Graph theory is a branch of mathematics and computer science that studies the properties and applications of graphs. A graph is a collection of nodes (or vertices) connected by edges (or arcs). Graph theory provides a framework for modeling and analyzing relationships and interactions in various systems. Key concepts in graph theory include: 1. **Vertices and Edges**: The basic building blocks of a graph. Vertices represent entities, while edges represent the connections or relationships between them.

Mathematical analysis is a branch of mathematics that deals with the properties and behaviors of real and complex numbers, functions, sequences, and series. It provides the rigorous foundation for calculus and focuses on concepts such as limits, continuity, differentiation, integration, and sequences and series convergence. Key topics within mathematical analysis include: 1. **Limits**: Exploring how functions behave as they approach a specific point or infinity.

**Probability and Statistics** are two related but distinct branches of mathematics that deal with uncertainty and data analysis. ### Probability Probability is the branch of mathematics that deals with the likelihood or chance of different outcomes occurring. It provides a framework for quantifying uncertainty and making predictions based on known information. Some key concepts in probability include: - **Experiment**: A procedure that yields one of a possible set of outcomes (e.g., rolling a die).

Historians of mathematics are scholars who study the development, context, and impact of mathematical ideas throughout history. This field, often referred to as the history of mathematics, involves examining ancient texts, manuscripts, and artifacts to understand how mathematical concepts, techniques, and practices evolved over time and how they influenced various cultures and societies.

Quaternions are a number system that extends complex numbers and was first introduced by the Irish mathematician William Rowan Hamilton in 1843. The historical treatment of quaternions encompasses their discovery, development, and applications, as well as the controversies and advancements in mathematical theory associated with them. ### Discovery and Development 1. **Early Concepts**: Before quaternions were formally defined, mathematicians used various forms of complex numbers.

The historiography of mathematics is the study of the history of mathematics and how it has been interpreted, understood, and communicated over time. This field focuses not only on the historical development of mathematical concepts, theories, and practices, but also on how these developments have been recorded and analyzed by historians, scholars, and mathematicians themselves.

In the context of Wikipedia and other collaborative encyclopedia projects, a "stub" is a short article or entry that provides limited information on a topic and is often marked for expansion. The "History of mathematics" stubs would refer to short articles related to various aspects of the historical development of mathematics that need further elaboration. These stubs can cover a wide range of topics, such as: - Key mathematicians and their contributions throughout history. - Important mathematical discoveries and theories.

Mathematical problems are questions or challenges that require the application of mathematical concepts, principles, and techniques to find solutions or answers. These problems can arise in various fields, including pure mathematics, applied mathematics, engineering, science, economics, and beyond. Mathematical problems can be categorized in several ways: 1. **Type of Mathematics**: - **Arithmetic Problems**: Involving basic operations like addition, subtraction, multiplication, and division.

"Mathematics by culture" refers to the idea that mathematical practices, concepts, and understanding are influenced by the cultural context in which they are developed and used. It emphasizes that mathematics is not a universal language in a vacuum but is shaped by social, historical, philosophical, and cultural factors. Here are some key aspects to consider: 1. **Cultural Context**: Different cultures have developed unique mathematical ideas, systems, and tools that reflect their specific needs, environments, and philosophies.

The Antikythera mechanism is an ancient Greek analog device, believed to be one of the earliest known mechanical computers. It was discovered in a shipwreck off the coast of the Greek island Antikythera in 1901 and dates to around 150-100 BCE. The device is made up of a complex system of gears and is thought to have been used to calculate astronomical positions and predict celestial events, such as eclipses and the positions of the sun and moon.

Eudemus of Rhodes was an ancient Greek philosopher and a significant figure in the Peripatetic school, which was founded by Aristotle. He is generally thought to have lived during the 4th century BCE and is most commonly recognized for his contributions to ethics and the study of logic, as well as for his work on the history of philosophy, particularly his study of previous philosophical doctrines. Eudemus is often noted for his efforts in systematizing and clarifying Aristotle's teachings.

Brahmagupta's interpolation formula is a technique for finding the value of a polynomial at a certain point, based on its values at known points. It is often used in the context of numerical analysis and can be particularly useful in the interpolation of data points. Brahmagupta's formula can be derived from the idea of using differences and polynomial interpolation, and it's closely related to what we now know as finite differences.

Blackboard bold, also known as double-struck or gothic bold, is a typeface style used primarily in mathematics and physics notation. It is characterized by the use of boldface letters that resemble standard characters but have a more stylized appearance, often involving a double line effect. In typesetting, it is commonly used to represent certain sets or specific mathematical objects.

The MRB constant, or the Molar Reference Boiling point constant, is a value used in thermodynamics and physical chemistry to describe the boiling point of substances at a standard pressure, typically 1 atmosphere. It is particularly relevant for understanding the behavior of substances during phase transitions and in the context of calculations involving colligative properties.

"Gaṇita-sāra-saṅgraha" is a significant historical text in the field of mathematics, particularly in Indian mathematics. Written by the mathematician Bhāskara I in the 7th century CE, it serves as a concise compilation of various mathematical concepts and methods. The title translates to "Essence of Mathematics" or "Compendium of Mathematics." The work is primarily notable for its early treatment of arithmetic, algebra, and geometry.

George Gheverghese Joseph is a distinguished mathematician and scholar known for his contributions to the history of mathematics, particularly in the context of the mathematics of the Indian subcontinent. He holds academic positions and has been involved in promoting the understanding of the historical and cultural aspects of mathematics. Joseph is also recognized for his advocacy of diverse mathematical perspectives and for highlighting the contributions of non-Western mathematicians.

The Hobbes-Wallis controversy refers to a philosophical and scientific debate from the 17th century that centered around the nature of mathematical truths and the existence of absolute space and time. This controversy primarily involved Thomas Hobbes, an English philosopher, and John Wallis, an English mathematician and theologian. The disagreement arose over several issues related to geometry and the nature of mathematical proofs. Hobbes was critical of the geometric methods employed by Wallis and other mathematicians of the time.

Iatromathematicians, or iatromathematics, refers to a historical approach where mathematics was applied to medicine. The term combines "iatro," meaning physician or medicine, with "mathematics." Iatromathematicians sought to use mathematical principles to understand and treat medical conditions, often through the analysis of bodily functions, medical statistics, and the quantitative assessment of diseases.