Academic Articles & Research Papers

On proof and progress in mathematics

This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics".Their article raises interesting i...

Mathematics in the streets and in schools

An analysis of everyday use of mathematics by working youngsters in commercial transactions in Recife, Brazil, revealed computational strategies different from those taught in schools. Performance on mathematical problems embedded in real‐l...

Visualization and Mathematics

DAF-UNet: Deformable U-Net with Atrous-Convolution Feature Pyramid for Retinal Vessel Segmentation

Segmentation of retinal vessels from fundus images is critical for diagnosing diseases such as diabetes and hypertension. However, the inherent challenges posed by the complex geometries of vessels and the highly imbalanced distribution of ...

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

Mathematical Capabilities of ChatGPT

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...

Mathematics without Numbers

Abstract Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is ...

The Handbook of Mathematical Cognition

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M. Brysbaert, Number Recognition in Different Forma...

Introduction to Mathematical Logic.

is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and...

Wireless Link-Quality Estimation in Smart Grid Environments

Recently, wireless sensor networks (WSNs) have gained great attention from the research community for various smart grid applications, including advanced metering infrastructure (AMI), power outage detection, distribution automation, towers...

Satellite-derived prediction on habitat modelling of skipjack tuna (Katsuwonus pelamis) in the Makassar Strait, Indonesia

The Makassar Strait is one of the Indonesian Throughflow (ITF) branches that transports warm water masses from the Pacific Ocean to the Indian Ocean. These water masses have a significant impact on oceanographic parameters, which in turn af...

The Mathematical Brain

The concept of numbers and the ability to recognize and process them is innate, part of everyone's intellectual apparatus whether they've had formal education or not. This instinct is not dependent on basic intelligence or general knowledge...

Survey of Hybrid Cloud Workflow Scheduling

In the context of data explosion,traditional cloud computing is faced with the dilemma of insufficient local cloud resources and high expansion cost.However,the newly emerging hybrid cloud combining resource-rich public cloud and data-sensi...

The application of cosine similarity measures with Laplacian energy to q-rung orthopair fuzzy graphs in decision-making problems

Q-rung orthopair fuzzy sets (q-ROFS), which are better than the intuitionistic and Pythagorean fuzzy sets, are a significant tool for expressing ambiguous information. Their key feature is that their ability to represent a larger space of u...

Mathematical Methods for Physicists

This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed...

An η-Intuitionistic Fuzzy Rings Structure

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. ...

Mathematical Methods for Physicists

Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian ...

Methods of Mathematical Physics

Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intu...

Methods of Mathematical Physics

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical int...

The Mathematics of Marriage

Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage pro...