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Sanjeev Katariya

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Formal Science

Formal science is involved in the study of formal systems. It includes systems theory, and theoretical computer science. The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts. The formal sciences are therefore a priori disciplines and because of this, there is disagreement on whether they actually constitute a science. Nevertheless, the formal sciences play an important role in the empirical sciences.

1. Systems Theory

Systems theory is the interdisciplinary study of systems. A system is a cohesive conglomeration of interrelated and interdependent parts that is either natural or man-made. Every system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose or nature and expressed in its functioning. In terms of its effects, a system can be more than the sum of its parts if it expresses synergy or emergent behavior. Changing one part of the system usually affects other parts and the whole system, with predictable patterns of behavior. For systems that are self-learning and self-adapting, the positive growth and adaptation depend upon how well the system is adjusted with its environment. Some systems function mainly to support other systems by aiding in the maintenance of the other system to prevent failure. The goal of systems theory is systematically discovering a system's dynamics, constraints, conditions and elucidating principles (purpose, measure, methods, tools, etc.) that can be discerned and applied to systems at every level of nesting, and in every field for achieving optimized equifinality.


  • Abstract systems theory (also see: formal system)
    It is a mathematical theory of systems based on the "top-down"-formalization-approach of formal systems. A formal system is used to infer theorems from axioms according to a set of rules. These rules used to carry out the inference of theorems from axioms are known as the logical calculus of the formal system. A formal system may represent a well-defined system of abstract thought. Spinoza's Ethics imitates the form of Euclid's Elements. Spinoza employed Euclidean elements such as "axioms" or "primitive truths", rules of inferences, etc., so that a calculus can be built using these
  • Action Theory
    In sociology, action theory is the theory of social action presented by the American theorist Talcott Parsons. Parsons established action theory to integrate the study of social order with the structural and voluntaristic aspects of macro and micro factors. In other words, he was trying to maintain the scientific rigour of positivism, while acknowledging the necessity of the "subjective dimension" of human action incorporated in hermeneutic types of sociological theorizing. Parsons sees motives as part of our actions. Therefore, he thought that social science must consider ends, purposes and ideals when looking at actions. Parsons placed his discussion within a higher epistemological and explanatory context of systems theory and cybernetics.
  • Adaptive systems theory (also see: complex adaptive system)
    An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological homeostasis or evolutionary adaptation in biology. Feedback loops represent a key feature of adaptive systems, such as ecosystems and individual organisms; or in the human world, communities, organizations, and families.
  • Applied general systems theory (also see: general systems theory)
    It is a multidisciplinary formal approach to modelling of systems and processes of ‘Applied Systems Theory’ makes it suitable for managers, engineers, students, researchers, academics and professionals from a wide range of disciplines. Applied systems theory can be used to describe, analyze,  and design biological, engineering and organizational systems as well as getting a better understanding of societal problems. It covers areas like abductive reasoning, the relevance of systems theories for research methods and problem analysis and solving based on systems theories.
  • Applied multidimensional systems theory
    Is a study of Multidimensional signal processing. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications.
  • Archaeological systems theory (also see: Systems theory in archaeology)
    Systems theory in archaeology is the application of systems theory and systems thinking in archaeology. It originated with the work of Ludwig von Bertalanffy in the 1950s, and is introduced in archaeology in the 1960s with the work of Sally R. Binford & Lewis Binford's "New Perspectives in Archaeology" and Kent V. Flannery's "Archaeological Systems Theory and Early Mesoamerica".
