TopologyIn mathematics, topology (from the Greek words τόπος, and λόγος) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Computer engineeringComputer engineering (CoE or CpE) is a branch of electronic engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers require training in electronic engineering, computer science, hardware-software integration, software design, and software engineering. It uses the techniques and principles of electrical engineering and computer science, and can encompass areas such as artificial intelligence (AI), robotics, computer networks, computer architecture and operating systems.
LinguisticsLinguistics is the scientific study of language. The modern-day scientific study of linguistics takes all aspects of language into account — i.e., the cognitive, the social, the cultural, the psychological, the environmental, the biological, the literary, the grammatical, the paleographical, and the structural. Linguistics is based on a theoretical as well as descriptive study of language, and is also interlinked with the applied fields of language studies and language learning, which entails the study of specific languages.
HistoryHistory (derived ) is the systematic study and documentation of the human past. The period of events before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well as the memory, discovery, collection, organization, presentation, and interpretation of these events. Historians seek knowledge of the past using historical sources such as written documents, oral accounts, art and material artifacts, and ecological markers.
Formal sciencesFormal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems.
Applied sciencesThe following outline is provided as an overview of and topical guide to applied science: Applied science – the branch of science that applies existing scientific knowledge to develop more practical applications, including inventions and other technological advancements. Science itself is the systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Applied cryptography – applications of cryptography.
HumanitiesHumanities are academic disciplines that study aspects of human society and culture. In the Renaissance, the term contrasted with divinity and referred to what is now called classics, the main area of secular study in universities at the time. Today, the humanities are more frequently defined as any fields of study outside of natural sciences, social sciences, formal sciences (like mathematics) and applied sciences (or professional training).
Social sciencesSocial science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of society", established in the 19th century. In addition to sociology, it now encompasses a wide array of academic disciplines, including anthropology, archaeology, economics, human geography, linguistics, management science, communication science and political science.
Academic disciplinesAn academic discipline or academic field is a subdivision of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part) and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties within colleges and universities to which their practitioners belong. Academic disciplines are conventionally divided into the humanities, including language, art and cultural studies, and the scientific disciplines, such as physics, chemistry, and biology; the social sciences are sometimes considered a third category.
