representation math meaning

Representation (mathematics) In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships ...

Representations are considered to be mathematically conventional, or standard, when they are based on assumptions and conventions shared by the wider mathematical community. Examples of such conventional mathematical representations include base ten numerals, abaci, number lines, Cartesian graphs, and algebraic equations written using standard ...

Chapter 2 is devoted to the basics of representation theory. Here we review the basics of abstract algebra (groups, rings, modules, ideals, tensor products, symmetric and exterior powers, etc.), as well as give the main de nitions of representation theory and discuss the objects whose representations we will study (associative algebras,

The meaning and interpretation of representation is not uniform. Various types of definitions and interpretations are attributed to the notion of representation, particularly in teaching and learning mathematics (Zazkis & Liljedahl, 2004) because the meaning and interpretation of representation depends on the mathematical context (Mesquita, 1998).

Put simply, a mathematical problem can be represented using concrete or physical materials, the problem can then be represented using a diagram or picture and the same problem can be represented in the abstract, using symbolic notation: 1, 2, 3. + , -, =. Within these approaches there are variations and different representations, but they ...

Algebraic. A function is represented using a mathematical model. Numerical. A function is represented using a table of values or chart. Visual. In this way of representation, the function is shown using a continuous graph or scooter plot. Verbal. Word description is used in this way to the representation of a function.

Representation theory was born in 1896 in the work of the German mathematician F. G. Frobenius. This work was triggered by a letter to Frobenius by R. Dedekind. ... the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students, and its extended version given by the ...

Definition 1.9. A representation of an algebra A (also called a left A-module) is a vector space. V together with a homomorphism of algebras δ : A ⊃ EndV . Similarly, a right A-module is a space V equipped with an antihomomorphism δ : A ⊃ EndV ; i.e., δ satisfies δ(ab) = δ(b)δ(a) and δ(1) = 1.

dimensional representation of U is a direct sum of irreducible representations. As another example consider the representation theory of quivers. A quiver is a finite oriented graph Q. A representation of Q over a field k is an assignment of a k-vector space Vi to every vertex i of Q, and of a linear operator Ah: Vi ⊃ Vj to every directed

Definitions. As most commonly interpreted in education, mathematical representations are visible or tangible productions - such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, written words, mathematical expressions, formulas and equations, or depictions on the screen of a computer or ...

representation are important to consider in school mathematics. Fig. 3.8. A child's representation of five and one-half Some forms of representation—such as diagrams, graphical displays, and symbolic expressions—have long been part of school mathematics. Unfortunately, these representations and others have often been taught and

Representation theory studies how algebraic structures "act" on objects. A simple example is how the symmetries of regular polygons, consisting of reflections and rotations, transform the polygon.. Representation 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 ...

Given any representation ρ of Gon a space V of dimension n, a choice of basis in V identifies this linearly with Cn. Call the isomorphism φ. Then, by formula (1.10), we can define a new representation ρ 2 of Gon Cn, which is isomorphic to (ρ,V). So any n-dimensional representation of Gis isomorphic to a representation on Cn. The use of an ...

A representation of G is a group action of G on V that is linear (so preserves the vector space structure of V) - i.e. for every g ∈ G, u, v ∈ V, μ, λ ∈ k g(λu + μv) = λg(u) + μg(v). This is the definition that you have been given. With V as before, an equivalent definition is this:

Symmetries occur throughout mathematics and science. Representation theory seeks to understand all the possible ways that an abstract collection of symmetries can arise. Nineteenth-century representation theory helped to explain the structure of electron orbitals, and 1920s representation theory is at the heart of quantum chromodynamics.

When the coefficients are contained in the complex numbers, representations of groups have been studied for a long time, and have many applications. With coefficients in the integers modulo $2$, for example, the algebras and their representations are much harder to understand. For some groups, the representations have 'finite type'.

This was our first example of translating between two different representations (connecting visual to concrete). Now, we can support students even further by helping them represent their understanding with symbols. Here the student counts the collection of five counters and writes the numeral "5" below it. They do the same for the four ...

Algebra: The branch of mathematics that substitutes letters for numbers to solve for unknown values. Algorithm: A procedure or set of steps used to solve a mathematical computation. Angle: Two rays sharing the same endpoint (called the angle vertex). Angle Bisector: The line dividing an angle into two equal angles.

Representation is NCTM's Professional Development Focus of the Year (FOY) for 2006-2007. The theme we will use to promote this FOY is "Show Me the Math: Learning through Representation.". Movie buffs will notice a play on the phrase "Show me the money," which was popularized by the film Jerry Maguire. We chose this phrase because it ...

Symbolic representation in mathematics is the practice of using symbols to express mathematical ideas. Symbols can represent numbers (like '1' or 'π'), operations (such as '+' for addition or '−' for subtraction), relations (like '=' for equality or '≤' for less than or equal to), or functions (such as 'f (x ...

Algebra representation. In 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 ...

A contextual representation is much like it sounds. We are giving context to an idea. It is how math can be applied in the real world. Given that we learn math to help us solve real-world problems, it's a pretty important representation. Example. Let's look back at the red and yellow counters from our previous discussions.

representation: [noun] one that represents: such as. an artistic likeness or image. a statement or account made to influence opinion or action. an incidental or collateral statement of fact on the faith of which a contract is entered into. a dramatic production or performance. a usually formal statement made against something or to effect a ...