provides substantial evidence of Quran’s divine authorship and its perfect protection from human tampering. Essentially, this study has proposed a new research direction in numerological studies of the Quran. This study is textually based on the text delivered to Prophet Muhammad and drawn using the primary 28 alphabets of the Arabic language (Uthmanic manuscript), the 112 un-numbered Basmalahs and the names of the Quran chapters. A numerical value (70.44911244) which is referred to in this study as the Quran Constant (QC) was derived to represent the mathematical design of the Quran. The Quran Constant has been found to be fundamental to the current study, whereby the Quran Constant manifests in all derived mathematical equations. The ratio of the total number of chapters in the Quran (114) which represents the physical design of the Quran divided by the Quran Constant (70.44911244) which represents the mathematical design of the Quran gives 1.6181893; it is amazingly almost equal to the golden ratio. This study has also discovered that Almighty God embedded mathematical equations in the composition of the Quran that can easily lead to determination of the Quran’s primary statistics (words, verses and chapters). This study has admirably discovered three elegant mathematical equations that determine the total number of words, verses and chapters with great accuracy. More importantly, letters/word ratio calculated in this study can be practically seen as a validation criterion of both the total number of letters and the total number of words in the Quran. Finally, what does this proof? It proves that the Quran’s miraculous mathematical structure discovered in this study provides unequivocal mathematical proof that the Quran was divinely authored and has been perfectly preserved from the day it was revealed. Indeed, we are witnessing a mathematical phenomenon of earth-shattering proportions~ a miracle beyond earthly justification and human comprehension.

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Krause, Merton S. "Trying to Discover Sufficient Condition Causes." Methodology 6, no. 2 (January 2010): 59–70. http://dx.doi.org/10.1027/1614-2241/a000007.

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Scientific human psychology is ultimately obligated to be able to describe, predict, and causally explain the psychological phenomena of every individual person. If all of this can be done in terms of the interrelations of linear combinations of variables, then our heavy reliance on statistical linear models will have been justified. But can it? The rather imperfect fits of such models to our data do not provide such justification, so perhaps more fundamental forms of data representation would be prudent to look into, given our modern computing capabilities. Such a form is offered in this paper: point-to-point mappings from independent-variable to dependent-variable hyperspaces. Its mathematical relationship to linear models is defined and explains why linear models may often not be capable of fitting psychological data.

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Filipenko, A. "METHODOLOGICAL DISCOURSE IN ECONOMIC SCIENCE." ACTUAL PROBLEMS OF INTERNATIONAL RELATIONS, no. 132 (2017): 97–108. http://dx.doi.org/10.17721/apmv.2017.132.0.97-108.

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The article investigates the main approaches in the field of economic methodology. There are two methodological trends that emerged under the philosophy of science: naturalistic and constructivist. The first originates from Aristotle’s materialism, the second – from Plato’s ideas. Naturalized approaches eliminates distinction between the “context of discovery” and the “context of justification”. Constructivism related to cognitive methodological paradigm. It means that it is more sociological in nature, concerned with connections between individuals – with learning, inter-subjectivity, and social knowledge. Thus, the main methodological views on economic theory can, on the one hand, explain the economic life in all its dimensions – the micro – macro – and geo-economic levels, establish certain patterns and trends. On the other hand, using a variety of methods – logical, mathematical, statistical, computer models and programs, new phenomena and processes of local or global nature are explored. That creates conditions for accumulation of empirical and theoretical material that enriches the economic theory, generally shaping the economic science.

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Albert, Mélisande, Yann Bouret, Magalie Fromont, and Patricia Reynaud-Bouret. "Surrogate Data Methods Based on a Shuffling of the Trials for Synchrony Detection: The Centering Issue." Neural Computation 28, no. 11 (November 2016): 2352–92. http://dx.doi.org/10.1162/neco_a_00839.

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We investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered quantities—that is, quantities with zero mean under independence—to construct correct p-values, meaning that the corresponding tests control their false positive (FP) rate. Thanks to this study, we introduce a method, named permutation UE, which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count. Each involved single test of this procedure achieves the prescribed level, so that the corresponding multiple testing procedure controls the false discovery rate (FDR), and this with as few assumptions as possible on the underneath distribution, except independence and identical distribution across trials. The mathematical meaning of this assumption is discussed, and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross-trials stationarity. Some simulations show, moreover, that permutation UE outperforms the trial-shuffling of Pipa and Grün ( 2003 ) and the MTGAUE method of Tuleau-Malot et al. ( 2014 ) in terms of single levels and FDR, for a comparable amount of false negatives. Application to real data is also provided.