  • Systems theory in anthropology
    Systems theory in anthropology is an interdisciplinary, non-representative, non-referential, and non-Cartesian approach that brings together natural and social sciences to understand society in its complexity.
  • Associated systems theory
  • Behavioral systems theory
    Behavioral Systems Theory (BST) is the confluence of principles from behavior analysis and dynamical systems theory applied to human development. BST takes a natural science approach to the study of the changes in behavior/environment relationships over the lifespan. In BST, simple mechanisms produce complex developmental outcomes. The parallelism between natural selection and learning is emphasized and the importance of principles of operant learning in development is stressed. Development is considered to be multidirectional, multiply determined and multileveled. Among the BST principles described are reciprocal determinism, nonlinearity, coalescent organization, leading parts, control parameters, and attractor states. The role of contingencies in organizing patterns of behavior is presented. Weight is placed on development as skills learning. 
  • Biochemical systems theory
    Biochemical systems theory is a mathematical modelling framework for biochemical systems, based on ordinary differential equations (ODE), in which biochemical processes are represented using power-law expansions in the variables of the system.
  • Biomatrix systems theory
    Biomatrix systems theory claims to be an integrated systems theory. It was developed through an interdisciplinary PhD programme at the University of Cape Town. The aim being to identify generic organizing principles of all systems and the differences between social, natural and technological systems.
  • Body system
    Throughout the course of human evolution, humans have been solving complex problems. Various system theories such as General Systems Theory, Chaos Theory, Complex-Adaptive Systems, and Integral Theory apply and are discussed within the context of the human body. Different systems of varying context, such as: (1) when facilitating sustainable changes in organizations; (2) when promoting the unification of health care teams to enhance patient care; and (3) when explaining treatment principles in oncology arr working examples. Systems theory has many applications, not only in leadership and organization, but also in oncology.
  • Complex adaptive systems theory (also see: complex adaptive system)
  • Complex systems theory[(also see: complex systems)
  • Computer-aided systems theory
  • Conceptual systems theory (also see: conceptual system)
  • Control systems theory(also see: control system)
  • Critical systems theory (also see: critical systems thinking, and critical theory)
  • Cultural Agency Theory
  • Developmental systems theory
  • Distributed parameter systems theory
  • Dynamical systems theory
  • Ecological systems theory (also see: ecosystem, ecosystem ecology)
  • Economic systems theory (also see: economic system)
  • Electric energy systems theory
  • Family systems theory (also see: systemic therapy)
  • Fuzzy systems theory (also see: fuzzy logic)
  • General systems theory
  • Human systems theory (see: human systems)
  • Infinite dimensional systems theory
  • Large scale systems theory
  • Liberating systems theory
  • Linear systems theory (also see: linear system)
  • Living systems theory
  • LTI system theory
  • Macrosystems theory
  • Mathematical systems theory
  • Medical ethics systems theory
  • Modeling systems theory
  • Modern control systems theory
  • Modern systems theory
  • Multidimensional systems theory
  • Nonlinear stochastic systems theory (also see: stochastic modeling).General system approach
  • Operating systems theory(also see: operating system)
  • Open systems theory(also see: open system)
  • Pattern language
    Was also first conceived by an Austrian and has many similarities with systems thinking. It too is a way of describing how things work holistically, but disaggregated into patterns which interact to give emergent properties. Originally applied to architecture it has been extended into many other fields.
  • Physical systems theory (also see: physical system)
  • Pulley system
  • Retrieval system theory
  • Social systems theory (also see: social system)
  • Sociotechnical systems theory
  • Social rule system theory
  • Transit systems theory
  • World-systems theory

