175 results
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152. Bitter divisions over controversial maths proof.
- Author
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Wilkins, Alex
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MATHEMATICS , *PRIME numbers - Abstract
A controversial mathematical proof known as the ABC conjecture has sparked bitter divisions among mathematicians. In 2012, Shinichi Mochizuki published a 500-page proof of the conjecture, but many found it incomprehensible. Kirti Joshi at the University of Arizona has now proposed a proof that he claims fixes the problems with Mochizuki's work, but Mochizuki and his supporters remain unconvinced. The debate centers around a part of Mochizuki's proof called Conjecture 3.12, which Joshi believes he has addressed more satisfactorily. However, the paper has not been peer-reviewed, and the controversy continues. [Extracted from the article]
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- 2024
153. Preface: The 5th International Seminar of Innovation in Mathematics and Mathematics Education (5th ISIMMED) and the 7th International Seminar on Science Education (7th ISSE).
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SCIENCE education , *MATHEMATICS education , *SEMINARS , *MATHEMATICS - Abstract
The document is a preface to the 5th International Seminar of Innovation in Mathematics and Mathematics Education (5th ISIMMED) and the 7th International Seminar on Science Education (7th ISSE). The seminar, held virtually in November 2021, focuses on the theme of "Technological pedagogical content knowledge (TPACK) in the current trend of science technology engineering mathematics (STEM) Education." The seminar aims to provide practical solutions for teachers facing challenges in integrating technology into their classrooms, such as increasing student motivation and creating a visual and engaging learning atmosphere. The seminar has accepted 186 papers and 145 participants from Indonesia and the Philippines, with selected papers published by AIP Publisher. The preface expresses gratitude to keynote and invited speakers, as well as organizers, reviewers, authors, and committee members. [Extracted from the article]
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- 2024
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154. Making decisions about attainment grouping in mathematics: teacher agency and autonomy in Norway.
- Author
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Eriksen, Elisabeta, Solomon, Yvette, Bjerke, Annette Hessen, Gray, James, and Kleve, Bodil
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EDUCATIONAL attainment , *MATHEMATICS , *TEACHERS , *FREEDOM of teaching , *DECISION making - Abstract
Grouping by attainment is a relatively new and contested practice in Norway, where strong historical discourses of heterogeneous education are under pressure from international test comparisons, particularly in mathematics. At the same time, research indicates that Norwegian teachers have a high degree of autonomy in education policy enactment. Analysing thirteen Norwegian mathematics teachers' reflections on grouping practices, we seek to understand their decision-making processes within this context. Our findings indicate that teachers report a high degree of autonomy in grouping practices which is exercised through considerable diversity in practice and defended when necessary. Using an ecological model of teacher agency reveals how teachers explore and explain their highly situated practice and its tensions and contradictions. We find that teachers who are removed from the central locus of autonomy have less to draw on in making and justifying their pedagogic choices, while those who are more central are able to continually reassess in this highly sensitive arena. We note the implications for practice and research on attainment grouping, particularly the need for teacher autonomy and support for professionally-based local decision-making. [ABSTRACT FROM AUTHOR]
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- 2024
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155. Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books.
- Author
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Gaskell, Roger
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MATHEMATICS , *SCIENCE museums , *HISTORY of mathematics , *MATHEMATICS education , *MATHEMATICAL instruments , *MARGINALIA - Abstract
"Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books" is a collection of eleven essays that examine the intellectual and physical practices of mathematical writing, publishing, and reception in early modern Europe. The book focuses on the figure of Henry Savile, a patron of mathematical teaching, and explores topics such as the use of diagrams, the history of mathematical libraries, the challenges of publishing scholarly editions, and the analysis of marginalia. The essays provide valuable insights into the history of mathematics as a part of human culture and will be of interest to researchers studying the intellectual and social aspects of mathematics. [Extracted from the article]
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- 2024
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156. Using abstraction to analyze instructional tasks and their implementation.
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Moore, Kevin C., Wood, Erin, Welji, Shaffiq, Hamilton, Mike, Waswa, Anne, Ellis, Amy B., and Tasova, Halil I.
