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  Formal Sciences

Formal Science is the study of formal language disciplines such as Logic, Mathematics, Statistics, Theoretical Computer Science, Artificial Intelligence (AI), Information Theory, Game Theory, Systems Theory, Decision Theory, and Theoretical Linguistics. The Formal Sciences are linguistic tools for describing abstract structures described by symbolic systems. The Formal Sciences are language tools concerned with characterizing abstract structures expressed by symbolic systems, whereas the Natural Sciences and Social Sciences utilize empirical approaches to characterize physical and social systems, respectively. Natural Science, Social Science, and actuarial science all benefit from Formal Sciences since they provide information about the structures used to represent the physical and contemporary world, as well as the conclusions that can be reached from them. Mathematics is a formal science, also known as the science of numbers. Computer Science, Mathematics, Statistics, Information Science, and Systems Science are examples of Formal Science branches. 

Formal Sciences predate the scientific method, with the first mathematical books originating from 1800 BC (Babylonian mathematics), 1600 BC (Egyptian mathematics), and 1000 BC (Indian mathematics). From then on, other cultures such as Greek, Arab, and Persian made significant contributions to mathematics, while the Chinese and Japanese created their own mathematical legacy independent of more distant nations.

Since a lot of other Formal Science disciplines rely heavily on Mathematics, they did not exist until mathematics had progressed to an advanced degree. The earliest studies of probability theory were begun by Pierre de Fermat and Blaise Pascal (1654), as well as Christiaan Huygens (1657). Gauss and Laplace created the mathematical theory of statistics in the early 1800s, which also described how statistics are used in insurance and government accounting. In the early twentieth century, mathematical statistics was recognized as a mathematical field.

The advent of new Mathematical Sciences and Engineering fields such as Operations Research and Systems Engineering widened and enhanced Mathematics in the mid-twentieth century. Basic research in Electrical Engineering aided these areas, as did the development of electrical computing, which boosted information theory, numerical analysis (scientific computing), and Theoretical Computer Science. The field of Mathematical Logic, which includes the theory of computation, improves Theoretical Computer Science as well.

List of Subjects:

  • Artificial Intelligence and Machine Learning
  • Game Design and Development
  • Algorithms, Combinatorics, and Optimization
  • Computer Security and Reliability
  • Data Science/Analytics
  • Human-Computer Interaction (HCI)
  • Software Development
  • Computational Biology (Bioinformatics)
  • Software Engineering
  • Information Systems
  • Software Systems
  • Robotics
  • Computer Networking
  • Cloud Computing
  • Information Science
  • Computer Architecture and Engineering
  • Computer Graphics
  • Image Processing
  • Scientific Visualization
  • Cyber Security
  • List of Subjects:

  • Pure Mathematics
  • Mathematical Logic
  • Foundations of Mathematics
  • Algebra
  • Field Theory
  • Group Theory
  • Homological Algebra
  • K-Theory
  • Lattice Theory (Order Theory)
  • Lie Algebra
  • Linear Algebra (Vector Space)
  • Multilinear Algebra
  • Non-Associative Algebra
  • Representation Theory
  • Ring Theory
  • Universal Algebra
  • Analysis
  • Complex Analysis
  • Functional Analysis
  • Harmonic Analysis
  • Non-Standard Analysis
  • Ordinary Differential Equations
  • P-Adic Analysis
  • Partial Differential Equations
  • Real Analysis
  • Probability Theory
  • Ergodic Theory
  • Measure Theory
  • Stochastic Process
  • Geometry and Topology
  • Affine Geometry
  • Algebraic Geometry
  • Algebraic Topology
  • Convex Geometry
  • Differential Topology
  • Discrete Geometry
  • Finite Geometry
  • Galois Geometry
  • General Topology
  • Geometric Topology
  • Integral Geometry
  • Noncommutative Geometry
  • Non-Euclidean Geometry
  • Projective Geometry
  • Number Theory
  • Algebraic Number Theory
  • Analytic Number Theory
  • Arithmetic Combinatorics
  • Geometric Number Theory
  • Applied Mathematics
  • Approximation Theory
  • Combinatorics
  • Cryptography
  • Dynamical Systems
  • Game Theory
  • Graph Theory
  • Information Theory
  • Quantum Mechanics
  • Numerical Analysis
  • Operations Research
  • Statistics
  • Theory of Computation
  • Linear Programming
  • Data Science
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