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Sovilj, Ranko, and Sanja Stojković Zlatanović. "Pravne, socijalne i etičke implikacije editovanja humanog genoma primenom tehnologije CRISPR/Cas9." Anali Pravnog fakulteta u Beogradu 69, no. 3 (September 24, 2021): 625–45. http://dx.doi.org/10.51204/anali_pfbu_21305a.

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Discovery of CRISPR/Cas9 technology produced a revolution in human medicine, because of the availability, efficiency and low cost, which has raised a number of questions. Given that by applying CRISPR/Cas9 technology we can program our future children and extend their life expectancy, question is whether we should allow it. The point of the paper is to determine the limits of legal admissibility and ethical justification of this procedure, considering contemporary legal theoretical views, ethical values and social significance. Using normative, comparative and sociological method the authors analyze the impact of biotechnology development, in the context of genetic interventions, on redefining the regulatory framework. Critical consideration in the context of legal standardization of human genetic interventions and meeting the interests of all participants, has been identified as a core subject of research, which will be considered in accordance with a holistic approach to the realization of human rights.

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Sliusarenko, M., O. Semenenko, T. Akinina, O. Zaritsky, and V. Ivanov. "DETERMINATION OF THE DISTRIBUTION FUNCTION OF THE TIME BETWEEN FAILURES OF A WEAPON MODEL WITHOUT TAKING INTO ACCOUNT THE ENEMY’S FIRE IMPACT." Collection of scientific works of Odesa Military Academy, no. 11 (December 27, 2019): 39–45. http://dx.doi.org/10.37129/2313-7509.2019.11.39-45.

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In the article, based on the analysis of the requirements for the readiness of weapons and military equipment during combat use and the reliability of their operation in the course of combat operations, it was discovered that one of the reasons that causes a discrepancy between the declared failures and real ones may be the incorrect choice and justification of the time distribution function up to the refusal of military means. As a rule, during the development of these tools, the function of distribution of time to failure is chosen by analogy with similar patterns of weapons and military equipment. In the theory of reliability, special attention is given to choosing the function of time-breaking non-response (failures or failures). Therefore, the article deals with the questions of evaluating the effectiveness of functioning of complex systems and methods of modeling the processes of their functioning, taking into account the laws of the distribution of random variables. The discrepancy between the declared irregularity of the military apparatus and the fact that is actually observed in the troops can be explained by the incorrectly accepted hypothesis about the distribution of time to failure. Therefore, the article analyzes the order of the justification of such a function without taking into account the enemy's fire impact and the proposed variant of determining the function of distribution of the time of work until the refusal of the model of military equipment. The article also cites the reasons for the discrepancy between the claimed missile defense equipment and what is actually observed in the troops. The proposed mathematical model of faultlessness, which at stages of designing and design will allow to set requirements to the model of technology with the help of analytical description. The sequence of calculations of non-failure indexes based on the use of Weibull distribution is substantiated.

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Dmitriev, I. S. "“I didn’t really think about it ” (M. Planck and the Quantum Revolution)." Discourse 5, no. 5 (December 18, 2019): 5–19. http://dx.doi.org/10.32603/2412-8562-2019-5-5-5-19.

