The Calcutta Mathematical Society, established in 1908, is one of the oldest mathematical societies in India. Its primary objective is to promote the study and research of mathematics in India and to foster a community among mathematicians. The society plays a vital role in organizing seminars, conferences, and lectures, as well as facilitating the publication of mathematical research and journals. It serves as a platform for mathematicians, researchers, and students to exchange ideas and collaborate in various areas of mathematics.

Āryabhaṭa, an ancient Indian mathematician and astronomer who lived in the 5th century CE, is known for his significant contributions to mathematics and astronomy. One of his noteworthy achievements is the computation of sine values for various angles, which are often organized in a sine table. In Āryabhaṭa's sine table, the sine values are typically expressed as a function of a circle's radius (usually taken to be 1 for simplicity).

The "kos" is a unit of measurement that is used in various contexts, but most commonly it refers to a unit of distance. It is often associated with the term "kilo" or "kilometer," particularly in some regions or languages. However, it's worth noting that "kos" can also refer to a popular term in some sports, particularly in cricket, where it may denote a certain type of scoring or bowling.

"Kuṭṭaka" is a term from ancient Indian philosophy and literature, often associated with the context of debates or discussions, particularly in the field of logic and epistemology in Buddhism and Jainism. In these philosophical traditions, "kuṭṭaka" can refer to a specific kind of argument or fallacy. In a broader context, "kuṭṭaka" can also mean a strategy or method in dialectical engagements, where it involves sharp exchanges of ideas or critiques.

"Mathematics in India" is a book by Kim Plofker, published in 2009. The book offers a comprehensive overview of the history and development of mathematics in India, from ancient times through the medieval period to the modern era. Plofker explores the contributions of Indian mathematicians and the influence of Indian mathematics on the global mathematical landscape.

The Ramanujan Mathematical Society (RMS) is an organization dedicated to the promotion and development of mathematics research and education, especially in India. Founded in 2005, the society is named after the famed Indian mathematician Srinivasa Ramanujan, who made significant contributions to mathematical analysis, number theory, and continued fractions.

The **Tantrasamgraha** is a significant text in the tradition of Shaiva Tantra. Attributed to the 10th-century philosopher and saint **Abhinavagupta**, the Tantrasamgraha serves as a concise summary and synthesis of various Tantric teachings and practices associated with Shaivism.

In linguistics, defeasibility refers to a property of certain statements, conclusions, or arguments whereby they can be overridden or retracted in light of new information or evidence. This concept is often discussed within the context of semantics, pragmatics, and logic. In semantics, for example, defeasibility can apply to the meaning of certain sentences that can be modified or negated based on contextual factors.

Epilogism is not a widely recognized term in modern usage, but it might refer to a few concepts depending on the context in which it's used. In general, the prefix "epi-" suggests something related to an "epilogue," which is a concluding section of a literary work that provides closure or additional commentary on the main content.

The Kepler–Bouwkamp constant, denoted as \( K \), is a mathematical constant that appears in the context of the geometrical relationships between regular polygons and circles, particularly in relation to the packing of spheres and the computation of certain areas and volumes in geometry. It can be expressed in terms of elliptic integrals and has a numerical value of approximately: \[ K \approx 0.

Explicature is a term used in linguistics, particularly in the field of pragmatics, to refer to the aspects of meaning that arise from the contextual interpretation of an utterance. It involves the process of elaborating the literal meaning of a sentence to include contextually relevant information that is not explicitly stated but is inferred by the listener. In transactional communication, explicature helps to clarify the speaker's intended meaning based on the context in which the utterance is made.

The equation \( xy = yx \) describes a relationship between the variables \( x \) and \( y \). It essentially states that the product of \( x \) and \( y \) is equal to the product of \( y \) and \( x \). This equation holds true for any real numbers \( x \) and \( y \) due to the commutative property of multiplication, which states that the order of multiplication does not affect the result.

Braess's paradox is a concept in traffic flow and game theory that suggests that adding extra capacity to a network can sometimes lead to a decrease in overall efficiency. The paradox is named after the mathematician Dietrich Braess, who formulated it in 1968. In essence, Braess's paradox occurs when individual users of a network (such as drivers on a road network) behave in their own self-interest, and their decisions lead to a less efficient outcome for the entire system.

An externality is an economic concept that refers to a situation where the actions of individuals or businesses have an impact on third parties who are not directly involved in the transaction. Externalities can be either positive or negative. 1. **Negative Externality**: This occurs when the actions of an individual or company result in harmful effects on others. For example, pollution from a factory can adversely affect the health of people living nearby or the quality of natural resources.

Khinchin's constant is a mathematical constant that appears in the context of the theory of continued fractions. Named after the Russian mathematician Aleksandr Khinchin, it is typically denoted by the symbol \( K \) and is approximately equal to \( 2.685452 \). Khinchin's constant arises in the study of the properties of the continued fraction representations of real numbers.

The Price of Anarchy (PoA) is a concept in game theory that measures the efficiency of equilibria in non-cooperative games, particularly in the context of congestion games. In congestion games, players compete for limited resources, and their shared interactions can lead to suboptimal outcomes for the group as a whole.

The Price of Stability (PoS) is a concept in game theory and algorithmic social choice that measures the efficiency of equilibria in games, particularly in the context of strategic interactions among multiple agents or players. Specifically, it quantifies how much the performance of the best Nash equilibrium (a stable state where no player has anything to gain by changing only their own strategy) deviates from the optimal outcome that could be achieved with cooperation.

Immediate inference is a type of logical reasoning that allows one to draw conclusions directly from a single statement, without needing to refer to any other premises or statements. It involves deducing a specific proposition from a general one. In the context of syllogistic logic, immediate inference takes a basic form, often working with universal or categorical statements.