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STUDENT engagement , *MATHEMATICAL forms , *MATHEMATICS education , *EDUCATIONAL outcomes , *MATHEMATICS - Abstract
Over the past few decades, Piaget's forms of abstraction have proved productive for developing explanatory models of student and teacher knowledge, yet the broader applicability of his abstraction forms to mathematics education remains an open question. In this paper, we adopt the Piagetian forms of abstraction to accomplish two interrelated goals. Firstly, we analyze instructional tasks to develop hypothetical accounts of the abstractions that might occur during students' engagement with them. Secondly, we draw on middle- and secondary-grades classroom data to discuss the abstractions that occurred during the implementation of those instructional tasks. Because this paper represents an initial attempt at extending the applicability of Piagetian forms of abstraction, we close with potential implications of such use and possible avenues for future research. Most notably, we highlight the complexities involved in supporting abstraction through curriculum and instruction. • We examine task materials and implementation. • We differentiate between forms of abstraction. • We identify abstraction's viability for such analysis. • We differentiate between student learning outcomes. • We suggest avenues for future research. [ABSTRACT FROM AUTHOR]
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- 2024
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157. Corrigendum: Model theory of fields with virtually free group actions: (Proc. Lond. Math. Soc. (2) 118 (2019), no. 2, 221–256).
- Author
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Beyarslan, Özlem and Kowalski, Piotr
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FREE groups , *MATHEMATICS , *MODEL theory - Abstract
There is an irreparable error in the proof of Theorem 3.26 in the above‐mentioned paper and we withdraw the claim of having proved that theorem. In fact, that theorem is false in a very strong sense. [ABSTRACT FROM AUTHOR]
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- 2024
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158. Towards an ecological mathematics.
- Author
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Unnithan Kumar, Siddharth
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Mathematics plays a fundamental role in ecological research, yet its uses remain strikingly separate from advances in the environmental social sciences and humanities. In this paper, I work to address this impasse and outline the motivation and scope for an ‘ecological mathematics’, an approach to doing mathematics in environmental research which foregrounds relationship, embodiment and human difference. I begin by tracing the historical emergence of mathematics in ecology, noting how life processes have been conceptualised in a way which forces them to fit the ideals of mathematical models transplanted from the physical sciences. I then investigate the cultural factors shaping the evolution of mathematical thought, eliciting a malleability in how mathematical knowledge relates to the more-than-human world. This provides a place from which to rethink the role of abstraction in ecological thought, and develop mathematical methods grounded in ecological concepts. Drawing on ethnographic and perceptual accounts of space and time, I work with topological concepts from both mathematics and the social sciences to suggest a new correspondence between these subjects, elaborating a way of employing mathematical techniques which enliven, rather than deaden, the ecologies under study. The paper concludes with important philosophical clarifications to the approach of an ecological mathematics. [ABSTRACT FROM AUTHOR]
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- 2024
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159. Boundedness criteria for a class of indirect (and direct) chemotaxis-consumption models with signal-dependent sensitivity in high dimensions.
- Author
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Chiyo, Yutaro, Sugawara, Kazuma, and Yokota, Tomomi
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CHEMOTAXIS , *MATHEMATICS - Abstract
This paper is concerned with an indirect chemotaxis-consumption model with sensitivity function χ (v). Frassu and Viglialoro (Appl. Math. Lett.; 2022; 132; 108108) showed global existence and boundedness in the case that χ is a constant. However, there is a room for improvement of the main claim. This paper improves the result and extends it in the case that χ depends on v. [ABSTRACT FROM AUTHOR]
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- 2024
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160. Correction: Alohali et al. Ricci Vector Fields Revisited. Mathematics 2024, 12 , 144.
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Alohali, Hanan, Deshmukh, Sharief, and Vîlcu, Gabriel-Eduard
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MATHEMATICS - Abstract
This correction notice addresses an omission in a previously published paper titled "Ricci Vector Fields Revisited." The authors apologize for not including acknowledgements in the original paper and express their gratitude for the support received from King Saud University in Riyadh, Saudi Arabia. The authors assure readers that this correction does not impact the scientific conclusions of the paper. The correction has been approved by the Academic Editor and the original publication has been updated. The authors of the paper are Hanan Alohali, Sharief Deshmukh, and Gabriel-Eduard Vîlcu. [Extracted from the article]
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- 2024
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161. Preface: The 6th International Conference on mathematics and mathematics education (ICM2E 2022).