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Introduction. In the philosophy of science great attention is traditionally paid to theoretical knowledge. However, scientific theories are considered, as a rule, as something already formed, whereas the analysis of the birth and formation of the theory plays a much smaller role. Among the various issues that arise at the intersection of philosophy and history of science the great attention of researchers is attracted by the question about the nature of scientific revolutions. In this work, the question is studied by examing the Planck’s discovery– whether a conservative in science to make a scientific revolution?Methodology and sources. Methodologically, the work is based on historical and scientific analysis of primary sources and research literature. Results and discussion. The paper according the results of the study of primary sources shows that the only desire Planck in his study of blackbody radiation and the only justification for his “Akt der Verzweilung” (Act of delays) was to obtain a “correct” mathematical formula “at any price”. As for the scientific revolution on 14 December 1900 – date of Planck’s speech at a meeting of the German physical society report on “the Theory of the distribution of the radiation energy of the normal spectrum” – that is the result of later historical reconstruction. Moreover, this “revolution” in 1900, and in subsequent years remained unnoticed by anyone, including Planck himself. Thus, the result of the study is a new look at the specifics of the contribution of the scientist standing on conservative scientific positions in the scientific revolution.Conclusion. Under certain circumstances, the main of which are the character of the task and readiness of the researcher, at least in part to “sacrifice principles” (or to simulate a departure from tradition) for the sake of formal success, the conservator may contribute to the further development of events that will eventually lead to the scientific revolution.

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Волошинов, Д., and Denis Voloshinov. "On the Peculiarities of the Constructive Solution For Dandelin Spheres Problem." Geometry & Graphics 6, no. 2 (August 21, 2018): 55–62. http://dx.doi.org/10.12737/article_5b559f018f85a7.77112269.

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This paper is devoted to analysis of Dandelin spheres problem based on the constructive geometric approach. In the paper it has been demonstrated that the traditional approach used to this problem solving leads to obtaining for only a limited set of heterogeneous solutions. Consideration of the problem in the context of plane and space’s projective properties by structural geometry’s methods allows interpret this problem’s results in a new way. In the paper it has been demonstrated that the solved problem has a purely projective nature and can be solved by a unified method, which is impossible to achieve if conduct reasoning and construct proofs only on affine geometry’s positions. The research’s scientific novelty is the discovery and theoretical justification of a new classification feature allowing classify as Dandelin spheres the set of spheres pairs with imaginary tangents to the quadric, as well as pairs of imaginary spheres with a unified principle for constructive interrelation of images, along with real solutions. The work’s practical significance lies in the extension of application areas for geometric modeling’s constructive methods to the solution of problems, in the impro vement of geometric theory, in the development of system for geometric modeling Simplex’s functional capabilities for tasks of objects and processes design automation. The algorithms presented in the paper demonstrate the deep projective nature and interrelation of such problems as Apollonius circles and spheres one, Dandelin spheres one and others, as well as lay the groundwork for researches in the direction of these problems’ multidimensional interpretations. The problem solution can be useful for second-order curves’ blending function realization by means of circles with a view to improve the tools of CAD-systems’ design automation without use of mathematical numerical methods for these purposes.

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Haddon, R. "Exercise – a mathematical justification." Journal of The Royal Naval Medical Service 103, no. 1 (2017): 61. http://dx.doi.org/10.1136/jrnms-103-61.

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Ostrowska, Urszula. "„Teraz […] już wiem, czego należy się wystrzegać i co czynić, by osiągnąć prawdę…”. Wokół Kartezjańskiej koncepcji cogito." Język. Religia. Tożsamość. 1, no. 23 (July 29, 2021): 317–32. http://dx.doi.org/10.5604/01.3001.0015.0344.

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The desire to achieve unquestionable knowledge and experience in history with the history of events in all spheres of history from time immemorial. For every scientist, finding the truth is conditio sine qua non, a challenge and a duty. In the course of the history of human thought in its development tirelessly searched for the most effective ways of achieving a revealing one that meets scientific criteria. In the history of science so far, many concepts in this field arouse unique ones for various reasons. Reflection on the legacy of the French physicist and mathematician René Descartes (1596-1650), one of the most outstanding scholars of the 17th century and one of the most famous and effective philosophers in history, is an inspiring source of research, his works, the reading of which verbally motivates reflection and also to the endless endeavors of mankind in the pursuit of knowledge to the discovery of truth. By exposing the power of reason of reason as the axis, I made the thinking person, adopting the credo in the form of I think, therefore I am… as the first principle of philosophy. There are interesting interpretations of Descartes' sentences, which testify to a fairly strong tradition on a global scale. The assessment from the justification of the grounds to questioning Descartes' concept must be found that the undoubted merit of the philosopher is inspiring his contemporaries and successors with faith in the power of reason and motivating them to take actions that prove its power, including efforts to put them into practice.

