Theoretical computer science
Overview
 
Theoretical computer science (TCS) is a division or subset of general computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

 and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 which focuses on more abstract or mathematical aspects of computing.

These divisions and subsets include analysis of algorithms
Analysis of algorithms
To analyze an algorithm is to determine the amount of resources necessary to execute it. Most algorithms are designed to work with inputs of arbitrary length...

 and formal semantics of programming languages
Formal semantics of programming languages
In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation...

. Technically, there are hundreds of divisions and subsets besides these two. Each of the multiple parts have their own individual personal leaders (of popularity) and there are many associations and professional social groups and publications of distinction.
It is not easy to circumscribe the theory areas precisely and the ACM
Association for Computing Machinery
The Association for Computing Machinery is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...

's Special Interest Group on Algorithms and Computation Theory (SIGACT) describes its mission as the promotion of theoretical computer science and notes:
To this list, the ACM's journal Transactions on Computation Theory adds coding theory
Coding theory
Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding...

, computational learning theory
Computational learning theory
In theoretical computer science, computational learning theory is a mathematical field related to the analysis of machine learning algorithms.-Overview:Theoretical results in machine learning mainly deal with a type of...

 and theoretical computer science aspects of areas such as databases, information retrieval
Information retrieval
Information retrieval is the area of study concerned with searching for documents, for information within documents, and for metadata about documents, as well as that of searching structured storage, relational databases, and the World Wide Web...

, economic models and networks
Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information....

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