An aperiodic set of tiles is a collection of shapes (tiles) that can be used to cover a plane without gaps or overlaps, but cannot form a periodic tiling pattern. This means that while the tiles can create infinitely large patterns, those patterns cannot repeat in a regular manner.

The field of statistics has a rich history, and many important publications have shaped its development. Here are some key works and publications that are widely regarded as significant in the field of statistics: 1. **"Statistical Methods for Research Workers" by Ronald A. Fisher (1925)** - This book introduced many concepts that are now fundamental in statistics, including the design of experiments and the analysis of variance. 2. **"The Design of Experiments" by Ronald A.

A list of mathematical societies includes organizations that promote the advancement, teaching, and application of mathematics. These societies often support research, publish journals, organize conferences, and provide resources for mathematicians and educators. Here are some notable mathematical societies from around the world: ### International Societies 1. **International Mathematical Union (IMU)** - Promotes international cooperation in mathematics. 2. **European Mathematical Society (EMS)** - Supports the development of mathematics in Europe.

Stochastic processes are mathematical objects that are used to describe systems or phenomena that evolve over time in a probabilistic manner. Here's a list of topics commonly associated with stochastic processes: 1. **Basic Concepts:** - Definition of stochastic processes - Sample space and probability measures - Random variables - Pathwise continuity and discontinuity 2. **Types of Stochastic Processes:** - Discrete-time vs. continuous-time processes - Discrete-state vs.

In the context of Wikipedia, a "stub" refers to an article that is considered to be incomplete or lacking in detail. The term "Materials Science stubs" would specifically refer to short or underdeveloped Wikipedia entries related to materials science. These stubs typically provide only basic information on a topic but can be expanded with more content, references, and details by contributors.

Mathematical physics is a discipline that applies rigorous mathematical methods and techniques to solve problems in physics and to understand physical phenomena. It seeks to establish a formal framework that can interpret or predict physical behavior based on mathematical principles. Key aspects of mathematical physics include: 1. **Formulation of Theories**: It involves the creation and development of mathematical models that describe physical systems, ranging from classical mechanics to quantum mechanics and general relativity.

Mathematicians are individuals who specialize in the field of mathematics, engaging in the study, research, and application of mathematical concepts, theories, and techniques. This role can encompass a wide range of activities, including: 1. **Research:** Conducting original research to develop new theories, solve complex problems, or explore mathematical relationships. This can involve a variety of branches such as algebra, geometry, number theory, calculus, and applied mathematics.

Mathematics and architecture are two interconnected fields that, while distinct in their primary focus, often overlap in various ways. ### Mathematics Mathematics is a discipline that deals with numbers, quantities, structures, space, and change. It encompasses various branches, including: - **Arithmetic**: The study of numbers and basic operations (addition, subtraction, multiplication, and division). - **Geometry**: The study of shapes, sizes, and properties of space.

"Mathematics by country" can refer to various aspects related to the field of mathematics in different countries, including: 1. **Educational Systems**: The way mathematics is taught and structured in schools and universities varies by country. For example, countries like Finland are known for their strong emphasis on education, including mathematics, while countries like the United States have a more decentralized and varied approach. 2. **Research and Contributions**: Different countries have made significant contributions to mathematics throughout history.

Mathematics literature encompasses a wide range of written works that explore, explain, and disseminate mathematical concepts, theories, and applications. This literature can take various forms and serves multiple purposes, including: 1. **Textbooks**: These are educational resources structured to teach specific areas of mathematics, such as algebra, calculus, statistics, and more, often used in academic settings. 2. **Research Papers**: Scholarly articles that present new findings, theories, or methodologies in mathematics.

Mesoscopic physics is a branch of condensed matter physics that studies systems whose size is on the order of the mean free path of electrons, typically ranging from a few nanometers to a few micrometers. At this scale, materials exhibit unique properties that differ significantly from those of bulk materials and from individual atoms or molecules. Key features and concepts in mesoscopic physics include: 1. **Quantum Coherence**: In mesoscopic systems, quantum effects become significant, and electrons can exhibit wave-like behavior.

Nemeth Braille is a braille code specifically designed for representing mathematical and scientific notation. Created by Dr. Abraham Nemeth in the 1960s, this system allows individuals who are visually impaired or blind to read and write mathematical symbols, equations, and scientific expressions in a tactile format using braille. Nemeth Braille includes unique braille symbols and rules to effectively convey a wide range of mathematical concepts such as numbers, arithmetic operations, algebra, geometry, calculus, and more.