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Swinnerton-Dyer, Peter. "The justification of mathematical statements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1835 (September 12, 2005): 2437–47. http://dx.doi.org/10.1098/rsta.2005.1658.

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The uncompromising ethos of pure mathematics in the early post-war period was that any theorem should be provided with a proof which the reader could and should check. Two things have made this no longer realistic: (i) the appearance of increasingly long and complicated proofs and (ii) the involvement of computers. This paper discusses what compromises the mathematical community needs to make as a result.

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Li, Jichun. "Mathematical justification for RBF-MFS." Engineering Analysis with Boundary Elements 25, no. 10 (December 2001): 897–901. http://dx.doi.org/10.1016/s0955-7997(01)00078-9.

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Arkoudas, Konstantine, and Selmer Bringsjord. "Computers, Justification, and Mathematical Knowledge." Minds and Machines 17, no. 2 (June 23, 2007): 185–202. http://dx.doi.org/10.1007/s11023-007-9063-5.

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Kim, Huijin, Seongkyeong Kim, and Jongkyum Kwon. "6th grade students' awareness of why they need mathematical justification and their levels of mathematical justification." Mathematical Education 53, no. 4 (November 30, 2014): 525–39. http://dx.doi.org/10.7468/mathedu.2014.53.4.525.

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MacLean, James. "Transcending the Discovery—Justification Dichotomy." International Journal for the Semiotics of Law - Revue internationale de Sémiotique juridique 25, no. 1 (November 2, 2011): 123–41. http://dx.doi.org/10.1007/s11196-011-9244-7.

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Firdausy, Masyita Putri, and Abdul Haris Rosyidi. "MATHEMATICAL JUSTIFICATION OF SENIOR HIGH SCHOOL STUDENTS IN STATISTICS." MATHEdunesa 9, no. 2 (July 8, 2020): 297–304. http://dx.doi.org/10.26740/mathedunesa.v9n2.p297-304.

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Justification is the process of justifying a claim that is supported with evidence. Justification is the center of mathematics. Justification plays an important role in learning because it can help students improve understanding of mathematical concepts. By using a qualitative approach, this study aims to analyze the mathematical justification of high school students in solving problems on statistical topics. This research was conducted on 122 high school students by giving justification test questions on the topic of statistics resulted in 17% (21 students) included in the level justification level 3, 16% (19 students) included in level 2, 47% (47 students) included in level 1, and 20% (25 students) the rest are included in level 0. Further analysis was carried out to see the mathematical justification process by each level. The mathematical justification process consists of three stages, 1) the process of recognition; 2) the development process (building-with), and 3) understanding (awareness) process. Level 3 and level 2 students can recognize the problem and determine the right strategy to solve the problem, level 3 and level 2 students are also able to execute the strategy and interpret the results of the calculations they have done. The difference in level 3 and level 2 students lies in the understanding the concepts they have. Level 1 students can recognize problems and determine solution strategies. Although level 1 students can recognize and do calculations well, level 1 students fail in interpreting the results of calculations performed. While students who are level 0 are not able to recognize the problem, so level 0 students do not carry out the justification process.

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Shahruz, S. M. "Elimination of vibration localization: a mathematical justification." Journal of Sound and Vibration 283, no. 1-2 (May 2005): 449–58. http://dx.doi.org/10.1016/j.jsv.2004.05.016.

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Bresch, Didier, and Pascal Noble. "Mathematical Justification of a Shallow Water Model." Methods and Applications of Analysis 14, no. 2 (2007): 87–118. http://dx.doi.org/10.4310/maa.2007.v14.n2.a1.

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de Oliveira, César R., and Marciano Pereira. "Mathematical Justification of the Aharonov-Bohm Hamiltonian." Journal of Statistical Physics 133, no. 6 (November 11, 2008): 1175–84. http://dx.doi.org/10.1007/s10955-008-9631-y.

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Mizrahi, Moti. "Proof, Explanation, and Justification in Mathematical Practice." Journal for General Philosophy of Science 51, no. 4 (August 28, 2020): 551–68. http://dx.doi.org/10.1007/s10838-020-09521-7.

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Kuz'menko, N. E., and A. V. Stolyarov. "Mathematical justification of the r-centroid approximation." Journal of Quantitative Spectroscopy and Radiative Transfer 35, no. 5 (May 1986): 415–18. http://dx.doi.org/10.1016/0022-4073(86)90027-0.

