AnimationAnimation is the method by which are manipulated to create moving images. In traditional animation, images are drawn or painted by hand on transparent celluloid sheets to be photographed and exhibited on film. Today, many animations are computer animations made with (CGI). Stop motion animation, in particular claymation, has continued to exist alongside these other forms. Animation is contrasted with live-action film, although the two do not exist in isolation. Many moviemakers have produced films that are a hybrid of the two.
Computer scienceComputer science is the study of computation, information, and automation. Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software). Though more often considered an academic discipline, computer science is closely related to computer programming. Algorithms and data structures are central to computer science.
Computer animationComputer animation is the process used for digitally generating animations. The more general term (CGI) encompasses both static scenes (s) and dynamic images (s), while computer animation refers to moving images. Modern computer animation usually uses 3D computer graphics to generate a three-dimensional picture. The target of the animation is sometimes the computer itself, while other times it is film. Computer animation is essentially a digital successor to stop motion techniques, but using 3D models, and traditional animation techniques using frame-by-frame animation of 2D illustrations.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Traditional animationTraditional animation (or classical animation, cel animation, or hand-drawn animation) is an animation technique in which each frame is drawn by hand. The technique was the dominant form of animation in cinema until the end of the 20th century, when there was a shift to computer animation in the industry, specifically 3D computer animation. Animation production usually begins after a story is converted into an animation film script, from which a storyboard is derived.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Computer science and engineeringComputer science and engineering (CSE) is an academic program at many universities which comprises scientific and engineering aspects of computing. CSE is also a term often used in Europe to translate the name of engineering informatics academic programs. It is offered in both undergraduate as well postgraduate with specializations. Academic programs vary between colleges, but typically include a combination of topics in computer science, computer engineering, and electrical engineering.
Theoretical computer scienceTheoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History of computer science While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved.
Algebra representationIn abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
