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.
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 **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.
"Sadratnamala" is a term that typically refers to a significant work in the context of Buddhist philosophy and literature. It is a Sanskrit text attributed to the famous Indian philosopher and scholar, Nagarjuna, who is known for his foundational contributions to Mahayana Buddhism and the development of the concept of emptiness (śūnyatā). The term "Sadratnamala" translates to "The Garland of Six Jewels" or "The Necklace of Six Gems.
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.
"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 term "Mathematical Sciences Foundation" can refer to different organizations or initiatives aimed at promoting the mathematical sciences, education, research, or community outreach. Generally, such foundations focus on advancing mathematical knowledge and its applications, supporting research, and enhancing the understanding of mathematics in society.
Madhava's sine table is an ancient mathematical table created by the Indian mathematician Madhava of Sangamagrama, who lived during the late 14th and early 15th centuries. It is known for being one of the first systematic tabulations of sine values for various angles. Madhava's methodology involved calculating the sine of angles as a series expansion, similar to what we now understand as Taylor or Maclaurin series.
Līlāvatī, often referred to in various contexts, is primarily known as a classical work on mathematics in Sanskrit, authored by the Indian mathematician Bhāskara II (also known as Bhāskara the Younger) in the 12th century. The full title of the work is "Līlāvatī," which translates to "the playful one" or "the playful beauty," indicating its intended accessibility and engagement.
"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.
"Kriyakramakari" generally refers to a person or entity that is involved in the process of action-oriented tasks or activities. The term can be broken down into "Kriya," which means action or activity, and "Kramakari," which implies organization or systematic execution. In various contexts, it could refer to individuals or organizations that specifically focus on operational processes, management of activities, or project implementation.
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.
Karanapaddhati is a significant text in the field of traditional Indian mathematics, particularly in the area of astronomy and astrology. It is attributed to the ancient Indian mathematician Bhaskara II, also known as Bhaskara the Great, who lived in the 12th century. The text serves as a compendium of mathematical techniques and methods used for calculations relating to celestial bodies and their movements.
The Indian Statistical Institute (ISI) is a premier academic institution dedicated to the research, teaching, and application of statistics, mathematics, and related subjects. Founded in 1931 by the renowned statistician Prasanta Chandra Mahalanobis, ISI has played a crucial role in the development of statistical methodology and its applications in various fields, including economics, agriculture, industry, and social sciences.
The history of Hindu mathematics is rich and multifaceted, spanning several centuries and contributing significantly to mathematical concepts, methods, and terminology. Hindu mathematics was developed in the Indian subcontinent, and its evolution can be traced through various periods, often corresponding with developments in culture, religion, and philosophy. ### Ancient Period 1. **Vedic Mathematics (1500 BCE - 500 BCE)**: - Early mathematical concepts can be found in the Vedas, particularly in rituals and astronomy.
"Ganita Kaumudi" is a historical work on mathematics by the Indian mathematician Bhaskara II, also known as Bhaskara the Younger. He lived in the 12th century CE and is one of the most eminent mathematicians and astronomers from ancient India. The "Ganita Kaumudi," which translates to "the moonlight of mathematics," is a comprehensive treatise that covers various topics in mathematics, including arithmetic, algebra, geometry, and more.
Chennai Mathematical Institute (CMI) is a premier academic institution located in Chennai, India, specializing in mathematics and its applications. Established in 1989, CMI is known for its focus on research and education in mathematics, computer science, and related areas. It offers various programs, including undergraduate and postgraduate degrees in mathematics, computer science, and physics, as well as doctoral programs.
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.