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Cho, Jin-seok, Dong-hwan Lee, and Sung-joon Kim. "An Analysis on Mathematical Justification Types of Potential Mathematical Gifted Students." Korean Science Education Society for the Gifted 9, no. 3 (December 26, 2017): 145–56. http://dx.doi.org/10.29306/jseg.2017.9.3.145.

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Leplin, Jarrett. "The Bearing of Discovery on Justification." Canadian Journal of Philosophy 17, no. 4 (December 1987): 805–14. http://dx.doi.org/10.1080/00455091.1987.10715919.

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The point of the traditional distinction between the contexts of discovery and justification is to insist on the normative character of epistemology. The point is not to dismiss from epistemology merely the genesis of ideas; into the context of discovery go also descriptions of evaluative practices and decisions. However ideas are created, scrutinized, and judged, it is only the approbation to which they are entitled, accorded or not, that allegedly matters to epistemology. The criticism, familiar since N.R. Hanson's Patterns of Discovery, that philosophy ought not to ignore the genesis of ideas is ironically conservative. If what is not normative epistemology is to be ignored, then the distinction would have us ignore even the reception and appraisal of scientific ideas.

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Halttunen, Rauno. "Justification as a Process of Discovery." Ratio Juris 13, no. 4 (December 2000): 379–91. http://dx.doi.org/10.1111/1467-9337.00163.

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Ouncharoen, Rujira, Vladik Kreinovich, and Hung T. Nguyen. "Why Lattice-valued fuzzy values? A mathematical justification." Journal of Intelligent & Fuzzy Systems 29, no. 4 (October 23, 2015): 1421–25. http://dx.doi.org/10.3233/ifs-151558.

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Новиков and Artur Novikov. "MATHEMATICAL JUSTIFICATION PROCESS SORTING FOREST SEEDS BY SIZE." Voronezh Scientific-Technical Bulletin 4, no. 2 (June 30, 2015): 51–56. http://dx.doi.org/10.12737/14384.

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Supriani, Yani, Frena Fardillah, Tu rmudi, and Tatang Herman. "Developing Students’ Mathematical Justification Skill Through Experiential Learning." Journal of Physics: Conference Series 1179 (July 2019): 012070. http://dx.doi.org/10.1088/1742-6596/1179/1/012070.

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Donaldson, James A., and Daniel A. Williams. "The Linear Shallow Water Theory: A Mathematical Justification." SIAM Journal on Mathematical Analysis 24, no. 4 (July 1993): 892–910. http://dx.doi.org/10.1137/0524055.

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Hauk, Shandy, and Matthew A. Isom. "Fostering College Students’ Autonomy in Written Mathematical Justification." Investigations in Mathematics Learning 2, no. 1 (September 2009): 49–78. http://dx.doi.org/10.1080/24727466.2009.11790290.

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Castiñeira, Gonzalo, and Ángel Rodríguez-Arós. "Mathematical justification of a viscoelastic elliptic membrane problem." Comptes Rendus Mécanique 345, no. 12 (December 2017): 824–31. http://dx.doi.org/10.1016/j.crme.2017.09.007.

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Swart, Torben, and Vidian Rousse. "A Mathematical Justification for the Herman-Kluk Propagator." Communications in Mathematical Physics 286, no. 2 (November 27, 2008): 725–50. http://dx.doi.org/10.1007/s00220-008-0681-4.

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Bieda, Kristen N., and Megan Staples. "Justification as an Equity Practice." Mathematics Teacher: Learning and Teaching PK-12 113, no. 2 (February 2020): 102–8. http://dx.doi.org/10.5951/mtlt.2019.0148.

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This article highlights the role of students' engagement in mathematical justification in supporting classrooms that provide equitable access to mathematics and develop students' agency for doing mathematics.

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Han Sang-Ki. "Context of Discovery and Context of Justification." Studies in Philosophy East-West ll, no. 58 (December 2010): 441–63. http://dx.doi.org/10.15841/kspew..58.201012.441.

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Hoyningen-Huene, Paul. "Context of discovery and context of justification." Studies in History and Philosophy of Science Part A 18, no. 4 (December 1987): 501–15. http://dx.doi.org/10.1016/0039-3681(87)90005-7.

