Hasil untuk "Mathematics"

D. Geary

G. Laumon, L. Moret-Bailly, Champs Alg ebriques

P. H. Leslie

R. Bull, G. Scerif

J. Hyde, E. Fennema, S. Lamon

A. Oxley

I. Mullis, Michael O. Martin, E. González et al.

G. Strang, L. Freund

G. Barton

G. Adomian

Abstract The decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions, closure approximations, perturbation theory, or restrictive assumptions on stochasticitiy.

P. Altrock, Lin L. Liu, F. Michor

E. Carey, Francesca Hill, Amy Devine et al.

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

Marie Amalric, S. Dehaene

Xiaojing Ye

This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory and algorithms of optimal control and reinforcement learning integrated with deep learning techniques, to contemporary generative models that drive today's advances in artificial intelligence.

Meenakshi Sudarvizhi Seenipeyathevar, Prasath Palaniappan, Vijayakumar Arumugam et al.

ABSTRACT This study deals with an integrated experimental‐machine learning framework for wear estimation in functionally graded composites made from recycled magnesium machining chips, using low‐cost ceramic fibers as reinforcement with the radial Modeling technique. The primary hurdle that is being addressed is the accurate prediction of wear behavior in spatially graded magnesium matrix composites, while simultaneously avoiding extensive experimental testing. Under varying degrees of applied loads (4.4 to 39 N), sliding speeds (0.45 to 4.5 m/s), and sliding distances (500 to 4500 m), the wear performance was experimentally assessed. Results demonstrate a hardness increment of 26.26% in the outer region compared to the inner region, while resistance to wear was enhanced by 19.8% in the outer zone due to the grading of ceramic fibers. A limited experimental dataset consisting of wear measurements from the inner, middle, and outer zones of the composite was utilized in developing and validating four machine‐learning models for wear rate prediction. The tree‐based ensemble methods significantly outperformed deep‐learning strategies, with the LightGBM model providing the best prediction performance across all zones and achieving optimization with a maximum tree depth of 5, 480 leaves, and a feature fraction of 0.05. Moreover, zone‐specific XGBoost models were also developed, employing customized learning rates and minimal loss reduction parameters in order to elevate prediction accuracy. The proposed machine‐learning framework thus provides a pathway for rapid and reliable wear rate estimation for ceramic fiber‐reinforced magnesium composites, significantly lessening experimental burden. Results highlight that recycled magnesium waste, when combined with ceramic reinforcement, can be effectively employed to produce sustainable and economically viable materials with improved wear resistance, particularly for automotive and industrial applications.

A. Nagel

Carlos Rojas Bruna

The gap between theory and practice in mathematics education, particularly in primary-teacher education, necessitates innovative teaching methodologies. This paper explores the implementation of academic portfolios as a teaching innovation in Algebra and Number Systems I and II courses within the primary teacher education programme at Pontificia Universidad Católica de Chile. The methodology involved integrating academic portfolios to align course content with essential learning outcomes for future teaching roles. Implementation begins with a negotiation between students and teachers to establish a learning contract, followed by an overview of course rules, content, objectives, materials, and grading rubrics. Preliminary findings indicate that this innovative method enhances engagement with mathematical concepts, improves assessment efficacy in teacher training, and may contribute to enhanced preparation of primary mathematics teachers. The study highlights the role of portfolios in making students active participants in their learning, significantly enhancing the educational experience of teacher candidates. These findings suggest a promising avenue for future educational assessments and methodologies in mathematics, indicating that academic portfolios can bridge the gap between theoretical knowledge and practical applications in mathematics teacher education, potentially enhancing teacher preparation. While this study shows promising results, further research with larger samples and longer timeframes would be beneficial to establish causality and long-term impacts.

Vincent Bouchard, Asia Matthews

Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the values of diversity, pluralism, cooperation, autonomy and experimentation are celebrated. In this perspective piece we propose anarchism as a philosophical framework to address the perceived cognitive dissonances of the current undergraduate mathematics curriculum. Are learning outcomes appropriate in an anarchist approach to education? How can we address the power dynamics of grading and assessment? How can assessment be done in the context of a process-based and horizontal approach that celebrates diversity and autonomy? Should grades be used, and if so, how could they be assigned non-hierarchically? At its core, anarchism aims at aligning thoughts and actions, and we argue that an anarchist viewpoint on undergraduate mathematics addresses the cognitive dissonances that currently plague our curriculum. We propose food for thought for individual instructors' practice, including ideas for incremental and large-scale changes.

Jenny Baur

The Ishango Bone, a prehistoric artifact dated to approximately 20,000 years ago and discovered near the Semliki River in what is now the Democratic Republic of Congo, has intrigued researchers for the past 75 years. The artifact displays sixteen groups of notches arranged in three columns. While its function remains debated, this study suggests that the first two columns consist exclusively of all prime or odd numbers between 9 and 21, with the exception of 15, which appears only in the third column as two grouped pairs. Five groupings totaling 30 could be identified, and their arrangement may follow a consistent pattern. Additional numerical relationships between all three columns can be interpreted to support all four basic arithmetic operations. It is hypothesized that the notches may have served as reference marker to lay out their values for storytelling or teaching in the form of mathematical art. This study aims to broaden perspectives on the Ishango Bone and its traditional interpretation as a simple tallying device, and to encourage a re-evaluation of the mathematical capabilities of prehistoric humans.

Anne Baanen, Matthew Robert Ballard, Johan Commelin et al.

The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing with breaking changes via a deprecation system, using code quality analysis tools (linters) to provide direct user feedback about common pitfalls, speeding up compilation times through conscious library (re-)design, dealing with technical debt as well as writing custom tooling to help with the review and triage of new contributions.