Hasil untuk "Mathematics"

I. Kra, S. R. Simanca

G. Berkolaiko, P. Kuchment

G. Aubert, Pierre Kornprobst

Michael O. Martin, A. Beaton, E. González et al.

P. K. Maji, A. R. Roy, R. Biswas

H. Stichtenoth

J. Vázquez

I. Blake, G. Seroussi, N. Smart

W. Thurston

J. Moon, G. Dantzig, C. L. Liu

M. Kline

A. Schoenfeld

Chuangxia Huang, Xiaodan Ding, Qian Wang

This study is devoted to the stability issue of a time-varying delayed Nicholson's blowflies equation of neutral type. By the aid of the Lyapunov stability theory and novel analysis techniques, two sharp conditions ensuring separately the global asymptotic stability of the zero equilibrium and positive equilibrium are derived, which completely cover the corresponding ones in the associated non-neutral equation. In addition, a numerical example is taken to support the availability of the theoretical results.

Gabriel Peyré

This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the development of new mathematics at the intersection of various fields. This article focuses on the application of analytical and probabilistic tools to model neural network architectures and better understand their optimization. Statistical questions (particularly the generalization capacity of these networks) are intentionally set aside, though they are of crucial importance. We also shed light on the evolution of ideas that have enabled significant advances in AI through architectures tailored to specific tasks, each echoing distinct mathematical techniques. The goal is to encourage more mathematicians to take an interest in and contribute to this exciting field.

Jeremy Avigad

This is an essay about the value of mathematical and symbolic reasoning in the age of AI.

Dennis Müller

This article analyzes the emerging ethical turn in mathematics education, arguing that it is a nuanced extension of the sociopolitical turn. While sociopolitical studies of mathematics have highlighted systemic issues and group concerns (e.g., equity, diversity, exclusion), the newer scholarship on ethics in mathematics presents a sharpened focus on the individual responsibility of learners, teachers, and mathematicians by explicitly engaging with philosophical ethics. We analyze key themes of the discourse, including the tension between "doing good" and "preventing harm," and present various philosophical foundations from which scholars have engaged with ethics: Levinas, non-Western perspectives, and pragmatism. We show that the ethical turn holds significant implications for training teachers, including self-reflection, responsibility towards the Other, historical and philosophical awareness, the role of mathematics in society, individual flexibility, cultural sensitivity, and courage to navigate the complex reality of today's mathematics classrooms. The article is designed to also serve as an introduction to ethics in mathematics education.

K. Hart, Csms Mathematics Team

Fatrima Santri Syafri, Agus Susanta, Irwan Koto

Background: This research develops a foundational mathematics textbook for PGMI students based on the Rigorous Mathematical Thinking (RMT) framework, contextualized within houses of worship to foster deeper understanding of mathematical concepts. Aim: The study aims to design and evaluate the feasibility and effectiveness of the textbook while gauging students’ responses and performance improvements. Method: Using a research and development (R&D) model, this study validated the textbook through expert reviews and tested its practicality and effectiveness in small-scale and broader applications. Data were obtained through a combination of observations, interviews, surveys, and tests measuring students' conceptual comprehension. Statistical evaluations, including descriptive analysis and t-tests, were employed. Results: The textbook received validation from subject matter, presentation, and language experts, who confirmed its content and structural accuracy. Trial phases categorized the textbook as highly practical, while broader field testing indicated that students using the textbook demonstrated significantly greater improvement in conceptual understanding compared to those without it. Conclusion: The RMT-based textbook aligns with its intended objectives and provides a contextually appropriate tool for improving mathematical comprehension. These findings highlight its potential as an effective resource for mathematics learning in PGMI contexts.

Thenmozhi D, M. Eswara Rao, Ch. Nagalakshmi et al.

The current study presents a novel examination of heat transfer properties in a magnetohydrodynamic (MHD) flow of Casson fluid across a porous stretching sheet, uniquely incorporating the effects of heat source and variable viscosity. Unlike previous studies, this research employs the Lie similarity transformation to convert the governing equations into a dimensionless form. These transformed equations are then solved using advanced numerical techniques, specifically the fourth-order Runge-Kutta (RK) along with shooting method. The findings reveal that the velocity decreases with the adjustment of significant parameters such as the Casson fluid properties, variable viscosity, heat source, magnetic field, and porosity, leading to an inverse increase in temperature within the convection system. As the Prandtl number increases, the temperature gradient and thermal boundary layer thickness decrease, resulting in reduced heat transfer rates within the convection system. Likewise, an increase in the Schmidt number decreases the concentration gradient and mass transfer rate within the fluid. This novel approach provides new insights into the behavior of Casson fluids, with significant applications in industrial processes, energy systems, environmental engineering, material science, and aerospace and automotive industries, where understanding heat transfer mechanisms in complex systems can enhance efficiency, performance, and safety.

Richard Zach

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert's consistency program. Similar efforts continue, but have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages.