nauka: Relationship between mathematics and physics

Evidence: 100 • authority: 72

The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since antiquity, and more recently also by historians and educators. Generally considered a relationship of great intimacy, mathematics has been described as "an essential tool for physics" and physics has been described as "a rich source of inspiration and insight in mathematics". Some of the oldest and most discussed themes are about the main differences between the two subjects, their mutual influence, the role of mathematical rigor in physics, and the problem of explaining the effectiveness of mathematics in physics. In his work Physics, one of the topics treated b…

Evidence: 52 • authority: 92

Transferring ways of thinking and mathematizing: The statistical approach between physics and biology.. I pose the epistemological question of what makes the transfer of statistical approaches across disciplines, specifically between physics and biology, legitimate and fruitful despite intrinsic differences in their objects of study - a problem that resurfaces in contemporary interdisciplinary research relying on machine learning for statistical model building. I address it through the historical reconstruction of pivotal steps in the development of statistical thinking in the 19th century, where the appeal to the mathematical formalism of the Gaussian distribution acted as the visible trac…

Evidence: 47 • authority: 92

Academic field, not gender, moderates the association between math gender stereotype endorsement and arithmetic performance.. Gender differences in mathematics-related outcomes and attitudes, such as math anxiety (MA) and math self-concept (MSC), have been extensively studied among school samples, particularly in relation to the math achievement gap. Much less attention has been paid to the math-related differences among students who have already selected an academic field, and to the role played by endorsing the stereotype that mathematics is a male domain (math gender stereotype, MGS). This study investigates how MA, MSC, and MGS endorsement relate to arithmetic performance, and whether t…

Evidence: 41 • authority: 72

Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, social science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied m…

Evidence: 41 • authority: 92

Psychometric Validation of the STEM Disciplines Attitude Scale (SDAS): Investigating Measurement Invariance and Psychological Correlates in Italian High School Students.. Promoting positive student attitudes toward STEM is essential for fostering innovation; however, many existing measures do not adequately distinguish attitudes across specific disciplines, particularly within hard sciences such as physics and chemistry. This study presents the development and validation of the STEM Disciplines Attitude Scale (SDAS). Across three studies involving 2577 high school students, Exploratory and Confirmatory Factor Analyses supported a 25-item, five-factor structure assessing attitudes toward Mat…

Evidence: 35 • authority: 72

Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is widely used to model and solve problems in science, engineering, technology, economics, and everyday life. There are many areas of mathematics, including number theory (the study of integers and their properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the quantitative study of approximation and convergence), and se…

Evidence: — • authority: 92

Probabilistic Models, Compressible Interactions, and Neural Coding.. In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint distribution of many variables, as with the combinations of spiking and silence in large networks of neurons. In this probabilistic framework, we argue that simple models are possible if the mutual information between two halves of the system is consistently subextensive, and if this shared information is compressible. These conditions are not met generically, but they are met by real-world data, s…

Evidence: — • authority: 92

Left atrial geometry in atrial Fibrillation: A comparison between electroanatomical mapping and computed tomography.. Background Atrial fibrillation (AF) involves heterogeneous remodelling of the left atrium (LA), making accurate geometric quantification clinically relevant. CT is the reference standard for anatomical assessment, whereas electroanatomical mapping (EAM) provides intraprocedural reconstruction with electrophysiological information. However, agreement between both modalities remains incompletely characterized. Methods We retrospectively analyzed 211 patients undergoing first-time catheter ablation with pre-procedural CT imaging. LA volume, surface area, and sphericity were der…

Evidence: — • authority: 90

High-Precision Arithmetic in Mathematical Physics. For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.. Source: Mathematics. Year: 2015

Evidence: — • authority: 92

Two paths in persistence: Course and career motivations develop distinctly and relate to different precursors to career pursuit in college physics.. In trying to motivate college students toward career paths in science, technology, engineering, and mathematics (STEM), many scholars and policy-makers focus on promoting students' course- or field-related motivation. However, STEM fields each contain dozens of careers, the nuances of which are not often discussed during STEM coursework itself. Further, many students change career plans while remaining highly motivated for studying particular STEM courses or fields. In order to understand career plan development, it may be important to understa…

Evidence: — • authority: 90

Gestalt Theory of Cognition and “Solid” Sciences: Physics, Mathematics, and Artificial Intelligence. As all other "soft" sciences, Gestalt psychology has been under the influence of the outstanding achievements of "hard" sciences -mathematics, physics, and chemistry.The relationship between these two parties has always been complicated.When biology, geology, and sociology started to apply the strong scientific methods to research on their very complicated objects, Gestalt ideas on whole/parts relations came into high demand.Despite the attractiveness of holistic ideas, the benefits were very few, because Gestalt psychology didn't supply the main notions (Gestalt, good Gestalt, and Pragnanz)…

Evidence: — • authority: 90

Students’ experience of cultural differences between mathematics and physics. How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general “cultural” differences between the two disciplines have also been explored. However, there has been little examination of students’ own awareness and interpretations of these differences. We explore the undergraduate student experience of these cultural contrasts, and how students think they affect their learning. Through a qualitative exploratory study, including surveys and interviews wit…