The Wythoff symbol is a notation used in the field of polyhedra and tilings, particularly in the context of regular and semi-regular polychora (four-dimensional analogs of polyhedra). It provides a way to describe the symmetry and structure of these geometric shapes. The notation typically consists of two numbers separated by a vertical bar, and sometimes additional information is included. The two numbers represent the arrangement of vertex angles or the types of faces around a vertex.
The Global Digital Mathematics Library (GDML) is an initiative aimed at providing access to a wide range of mathematical resources in digital form. It seeks to aggregate, preserve, and disseminate mathematical knowledge, including research papers, textbooks, databases, and other educational materials. The GDML aims to promote collaboration among universities, research institutions, and libraries to enhance the accessibility of mathematical information for students, researchers, and educators worldwide.
The Polymath Project is an initiative aimed at solving mathematical problems through collaborative efforts, primarily using the internet and online platforms. It began in 2009 when mathematician Timothy Gowers initiated a blog post inviting mathematicians and enthusiasts to collectively tackle a specific mathematical problem, known as the "density of prime numbers in progressions.
The University of Chicago School Mathematics Project (UCSMP) is a comprehensive curriculum development initiative that was established in the late 1980s. It was designed to improve and reform mathematics education for K-12 students, with a focus on fostering deep understanding of mathematical concepts rather than rote memorization of procedures. Key features of the UCSMP include: 1. **Conceptual Understanding**: The curriculum emphasizes understanding mathematical concepts and their applications, encouraging students to explore and reason mathematically.
"Article proofs" typically refer to a stage in the academic publishing process where authors are provided with a formatted version of their manuscript, which is often referred to as a proof or galley proof. This version includes all the editorial revisions made after the original manuscript submission and allows authors to review the final layout, check for any typographical errors, and ensure that their work is accurately represented before the article is published in a journal.
Computer-assisted proofs are proofs in mathematics or formal logic that involve the use of computers to aid in the verification of the proof itself or to help find the proof. These proofs typically combine traditional mathematical reasoning with computational methods to handle large computations or complex combinatorial arguments that would be impractical or impossible to work through by hand. Key aspects of computer-assisted proofs include: 1. **Verification**: A computer can verify steps in a proof that are computationally intense.
The list of probabilistic proofs of non-probabilistic theorems includes various mathematical results that have been shown to hold true through probabilistic methods, even if they are not inherently probabilistic in nature. These proofs often use random processes or probabilistic techniques as tools to establish the truth of deterministic statements. Here are some notable examples: 1. **Probabilistic Method**: The general strategy of using probability theory to prove the existence of a combinatorial structure with certain properties.
A minimal counterexample is a specific type of counterexample that demonstrates that a certain statement or conjecture is false while also satisfying an additional criterion of minimality. In mathematical terms, a counterexample is an instance that disproves a given statement (for example, a theorem or conjecture).
A Probabilistically Checkable Proof (PCP) is a concept from theoretical computer science, particularly in the field of computational complexity and proof systems. A PCP is a type of proof for a mathematical assertion that can be verified by a probabilistic algorithm with certain characteristics: 1. **Probabilistic Verification**: The verifier, instead of reading the entire proof, can check the proof using random bits.
The Brown measure is a concept from functional analysis and operator theory, specifically relating to the study of non-commutative probability and free probability. It provides a way to analyze certain types of operators, particularly those that are related to random matrices and free random variables. The Brown measure is defined for a normal operator \( T \) on a Hilbert space.
Resistive skin time (RST) is a term primarily used in the fields of neurology and psychophysiology to describe the time it takes for the skin's electrical resistance to reach a stable value after a stimulus is applied. This concept is often associated with measurements of skin conductance, where changes in skin resistance can indicate physiological and psychological responses to stimuli.
Mathematics educators are professionals who specialize in teaching and facilitating the learning of mathematics. They can work at various educational levels, including elementary, middle, and high schools, as well as in colleges and universities. Their primary goal is to help students understand mathematical concepts, develop problem-solving skills, and encourage a positive attitude toward mathematics. Key roles of mathematics educators include: 1. **Curriculum Development**: Designing math curricula and instructional materials that are engaging and effective in teaching mathematical concepts.
Financial risk management is the process of identifying, assessing, and mitigating risks that could adversely affect an organization's financial health. It involves the implementation of strategies, policies, and tools designed to understand and control various types of financial risk, including: 1. **Market Risk**: This refers to the risk of losses due to changes in market prices, such as interest rates, foreign exchange rates, and equity prices. Market risk can be broken down further into interest rate risk, currency risk, and equity risk.
The Josiah Willard Gibbs Lectureship is an esteemed honor awarded by the American Chemical Society (ACS) in recognition of outstanding contributions in the field of chemical thermodynamics or statistical mechanics. Named after the prominent American scientist Josiah Willard Gibbs, who made significant advancements in these areas, the lectureship is typically awarded to chemists who have demonstrated exceptional research and scholarly activities. The recipient is invited to give a lecture at an ACS national meeting, showcasing their research and contributions to the field.
Mathematical maturity refers to a certain level of understanding, insight, and experience in mathematics that allows individuals to engage effectively with advanced mathematical concepts and problems. It's not just about having mastered specific topics or techniques, but rather encompasses a range of skills and attitudes. Here are some key aspects of mathematical maturity: 1. **Problem-Solving Skills**: The ability to approach and solve problems using appropriate methods, as well as the skill to devise strategies for tackling unfamiliar problems.
The relationship between mathematics and the concept of God has been a topic of philosophical, theological, and scientific inquiry for centuries. Here are some perspectives on this relationship: 1. **Mathematics as a Divine Language**: Some thinkers, like the ancient philosopher Pythagoras and the mathematician Galileo, have suggested that mathematics is a universal language created by God. In this view, the laws of nature can be expressed mathematically, revealing a divine order to the universe.
"Possible Worlds" is a play written by Canadian playwright Robert LePage. Premiering in 1986, the play explores themes of identity, reality, and the nature of existence. The narrative often intertwines the lives of its characters with complex storytelling techniques, incorporating multimedia elements that are characteristic of LePage's work. The play typically features a fragmented structure, where characters navigate different realities and alternative life paths, challenging conventional notions of time and space.
String art is a creative art form that involves creating visual designs or patterns by wrapping string, thread, or yarn around a series of points, typically nailed or pinned to a board or canvas. The process often includes a grid or framework, where the string is manipulated to form geometric shapes, intricate patterns, or images. The basic technique consists of: 1. **Framework Creation**: Points or nails are placed strategically on a surface, usually in a geometric pattern or shape.
"Touch" is an American television series that aired on Fox from March 2012 to May 2013. Created by Tim Kring, the show stars Kiefer Sutherland as Martin Bohm, a widowed father who struggles to connect with his mute, autistic son, Jake, played by David Mazouz. The central premise revolves around Jake's extraordinary ability to see patterns and connections in numbers, which he uses to interpret global events and interconnected lives.