Solvable groupIn mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable in radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0).
P-groupIn mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p. Abelian p-groups are also called p-primary or simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p.
Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
Orthogonal groupIn mathematics, the orthogonal group in dimension , denoted , is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations. The orthogonal group is sometimes called the general orthogonal group, by analogy with the general linear group. Equivalently, it is the group of orthogonal matrices, where the group operation is given by matrix multiplication (an orthogonal matrix is a real matrix whose inverse equals its transpose).
Quaternion groupIn group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset of the quaternions under multiplication. It is given by the group presentation where e is the identity element and commutes with the other elements of the group. Another presentation of Q8 is The quaternion group Q8 has the same order as the dihedral group D4, but a different structure, as shown by their Cayley and cycle graphs: In the diagrams for D4, the group elements are marked with their action on a letter F in the defining representation R2.
Relational databaseA relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. The term "relational database" was first defined by E. F. Codd at IBM in 1970. Codd introduced the term in his research paper "A Relational Model of Data for Large Shared Data Banks".
Fundamental groupIn the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger case of homeomorphic) have isomorphic fundamental groups.
User interface designUser interface (UI) design or user interface engineering is the design of user interfaces for machines and software, such as computers, home appliances, mobile devices, and other electronic devices, with the focus on maximizing usability and the user experience. In computer or software design, user interface (UI) design primarily focuses on information architecture. It is the process of building interfaces that clearly communicates to the user what's important. UI design refers to graphical user interfaces and other forms of interface design.
User interfaceIn the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines occur. The goal of this interaction is to allow effective operation and control of the machine from the human end, while the machine simultaneously feeds back information that aids the operators' decision-making process. Examples of this broad concept of user interfaces include the interactive aspects of computer operating systems, hand tools, heavy machinery operator controls and process controls.
Database modelA database model is a type of data model that determines the logical structure of a database. It fundamentally determines in which manner data can be stored, organized and manipulated. The most popular example of a database model is the relational model, which uses a table-based format. Common logical data models for databases include: Hierarchical database model This is the oldest form of database model. It was developed by IBM for IMS (information Management System), and is a set of organized data in tree structure.
MoodleMoodle is a free and open-source learning management system written in PHP and distributed under the GNU General Public License. Moodle is used for blended learning, distance education, flipped classroom and other online learning projects in schools, universities, workplaces and other sectors. Moodle is used to create custom websites with online courses and allows for community-sourced plugins. Moodle was originally developed by Martin Dougiamas with the goal of helping educators create online courses and focus on interaction and collaborative construction of content.
Table (database)A table is a collection of related data held in a table format within a database. It consists of columns and rows. In relational databases, and s, a table is a set of data elements (values) using a model of vertical columns (identifiable by name) and horizontal rows, the cell being the unit where a row and column intersect. A table has a specified number of columns, but can have any number of rows. Each row is identified by one or more values appearing in a particular column subset.
User-centered designUser-centered design (UCD) or user-driven development (UDD) is a framework of process (not restricted to interfaces or technologies) in which usability goals, user characteristics, environment, tasks and workflow of a product, service or process are given extensive attention at each stage of the design process. These tests are conducted with/without actual users during each stage of the process from requirements, pre-production models and post production, completing a circle of proof back to and ensuring that "development proceeds with the user as the center of focus.
Interaction techniqueAn interaction technique, user interface technique or input technique is a combination of hardware and software elements that provides a way for computer users to accomplish a single task. For example, one can go back to the previously visited page on a Web browser by either clicking a button, pressing a key, performing a mouse gesture or uttering a speech command. It is a widely used term in human-computer interaction. In particular, the term "new interaction technique" is frequently used to introduce a novel user interface design idea.
DatabaseIn computing, a database is an organized collection of data (also known as a data store) stored and accessed electronically through the use of a database management system. Small databases can be stored on a , while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance.
Human–computer interactionHuman–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design technologies that allow humans to interact with computers in novel ways. A device that allows interaction between human being and a computer is known as a "Human-computer Interface (HCI)".
Tangible user interfaceA tangible user interface (TUI) is a user interface in which a person interacts with digital information through the physical environment. The initial name was Graspable User Interface, which is no longer used. The purpose of TUI development is to empower collaboration, learning, and design by giving physical forms to digital information, thus taking advantage of the human ability to grasp and manipulate physical objects and materials.
Database normalizationDatabase normalization or database normalisation (see spelling differences) is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by British computer scientist Edgar F. Codd as part of his relational model. Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints.
Database indexA database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is accessed. Indexes can be created using one or more columns of a database table, providing the basis for both rapid random lookups and efficient access of ordered records.
Database designDatabase design is the organization of data according to a database model. The designer determines what data must be stored and how the data elements interrelate. With this information, they can begin to fit the data to the database model. A database management system manages the data accordingly. Database design involves classifying data and identifying interrelationships. This theoretical representation of the data is called an ontology. The ontology is the theory behind the database's design.
