Branches of new general mathematics

New General Mathematics (NGM) is a branch of mathematics that aims to provide a unified and comprehensive framework for understanding and analyzing various mathematical structures and phenomena. Here are some of the branches of New General Mathematics:

1. Algebraic Geometry: This branch deals with the study of geometric objects and their algebraic properties. It combines techniques from algebra and geometry to study the properties of curves, surfaces, and higher-dimensional objects.
2. Category Theory: This branch is concerned with the study of mathematical structures and their relationships. It provides a framework for abstracting and generalizing mathematical concepts and theories.
3. Homotopy Type Theory: This branch is a branch of mathematics that combines type theory and homotopy theory to study the properties of spaces and their relationships.
4. Non-Standard Analysis: This branch is a branch of mathematics that generalizes the traditional real number system to include non-standard models, such as infinitesimal and infinite numbers.
5. Fuzzy Mathematics: This branch is concerned with the study of fuzzy sets and fuzzy logic, which are used to model and analyze uncertain and imprecise information.
6. Intuitionistic Mathematics: This branch is a branch of mathematics that rejects the law of excluded middle and instead uses intuitionistic logic to study mathematical structures and properties.
7. Constructive Mathematics: This branch is concerned with the study of mathematical structures and properties using constructive methods, which are based on the idea that mathematical objects can be constructed using finite algorithms.
8. Mathematical Physics: This branch is concerned with the study of the mathematical foundations of physics, including the development of mathematical models and theories to describe physical phenomena.
9. Computational Mathematics: This branch is concerned with the study of mathematical algorithms and their implementation on computers, including numerical analysis, scientific computing, and computational geometry.
10. Mathematical Biology: This branch is concerned with the study of mathematical models and theories to describe biological systems and processes, including population dynamics, epidemiology, and systems biology.
11. Mathematical Finance: This branch is concerned with the study of mathematical models and theories to describe financial markets and instruments, including options pricing, risk management, and portfolio optimization.
12. Mathematical Ecology: This branch is concerned with the study of mathematical models and theories to describe ecological systems and processes, including population dynamics, community ecology, and conservation biology.
13. Mathematical Epidemiology: This branch is concerned with the study of mathematical models and theories to describe the spread of diseases and the development of interventions to control them.
14. Mathematical Neuroscience: This branch is concerned with the study of mathematical models and theories to describe the behavior of neurons and neural networks, including the study of brain function and behavior.
15. Mathematical Psychology: This branch is concerned with the study of mathematical models and theories to describe human behavior and cognition, including decision-making, perception, and learning.

These are just a few examples of the many branches of New General Mathematics. The field is constantly evolving, and new branches and subfields are emerging as researchers explore new areas of mathematics and their applications.