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MATHEMATICS conferences , *MATHEMATICS education , *CONFERENCES & conventions , *INDUSTRY 4.0 , *MATHEMATICS - Abstract
The 6th International Conference on Mathematics and Mathematics Education (ICM2E 2022) was held in Padang, Indonesia on September 3rd-4th, 2022. The conference focused on the theme of "Innovative Research of Mathematics and Mathematics Education to Face the 4th Industrial Revolution Challenges." It provided a platform for researchers, educators, and students to exchange ideas and discuss advancements in the field. The conference proceedings, published by AIP Proceedings, contain high-quality papers selected through a blind review process. The organizers express gratitude to all participants, authors, reviewers, keynote speakers, and committees for their contributions to the success of the conference. They look forward to the next ICM2E and hope it will be as exciting as its predecessors. [Extracted from the article]
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- 2024
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162. Erratum to The level four braid group (J. reine angew. Math. 735 (2018), 249–264).
- Author
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Brendle, Tara E. and Margalit, Dan
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MATHEMATICS , *BRAID group (Knot theory) , *ELECTRONIC journals - Abstract
The proof of the first statement of Theorem 5.1 of the paper referenced in the title is correct for k = 1 and incorrect for k ≥ 2 and should be considered an open problem. As such, the proof of the second statement is not correct for k ≥ 2 . [ABSTRACT FROM AUTHOR]
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- 2024
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163. A multi-view graph learning model with dual strategies for solving math word problems.
- Author
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Wang, Zhiwei, Lang, Qi, Liu, Xiaodong, and Jing, Wenlin
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KNOWLEDGE graphs , *REPRESENTATIONS of graphs , *NATURAL language processing , *DEEP learning , *MATHEMATICS , *GRAPH algorithms - Abstract
Recently, graph-based deep learning models have exhibited remarkable performance in generating solution expressions for the math word problem (MWP). However, most of these models have not taken into account the limitations and errors in constructing prior knowledge graphs, which may affect their accuracy and reliability in practical applications. In addition, during graph learning, they focus on extracting information from each given graph, while neglecting the adaptability and unification of graph representation learning. In this paper, we propose a novel multi-view graph learning-to-tree model with dual-strategy (MVG-DS-T), in which it performs adaptive and consistent multi-view representation learning through two benchmark graphs. Specifically, we construct benchmark graphs via semantic dependency parsing of MWP text, considering both semantic and quantitative aspects, i.e., semantic graph and quantitative graph. Then, the reconstruction strategy is employed to reconstruct the structure of the benchmark graphs to capture the adaptive representation information suitable for downstream tasks, while the alignment strategy is utilized to overcome the limitation of independent view representations by unifying the semantic and quantity embedding information through graph structure. Also, an adaptive length normalized loss balancing term for the tree-based decoder is introduced to control the model focus on label length during training, resulting in better equation generation. Extensive experiments demonstrate the effectiveness of the proposed approach on the MWP task. The empirical results show that MVG-DS-T achieves performance comparable to that of the state-of-the-art graph-based models in the existing literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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164. Retraction notice to "Some remarks on the uniqueness of decomposition into Cartesian product" [Topol. Appl. 201 (2016) 2–12].
- Author
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Michalik, Daria
- Subjects
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MATHEMATICS - Abstract
This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/policies/article-withdrawal). This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation. [ABSTRACT FROM AUTHOR]
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- 2024
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165. Retraction notice to "The decomposition uniqueness for infinite Cartesian products" [Topol. Appl. 230 (2017) 16–23].
- Author
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Michalik, Daria
- Subjects
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MATHEMATICS , *RETRACTORS (Surgery) - Abstract
This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/policies/article-withdrawal). This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation. [ABSTRACT FROM AUTHOR]
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- 2024
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166. Corrigendum to ''A Severi type theorem for surfaces in \mathbb{P}^6''.
- Author
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De Poi, Pietro and Ilardi, Giovanna
- Subjects
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CLASSIFICATION , *MATHEMATICS - Abstract
In Theorem 0.1 of the paper "A Severi type theorem for surfaces in \mathbb {P}^6" [Proc. Amer. Math. Soc. 149 (2021), pp. 591–605], we claimed to have given a complete classification of smooth surfaces in \mathbb {P}^6 with one 4-secant plane through the general point of \mathbb {P}^6, but the classification is still incomplete. [ABSTRACT FROM AUTHOR]
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- 2024
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167. The set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense.
