Mathematical statisticians are professionals who specialize in the field of statistics and are primarily focused on the mathematical theories and methodologies behind statistical analysis. Their work often involves developing new statistical methods, designing experiments, and analyzing data using mathematical frameworks. Key responsibilities and areas of focus for mathematical statisticians include: 1. **Theory Development**: They create new statistical theories and models to improve existing methodologies. This includes work on probability distributions, hypothesis testing, estimation techniques, and more.

Coding theory is an area of study in computer science and mathematics that focuses on the design and analysis of error-correcting codes and the representation of data. Coding theorists are researchers or practitioners who work in this field, exploring various aspects of coding, including: 1. **Error Detection and Correction**: Developing codes that allow for the detection and correction of errors in data transmission or storage. This is essential for reliable communication systems, such as those used in telecommunications, data storage, and computer networks.

Computer scientists are professionals who study, design, develop, and apply computational systems and methodologies to solve complex problems. They work in various areas, including algorithms, programming languages, software engineering, artificial intelligence, data structures, computer networks, cybersecurity, and more. Computer scientists typically engage in the following activities: 1. **Research**: Conducting theoretical and applied research to advance the field of computer science and develop new technologies.

Queueing theorists are researchers and practitioners who study queueing theory, which is a mathematical discipline that deals with the analysis of queues (i.e., waiting lines). This field is essential in various domains, especially in operations research, telecommunications, traffic engineering, and service systems. Queueing theory involves the study of several key components: 1. **Arrival Process**: How entities (customers, data packets, etc.) arrive at the service facility. This can be modeled using probability distributions (e.

"Statisticians by field" refers to the different areas or domains in which statisticians apply their skills and expertise. Statisticians work in a variety of industries and sectors, each with its own specific needs and applications for statistical analysis.

Pythagoreanism is a philosophical and religious doctrine founded by the ancient Greek philosopher Pythagoras (c. 570–495 BCE) and his followers, known as the Pythagoreans. This school of thought is notable for its contributions to mathematics, philosophy, and spirituality.

The American Mathematical Society (AMS) offers several awards to recognize outstanding contributions to mathematics, including research excellence, teaching, and service to the mathematical community. Some of the notable awards given by the AMS include: 1. **Steel Prize**: Awarded for outstanding research in mathematics. 2. **Bôcher Memorial Prize**: Recognizes distinguished research in analysis. 3. **Cole Prizes**: Given for notable research in algebra and number theory.

The University of Cambridge has a long-standing tradition of recognizing excellence in mathematics through various awards and prizes. Here are some notable ones: 1. **Smith's Prize**: Established in 1820, this prize is awarded annually to the best candidates in the Mathematical Tripos, which is the examination taken by undergraduate students in mathematics. 2. **Cambridge Mathematical Society Prizes**: These are awarded for outstanding performance in the Mathematical Tripos and other mathematics-related competitions or achievements.

Inca mathematics refers to the numerical and logistical systems used by the Inca Empire, which thrived in the Andean region of South America from the early 15th century until the Spanish conquest in the 16th century. The Incas did not have a written form of mathematics like many other civilizations; instead, they employed a sophisticated system based on the quipu, a device made of colored strings and knots that served as a means of record-keeping and information management.

Indian mathematics refers to the mathematical traditions and contributions that have developed in the Indian subcontinent over thousands of years. It encompasses a wide range of topics, including arithmetic, geometry, algebra, and astronomy.

The 20th century was a transformative period for mathematics, characterized by significant developments across various fields, including pure and applied mathematics. Here are some key highlights: 1. **Foundations and Logic**: The early 20th century saw a focus on the foundations of mathematics, particularly through the work of mathematicians like David Hilbert, Kurt Gödel, and Bertrand Russell.

The Faber–Jackson relation is an empirical relationship in astrophysics and cosmology that describes the correlation between the luminosity of a galaxy and the velocity dispersion of its stars, particularly in elliptical galaxies. This relation suggests that brighter galaxies tend to have a higher velocity dispersion, which is a measure of how fast the stars within the galaxy move.