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Карнаух, Богдан Петрович. "Fault in tort law: Moral justification and mathematical explication." Problems of Legality, no. 141 (June 12, 2018): 54–64. http://dx.doi.org/10.21564/2414-990x.141.126813.

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Jeong, In Su. "Effects of Mathematical Justification on Problem Solving and Communication." Education of Primary School Mathematics 16, no. 3 (December 31, 2013): 267–83. http://dx.doi.org/10.7468/jksmec.2013.16.3.267.

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Rodríguez-Arós, Á., and J. M. Viaño. "Mathematical justification of viscoelastic beam models by asymptotic methods." Journal of Mathematical Analysis and Applications 370, no. 2 (October 2010): 607–34. http://dx.doi.org/10.1016/j.jmaa.2010.04.067.

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Burlov, Vyacheslav, and Fedor Gomazov. "Method of mathematical justification for using 3D zebra crossing." Transportation Research Procedia 36 (2018): 95–102. http://dx.doi.org/10.1016/j.trpro.2018.12.049.

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Yoshida, Zensho. "Singular Casimir Elements: Their Mathematical Justification and Physical Implications." Procedia IUTAM 7 (2013): 141–50. http://dx.doi.org/10.1016/j.piutam.2013.03.017.

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Maslov, V. P. "On the mathematical justification of experimental and computer physics." Mathematical Notes 92, no. 3-4 (September 2012): 577–79. http://dx.doi.org/10.1134/s0001434612090301.

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Rodríguez-Arós, Ángel. "Mathematical justification of an elastic elliptic membrane obstacle problem." Comptes Rendus Mécanique 345, no. 2 (February 2017): 153–57. http://dx.doi.org/10.1016/j.crme.2016.10.014.

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Medvedev, Aleksandr Mikhaylovich, Vladimir Nikolaevich Savin, and Valentin Ivanovich Shipulin. "THE MATHEMATICAL JUSTIFICATION OF THE EXTRACTION PLANT ELEMENTS OPERATION." Sovremennaya nauka i innovatsii, no. 4 (2020): 69–75. http://dx.doi.org/10.37493/2307-910x.2020.4.10.

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Marsh, Julia, Jenine Loesing, and Marilyn Soucie. "Math by the Month: Mathematical Heroes." Teaching Children Mathematics 11, no. 5 (January 2005): 264–65. http://dx.doi.org/10.5951/tcm.11.5.0264.

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The “Math by the Month” activities are designed to engage students to think like mathematicians. Students may work on the activities individually or in small groups. No solutions are suggested so that students will look to themselves for mathematical justification, thereby developing the confidence to validate their work.

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Sukirwan, Sukirwan, Dedi Muhtadi, Hairul Saleh, and Warsito Warsito. "PROFILE OF STUDENTS' JUSTIFICATIONS OF MATHEMATICAL ARGUMENTATION." Infinity Journal 9, no. 2 (September 21, 2020): 197. http://dx.doi.org/10.22460/infinity.v9i2.p197-212.

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This study investigates the aspects that influence students' justification of the four types of arguments constructed by students, namely: inductive, algebraic, visual, and perceptual. A grounded theory type qualitative approach was chosen to investigate the emergence of the four types of arguments and how the characteristics of students from each type justify the arguments constructed. Four people from 75 students were involved in the interview after previously getting a test of mathematical argumentation. The results of the study found that three factors influenced students' justification for mathematical arguments, namely: students' understanding of claims, treatment given, and facts found in arguments. Claims influence the way students construct arguments, but facts in arguments are the primary consideration for students in choosing convincing arguments compared to representations. Also, factor treatment turns out to change students' decisions in choosing arguments, and these changes tend to lead to more formal arguments.

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ARTEMOV, SERGEI. "THE LOGIC OF JUSTIFICATION." Review of Symbolic Logic 1, no. 4 (December 2008): 477–513. http://dx.doi.org/10.1017/s1755020308090060.

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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the Goldman–Kripke ‘Red Barn’ paradox and analyze Russell’s ‘prime minister example’ in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning.

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Journal articles on the topic 'Mathematical discovery and justification'

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