- Author
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Petrović, Nevena Z., Pranić, Miroslav S., Stanić, Marija P., and Tomović Mladenović, Tatjana V.
- Subjects
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GAUSSIAN quadrature formulas , *ORTHOGONAL polynomials , *SENSES , *MATHEMATICS - Abstract
Laurie in [Math. Comp., 65(1996), pp. 739–747] introduced anti-Gaussian quadrature rule, that gives an error equal in magnitude but of opposite sign to that of the corresponding Gaussian quadrature rule. Guided by that idea, in this paper we consider a set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense (see [Numer. Math., 67(1994), pp. 271–288]), as well as the corresponding class of multiple orthogonal polynomials. The main properties of such quadrature rules and multiple orthogonal polynomials are proved and numerical methods for their constructions are presented. Some numerical examples are also included. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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168. Correction to: Tight Complexes Are Golod.
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MATHEMATICS , *MANUSCRIPTS - Abstract
This is a correction to: Kouyemon Iriye, Daisuke Kishimoto, Tight Complexes Are Golod, International Mathematics Research Notices, 2023; rnad221, https://doi.org/10.1093/imrn/rnad221.In the originally published version of this manuscript, Figure 1 and Figure 2 were incorrectly placed within the paper and the caption for figure 1 was omitted.These errors have been corrected. [Extracted from the article]
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- 2024
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169. Complete signed graphs with largest maximum or smallest minimum eigenvalue.
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Ghorbani, Ebrahim and Majidi, Arezoo
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EIGENVALUES , *REGULAR graphs , *COMPLETE graphs , *MATHEMATICS - Abstract
In this paper, we deal with extremal eigenvalues of the adjacency matrices of complete signed graphs. The complete signed graphs with maximal index (i.e. the largest eigenvalue) with n vertices and m ≤ ⌊ n 2 / 4 ⌋ negative edges have been already determined. We address the remaining case by characterizing those with m > ⌊ n 2 / 4 ⌋ negative edges. We also identify the unique signed graph with maximal index among complete signed graphs whose negative edges induce a tree of diameter at least d for any given d. This extends a recent result by Li, Lin, and Meng [Discrete Math. 346 (2023), 113250] who established the same result for d = 2. Finally, we prove that the smallest minimum eigenvalue of complete signed graphs with n vertices whose negative edges induce a tree is − n 2 − 1 − 1 + O (1 n). [ABSTRACT FROM AUTHOR]
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- 2024
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170. Generating functions and counting formulas for spanning trees and forests in hypergraphs.
- Author
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Liu, Jiuqiang, Zhang, Shenggui, and Yu, Guihai
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GENERATING functions , *HYPERGRAPHS , *APPLIED mathematics , *ALGEBRA , *TREE graphs , *MATHEMATICS , *SPANNING trees - Abstract
In this paper, we provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs in two different ways: (1) We represent spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam (2004) [1] and Pfaffian matrix tree theorem by Masbaum and Vaintrob (2002) [15]. • We provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper- Hafnians when orders and signs are not considered. • We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam [Advances in Applied Mathematics (2004) Vol. 33: 51-70] and Pfaffian matrix tree theorem by Masbaum and Vaintrob [Internat. Math. Res. Notices (2002) Vol. 27: 1397-1426]. [ABSTRACT FROM AUTHOR]
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- 2024
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171. Conceptualizing reasoning practices in the context of sociomathematical issues.
- Author
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Chorney, Sean, Evans, Kyle R., and Staples, Megan
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MATHEMATICS education , *SOCIAL context , *MATHEMATICS , *APPROXIMATE reasoning , *FAIRNESS - Abstract
In this conceptual paper, we explore a framework of reasoning practices for decision-making in context. We extend prior work related to socioscientific issues (SSI) (Sadler et al., 2007) to consider the applicability of this framework to sociomathematical issues, specifically using the context of fairness in political (re)districting. We illustrate the usefulness of the SSI framework for sociomathematical issues drawing on student work and reflections from two undergraduate courses. We conclude by suggesting adjustments to reasoning practices of the SSI framework that might uniquely reflect the nature of sociomathematical reasoning. We discuss implications of our findings for conceptualizing reasoning practices that include mathematical perspectives within social and political contexts and for mathematics education generally. • Reasoning about a societal issue consists of intertwining personal, practical, contextual, and mathematical meaning. • A framework based on Sadler, Barab & Scott's (2007) analysis of reasoning practices regarding socioscientific issues is useful for analyzing emergent student reasoning in the context of redistricting, a sociomathematical issue. • Students reason in multiple, sophisticated ways about the fairness of specific maps and redistricting processes. [ABSTRACT FROM AUTHOR]
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- 2024
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172. An exploratory mixed methods study about teacher candidates' descriptions of children's confusion, productive struggle, and mistakes in an elementary mathematics methods course.
