AlgebraAlgebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields.
Hardware engineeringComputer hardware includes the physical parts of a computer, such as the case, central processing unit (CPU), random access memory (RAM), monitor, mouse, keyboard, computer data storage, graphics card, sound card, speakers and motherboard. By contrast, software is the set of instructions that can be stored and run by hardware. Hardware is so-termed because it is "hard" or rigid with respect to changes, whereas software is "soft" because it is easy to change. Hardware is typically directed by the software to execute any command or instruction.
Computer securityComputer security, cyber security, digital security or information technology security (IT security) is the protection of computer systems and networks from attacks by malicious actors that may result in unauthorized information disclosure, theft of, or damage to hardware, software, or data, as well as from the disruption or misdirection of the services they provide. The field is significant due to the expanded reliance on computer systems, the Internet, and wireless network standards such as Bluetooth and Wi-Fi.
Classical logicClassical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Each logical system in this class shares characteristic properties: Law of excluded middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and idempotency of entailment Commutativity of conjunction De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.
Control theory and engineeringControl engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance.
High-performance computingHigh-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems. HPC integrates systems administration (including network and security knowledge) and parallel programming into a multidisciplinary field that combines digital electronics, computer architecture, system software, programming languages, algorithms and computational techniques. HPC technologies are the tools and systems used to implement and create high performance computing systems.
Systems theorySystems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior. Changing one component of a system may affect other components or the whole system.
Computer graphicsComputer 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. Computer graphics studies manipulation of visual and geometric information using computational techniques. It focuses on the mathematical and computational foundations of image generation and processing rather than purely aesthetic issues.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Artificial intelligenceArtificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of human beings or animals. AI applications include advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
