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Part of: Science Philosophy
Related: Natural science
Includes:Mathematics
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Definitions¶

Branch of science studying disciplines concerned with abstract [[Structures|structures]] described by formal systems, which use [[a priori]] knowledge, as opposed to empiricism

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Main resources¶

Formal science - Wikipedia

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Formal science - Wikipedia
- Cryptography, Logic, Mathematics, Computer science (Artificial Intelligence), Physics, Systems theory, Systems science
Branches of science - Wikipedia
- Information theory, [[Information science]], Data science, Systems theory, [[Decision theory]], Statistics
Linguistics

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AI¶

Formal sciences are disciplines that study formal systems, using mathematical and logical methods. They are crucial in developing the theoretical underpinnings for other scientific fields. Here's a comprehensive list of the various branches and sub-disciplines within formal sciences:

1. Mathematics ¶

Pure Mathematics
- Algebra
- Geometry
- Calculus
- Topology
- Number Theory
- Logic
- Combinatorics
- Set Theory
- Category Theory
- Graph Theory
Applied Mathematics
- Mathematical Physics
- Mathematical Finance
- Mathematical Economics
- Computational Mathematics
- Biomathematics
- Cryptography
- Game Theory
- Operations Research
- Probability Theory
- Statistics
- Differential Equations
- Dynamical Systems
- Numerical Analysis
- Optimization

2. Computer Science ¶

Theoretical Computer Science
- Algorithms
- Data Structures
- Computational Complexity
- Automata Theory
- Cryptography
- Quantum Computing
Computer Systems
- Operating Systems
- Distributed Computing
- Parallel Computing
- Computer Architecture
- Computer Networking
Software Engineering
- Systems Analysis
- Software Design
- Software Testing
- Human-Computer Interaction
Artificial Intelligence
- Machine Learning
- Natural Language Processing
- Robotics
- Computer Vision
- Expert Systems
Data Science
- Data Mining
- Big Data Analytics
- Information Retrieval
- Database Systems
Computer Graphics
- Image Processing
- Visualization
- Animation
- Virtual Reality
Information Systems
- Management Information Systems
- Geographic Information Systems

3. Logic¶

Mathematical Logic
- Propositional Logic
- Predicate Logic
- Modal Logic
- Temporal Logic
- Fuzzy Logic
Philosophical Logic
Computational Logic
Non-classical Logics
Logic in Computer Science
Model Theory
Proof Theory
Set Theory

4. Statistics¶

Descriptive Statistics
Inferential Statistics
Probability Theory
Biostatistics
Econometrics
Environmental Statistics
Psychometrics
Bayesian Statistics
Time Series Analysis
Multivariate Analysis
Experimental Design
Survey Methodology
Statistical Modeling

5. Systems Science¶

Systems Theory
Cybernetics
Complex Systems
Dynamical Systems
Systems Engineering
Control Systems
Network Science
Systems Biology
Systems Dynamics

6. Linguistics (as a Formal Science)¶

Computational Linguistics
Phonology
Syntax
Semantics
Morphology
Formal Grammars
Corpus Linguistics

7. Information Theory¶

Coding Theory
Signal Processing
Data Transmission
Compression Algorithms
Cryptanalysis
Quantum Information Theory

8. Decision Theory¶

Game Theory
Risk Analysis
Utility Theory
Social Choice Theory
Multi-Criteria Decision Analysis

9. Formal Semiotics¶

Semantics
Syntactics
Pragmatics
Semiotic Analysis

10. Formal Philosophy¶

Formal Epistemology
Formal Ethics
Formal Aesthetics

This list, while extensive, may not cover every specialized area as formal sciences are characterized by their continuous evolution and the emergence of new sub-disciplines. Each of these branches can be further divided into even more specialized fields, reflecting the depth and complexity of studying formal systems and their applications across various domains.

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