- Author
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Kalinec-Craig, Crystal and Rios, Anthony
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STUDENT teachers , *LEARNING , *TEACHER education , *PARENT-teacher conferences , *SENTIMENT analysis , *MATHEMATICS - Abstract
Recognizing and describing children's mathematical thinking in humanizing ways, especially when students engage in confusion, productive struggle, and mistakes, is a complex and challenging process. This paper describes an exploratory, mixed-methods study about how elementary teacher candidates (TCs) describe children's thinking as a right to exercise and to value their humanity when learning mathematics. The study analyzed transcripts from 64 TCs' summative assessments, which consisted of mock parent-teacher conferences (MPTC). Findings suggest that TCs described children's confusion, productive struggle, and mistakes (RotL 1 and 2) as: a teacher's observation, an opportunity for students to correct or clarify their thinking, an opportunity for teachers to adjust instruction or provide support, and as a normal part of the learning process. More importantly, some TCs reassured children that learners have fundamental rights when learning mathematics, especially when feeling confused and claiming a mistake. Implications for research and teacher education are discussed. Keywords: Elementary, teacher education, mathematics, mixed methods, rehumanizing, Torres' rights of the learner • Topic modeling and sentiment analysis helps to quantify and describe valence that arises from large amounts of text. • 32 TCs identified children's confusion, generalized struggle, and mistakes (Torres' RotL 1 and 2) in their MPTC across 50 instances. • Some TCs described children's confusion and mistakes as rights to exercise, a potential rehumanizing stance. [ABSTRACT FROM AUTHOR]
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- 2024
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173. Examples of compact embedded convex λ-hypersurfaces.
- Author
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Cheng, Qing-Ming, Lai, Junqi, and Wei, Guoxin
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SPHERES , *MATHEMATICS , *HYPERSURFACES , *CURVATURE - Abstract
In the paper, we construct compact embedded convex λ -hypersurfaces which are diffeomorphic to a sphere and are not isometric to a standard sphere. As the special case of our result, we solve Sun's problem (Int. Math. Res. Not. (2021) 11818–11844). In this sense, one can not expect to have Alexandrov type theorem for λ -hypersurfaces. [ABSTRACT FROM AUTHOR]
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- 2024
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174. Gerrymandering individual fairness.
- Author
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Räz, Tim
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FAIRNESS , *GERRYMANDERING , *METRIC spaces - Abstract
Individual fairness requires that similar individuals are treated similarly. It is supposed to prevent the unfair treatment of individuals on the subgroup level and to overcome the problem that group fairness measures are susceptible to manipulation or gerrymandering. The goal of the present paper is to explore the extent to which individual fairness itself can be gerrymandered. It will be proved that individual fairness can be gerrymandered in the context of predicting scores. Then, it will be argued that individual fairness is a very weak notion of fairness for some choices of feature space and metric. Finally, it will be discussed which properties of (individual) fairness are desirable. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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175. Why Machines Learn: The Elegant Math Behind Modern AI.
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MACHINE learning , *MATHEMATICS , *ARTIFICIAL intelligence , *MATHEMATICAL proofs , *PRINCIPAL components analysis - Abstract
Anil Ananthaswamy's book, "Why Machines Learn: The Elegant Math Behind Modern AI," attempts to explain how artificial intelligence (AI) works by scanning data for patterns and making predictions. However, the book's detailed breakdown of probability, principal component analysis, and eigenvectors may be difficult for readers without an advanced math degree to understand. While there are some interesting examples, such as how statisticians determined the authorship of the Federalist Papers, the book is primarily filled with complex equations and proofs. General readers may find it challenging to follow. [Extracted from the article]
- Published
- 2024
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