2. Computer Science

Computer science is the theory, experimentation, and engineering that form the basis for the design and use of computers. It involves the study of algorithms that process, store, and communicate digital information. A computer scientist specializes in the theory of computation and the design of computational systems.

Its fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory (which explores the fundamental properties of computational and intractable problems), are highly abstract, while fields such as computer graphics emphasize real-world visual applications. Other fields focus on challenges in implementing computation. For example, programming language theory considers various approaches to the description of computation, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems. Human–computer interaction considers the challenges in making computers and computations useful, usable, and universally accessible to humans.


  • Theoretical Computer Science,
    TCS is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
    • Computability or Recursion Theory
      Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory.
    • Computational Complexity Theory
      Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.
    • Information Theory  
      Algorithmic information theory principally studies complexity measures on strings (or other data structures). Because most mathematical objects can be described in terms of strings, or as the limit of a sequence of strings, it can be used to study a wide variety of mathematical objects, including integers.
    • Data Structures and Algorithms  
      Data structures and algorithms is the study of commonly used computational methods and their computational efficiency.
      • Analysis
      • Algorithms
      • Data Structures
      • Combinatorial Optimization
      • Computational Geometry
    • Theory of Computation  
      In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?"
      • Automata Theory
        Formal Language Theory
      • Computability Theory
      • Computational Complexity Theory
      • Cryptography
      • Quantum Computing Theory
    • Information and Coding Theory  
      Information theory is related to the quantification of information. This was developed by Claude Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data. Coding theory is the study of the properties of codes (systems for converting information from one form to another) and their fitness for a specific application. Codes are used for data compression, cryptography, error detection and correction, and more recently also for network coding. Codes are studied for the purpose of designing efficient and reliable data transmission methods.
    • Programming Language Theory
      Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of programming languages and their individual features. It falls within the discipline of computer science, both depending on and affecting mathematics, software engineering, linguistics and even cognitive science. 
      • Formal Semantics
      • Type Theory
      • Compiler Construction
      • Programming analysis and transformation
      • Comparative Programming Language Analysis
      • Generic and Meta programming
      • Domain-Specific Languages
      • Run-time System
      • Programming Languages
        - Application Programming Interfaces
  • Computer Systems
    Have grown to cover areas like digital logic, micro-architectures,  ubiquitous computer (IoT), operating systems, distributed systems, and systems architecture.
    • Computer Architecture and Engineering  
      Computer architecture, or digital computer organization, is the conceptual design and fundamental operational structure of a computer system. It focuses largely on the way by which the central processing unit performs internally and accesses addresses in memory. The field often involves disciplines of computer engineering and electrical engineering, selecting and interconnecting hardware components to create computers that meet functional, performance, and cost goals.
      • Digital Logic
      • Microarchitecture
      • Multiprocessing
      • Ubiquitous Computing
      • Systems Architecture
      • Operating Systems
    • Computer Performance Analysis
      Computer performance is the amount of work accomplished by a computer system. Depending on the context, high computer performance may involve one or more of the following
      • Short response time for a given piece of work 
      • High throughput (rate of processing work)
      • Low utilization of computing resource(s)
      • High availability of the computing system or application
      • Fast (or highly compact) data compression and decompression
      • High bandwidth
      • Short data transmission time
    • Concurrent, Parallel and Distributed Systems  
      Concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other. A number of mathematical models have been developed for general concurrent computation including Petri nets, process calculi and the Parallel Random Access Machine model. A distributed system extends the idea of concurrency onto multiple computers connected through a network. Computers within the same distributed system have their own private memory, and information is often exchanged among themselves to achieve a common goal. A good description of modern day distributed systems is available in github Cloud Native Landscape. 
    • Computer Networks  
      A computer network, or data network, is a digital telecommunications network which allows nodes to share resources. In computer networks, computing devices exchange data with each other using connections between nodes (data links.) These data links are established over cable media such as wires or optic cables, or wireless media such as WiFi.
    • Computer Storage
      Computer data storage, often called storage or memory, is a technology consisting of computer components and recording media that are used to retain digital data. It is a core function and fundamental component of computers.
    • Computer Security and Cryptography  
      Computer security is a branch of computer technology, whose objective includes protection of information from unauthorized access, disruption, or modification while maintaining the accessibility and usability of the system for its intended users. Cryptography is the practice and study of hiding (encryption) and therefore deciphering (decryption) information. Modern cryptography is largely related to computer science, for many encryption and decryption algorithms are based on their computational complexity.
    • Databases  
      An example of output from an SQL database query. A database is an organized collection of data. A relational database, more restrictively, is a collection of schemas, tables, queries, reports, views, and other elements. Database designers typically organize the data to model aspects of reality in a way that supports processes requiring information, such as (for example) modelling the availability of rooms in hotels in a way that supports finding a hotel with vacancies
    • No-SQL Databases  
      A NoSQL (originally referring to "non SQL" or "non relational") database provides a mechanism for storage and retrieval of data that is modeled in means other than the tabular relations used in relational databases. Such databases have existed since the late 1960s, but did not obtain the "NoSQL" moniker until a surge of popularity in the early twenty-first century, triggered by the needs of Web 2.0 companies such as Facebook, Google, and Amazon. NoSQL databases are increasingly used in big dataand real-time web applications. NoSQL systems are also sometimes called "Not only SQL" to emphasize that they may support SQL-like query languages.
      • Key-value store
      • Document store
      • Graph
      • Object database
      • Tabular
      • Tuple store
      • Triple/quad store (RDF) database
      • Hosted
      • Multivalue databases
      • Multimodel database
    • Mobile Systems
      Mobile computing is human–computer interaction by which a computer is expected to be transported during normal usage, which allows for transmission of data, voice and video. Mobile computing involves mobile communication, mobile hardware, and mobile software. Communication issues include ad hoc networks and infrastructure networks as well as communication properties, protocols, data formats and concrete technologies. Hardware includes mobile devices or device components. Mobile software deals with the characteristics and requirements of mobile applications
    • IoT systems  
      The Internet of Things (IoT) is the network of physical devices, vehicles, home appliances and other items embedded with electronics, software, sensors, actuators, and connectivity which enables these things to connect and exchange data, creating opportunities for more direct integration of the physical world into computer-based systems, resulting in efficiency improvements, economic benefits and reduced human intervention
    • Augmented Reality - Virtual Reality
      Augmented Reality (AR) is an interactive experience of a real-world environment whose elements are "augmented" by computer-generated perceptual information, sometimes across multiple sensory modalities, including visual, auditory, haptic, somatosensory, and olfactory. The overlaid sensory information can be constructive (i.e. additive to the natural environment) or destructive (i.e. masking of the natural environment) and is seamlessly interwoven with the physical world such that it is perceived as an immersive aspect of the real environment. In this way, augmented reality alters one’s ongoing perception of a real world environment, whereas virtual reality completely replaces the user's real world environment with a simulated one. Augmented reality is related to two largely synonymous terms: mixed reality and computer-mediated reality. Virtual reality (VR) is an interactive computer-generated experience taking place within a simulated environment, that incorporates auditory, visual, haptic, and other types of sensory feedback. This immersive environment can be similar to the real world or it can be fantastical, creating an experience that is not possible in ordinary physical reality. Augmented reality systems may also be considered a form of VR that layers virtual information over a live camera feed into a headset or through a smartphone or tablet device giving the user the ability to view three-dimensional images.
  • Computer Applications
    Have grown to cover wide ranging areas  like computer graphics, visualization, human computer interactions, scientific computing, artificial intelligence, 
    • Computer Graphics and Visualization
      Computer graphics is a sub-field of Computer Science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
      • Geometry
      • Animation
      • Rendering
    • Human-Computer Interactions
      Human–computer interaction (HCI) researches the design and use of computer technology, focused on the interfaces between people (users) and computers. Researchers in the field of HCI both observe the ways in which humans interact with computers and design technologies that let humans interact with computers in novel ways. As a field of research, human–computer interaction is situated at the intersection of computer science, behavioral sciences, design, media studies, and several other fields of study. 
      • User customization
      • Embedded computation
      • Augmented reality
      • Social computing
      • Knowledge-driven human–computer interaction
      • Brain–computer interfaces
    • Scientific Computing
      Computational science (also scientific computing or scientific computation (SC)) is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core it involves the development of models and simulations to understand natural systems.
      • Numerical Analysis
      • Computational Physics
      • Computational Chemistry
      • Bioinformatics
    • Artificial Intelligence
      Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence(NI) displayed by humans and other animals. In computer science AI research is defined as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of successfully achieving its goals. Colloquially, the term "artificial intelligence" is applied when a machine mimics "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving"
      • Reasoning and Problem Solving
        -- Embodied Agents
        -- Neural Net
        -- Statistical
      • Knowledge Representation
      • Knowledge Engineering
        -- Modeling
        -- Management
        -- Retrieval
        -- Tagging
        -- Method Engineering
      • Planning
      • Machine Learning
      • Natural Language Processing
      • Perception
      • Motion and Manipulation
      • Social Intelligence
      • Creativity
      • Ethics and Values
      • General Intelligence
      • Super Intelligence
      • Wisdom and Insight
      • Evolutionary Computation
    • Blockchain  
      A blockchain, originally block chain, is a continuously growing list of records, called blocks, which are linked and secured using cryptography. Each block typically contains a cryptographic hash of the previous block, a timestamp, and transaction data. By design, a blockchain is resistant to modification of the data. It is "an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way". For use as a distributed ledger, a blockchain is typically managed by a peer-to-peer network collectively adhering to a protocol for inter-node communication and validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without alteration of all subsequent blocks, which requires consensus of the network majority.
    • Enterprise Resource Planning
      Enterprise resource planning (ERP) is the integrated management of core business processes, often in real-time and mediated by software and technology. ERP is usually referred to as a category of business-management software — typically a suite of integrated applications—that an organization can use to collect, store, manage, and interpret data from these many business activities.
      • Product Planning and Purchase
      • Production Planning
      • Manufacturing or Service Delivery
      • Marketing
      • Sales
      • Materials Management
      • Inventory Management
      • Retail
      • Shipping
      • Payment
      • Financial Management
      • Financial Performance
  • Software Engineering
    Is the application of engineering to the development of software in a systematic method.  
    • Software requirements  
      The Software Requirements knowledge area (KA) is concerned with the elicitation, analysis, specification, and validation of software requirements as well as the management of requirements during the whole life cycle of the software product. It is widely acknowledged amongst researchers and industry practitioners that software projects are critically vulnerable when the requirements-related activities are poorly performed.
    • Software design  
      Design is defined as both “the process of defining the architecture, components, interfaces, and other characteristics of a system or component” and “the result of [that] process” . Viewed as a process, software design is the software engineering life cycle activity in which software requirements are analyzed in order to produce a description of the software’s internal structure that will serve as the basis for its construction.
    • Software development  
      The term software development/construction refers to the detailed creation of working software through a combination of coding, verification, unit testing, integration testing, and debugging. The Software Construction knowledge area (KA) is linked to all the other KAs, but it is most strongly linked to Software Design and Software Testing because the software construction process involves significant software design and testing.
      • View model
      • Business process and data modelling
      • Computer-aided software engineering
      • Integrated development environment
      • Modeling language
      • Programming paradigm
      • Reuse of solutions
    • Software testing  
      Software testing consists of the dynamic verification that a program provides expectedbehaviors on a finite set of test cases, suitably selected from the usually infinite execution domain.
    • Software quality  
      More recently, software quality is defined as the “capability of software product to satisfy stated and implied needs under specified conditions”  and as “the degree to which a software product meets established requirements; however, quality depends upon the degree to which those established requirements accurately represent stakeholder needs, wants, and expectations”
    • Software maintenance  
      Software development efforts result in the delivery of a software product that satisfies user requirements. Accordingly, the software product must change or evolve. Once in operation, defects are uncovered, operating environments change, and new user requirements surface.
    • Software configuration management  
      A discipline applying technical and administrative direction and surveillance to: identify and document the functional and physical characteristics of a configuration item, control changes to those characteristics, record and report change processing and implementation status, and verify compliance with specified requirements.
    • Software engineering management  
      Software engineering management can be defined as the application of management activities—planning, coordinating, measuring, monitoring, controlling, and reporting1—to ensure that software products and software engineering services are delivered efficiently, effectively, and to the benefit of stakeholders.
    • Software engineering process  
      Software engineering processes are concerned with work activities accomplished by software engineers to develop, maintain, and operate software, such as requirements, design, construction, testing, configuration management, and other software engineering processes.
    • Software engineering Modeling  
      Software engineering models and methods impose structure on software engineering with the goal of making that activity systematic, repeatable, and ultimately more success-oriented. Using models provides an approach to problem solving, a notation, and procedures for model construction and analysis.
    • Software engineering professional practice  
      The Software Engineering Professional Practice knowledge area (KA) is concerned with the knowledge, skills, and attitudes that software engineers must possess to practice software engineering in a professional, responsible, and ethical manner.
    • Software engineering economics  
      Software engineering economics is about making decisions related to software engineering in a business context. The success of a software product, service, and solution depends on good business management. Yet, in many companies and organizations, software business relationships to software development and engineering remain vague
    • Computing foundations  
      The scope of the Computing Foundations knowledge area (KA) encompasses the development and operational environment in which software evolves and executes. Because no software can exist in a vacuum or run without a computer, the core of such an environment is the computer and its various components.
    • Mathematical foundations  
      The SWEBOK Guide’s Mathematical Foundations KA covers basic techniques to identify a set of rules for reasoning in the context of the system under study. Anything that one can deduce following these rules is an absolute certainty within the context of that system. 
    • Engineering foundations  
      This Engineering Foundations knowledge area (KA) is concerned with the engineering foundations that apply to software engineering and other engineering disciplines.

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