CushionTheBlow (구 BluemoonSoft)

A Lyceum can be

an educational institution (often a school of secondary education in Europe), or
a public hall used for cultural events like concerts.

The precise usage of the term varies among various countries.

(See also Lyceum Movement for a discussion of the lyceum movement and its participants in the United States.)

Reference:
http://en.wikipedia.org/wiki/Lyceum

Primary education is the first stage of compulsory education. It is preceded by pre-school or nursery education and is followed by secondary education. In North America this stage of education is usually known as elementary education.

In most countries, it is compulsory for children to receive primary education, though in many jurisdictions it is permissible for parents to provide it. The transition to secondary school or high school is somewhat arbitrary, but it generally occurs at about eleven or twelve years of age. Some educational systems have separate middle schools with the transition to the final stage of education taking place at around the age of fourteen.

 The major goals of primary education are achieving basic literacy and numeracy amongst all pupils, as well as establishing foundations in science, geography, history and other social sciences. The relative priority of various areas, and the methods used to teach them, are an area of considerable political debate.

Typically, primary education is provided in schools, where the child will stay in steadily advancing classes until they complete it and move on to high school/secondary school. Children are usually placed in classes with one teacher who will be primarily responsible for their education and welfare for that year. This teacher may be assisted to varying degrees by specialist teachers in certain subject areas, often music or physical education. The continuity with a single teacher and the opportunity to build up a close relationship with the class is a notable feature of the primary education system.

Traditionally, various forms of corporal punishment have been an integral part of early education. Recently this practice has come under attack, and in many cases been outlawed, especially in Western countries.

Reference:
http://en.wikipedia.org/wiki/Primary_education

Compulsory education is education which children are required by law to receive and governments to provide. The compulsiveness is an aspect of public education. In some places homeschooling may be a legal alternative to attending school.

Compulsory education at the primary level was affirmed as a human right in the 1948 Universal Declaration of Human Rights. Many of the world's countries now have compulsory education through at least the primary stage, often extending to the secondary education.

Reference:
http://en.wikipedia.org/wiki/Compulsory_education

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is

ax^2 + bx + c = 0,
 
where a ≠ 0. (For a = 0, the equation becomes a linear equation.)

The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term or constant term.

Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared.

Reference:
http://en.wikipedia.org/wiki/Quadratic_equation

In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra.

Abstractly, an "algebraic structure" is the collection of all possible models of a given set of axioms. More concretely, an algebraic structure is any particular model of some set of axioms. For example, the monster group both "is" an algebraic structure in the concrete sense, and abstractly, "has" the group structure in common with all other groups. This article employs both meanings of "structure."

This definition of an algebraic structure should not be taken as restrictive. Anything that satisfies the axioms defining a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all groups are also semigroups and magmas.

Reference:
http://en.wikipedia.org/wiki/Algebraic_structure

In computational complexity theory, a function problem is a problem other than a decision problem, that is, a problem requiring a more complex answer than just YES or NO.

Notable examples include the travelling salesman problem, which asks for the route taken by the salesman, and the integer factorization problem, which asks for the list of factors.

Function problems are more awkward to study than decision problems because they don't have an obvious analogue in terms of languages, and because the notion of reduction between problems is more subtle as you have to transform the output as well as the input.

Function problems can be sorted into complexity classes in the same way as decision problems. For example FP is the set of function problems which can be solved by a deterministic Turing machine in polynomial time, and FNP is the set of function problems which can be solved by a non-deterministic Turing machine in polynomial time.

For all function problems in which the solution is polynomially bounded, there is an analogous decision problem such that the function problem can be solved by polynomial-time Turing reduction to that decision problem. For example, the decision problem analogue to the travelling salesman problem is this:

Given a weighted directed graph and an integer K, is there a Hamilton path (or Hamilton cycle if the salesman returning home is stipulated in the problem) with total weight less than or equal to K?
Given a solution to this problem, we can solve the travelling salesman problem as follows. Let n by the number of edges and w_i be the weight of edge i. First rescale and perturb the weights of the edges by assigning to edge i the new weight w'_i = 2^(n + 1)w_i + 2^i. This doesn't change the shortest Hamilton path, but makes sure that it is unique. Now add the weights of all edges to get a total weight M. Find the weight of the shortest Hamilton path by binary search: is there a Hamilton path with weight < M / 2; is there a path with weight < M / 4 etc. Then having found the weight W of the shortest Hamilton path, determine which edges are in the path by asking for each edge i whether there is a Hamiltonian path with weight W for the graph modified so that edge i has weight W + 1 (if there is no such path in the modified graph, then edge i must be in the shortest path for the original graph).

This places the travelling salesman problem in the complexity class FPNP (the class of function problems which can be solved in polynomial time on a deterministic Turing machine with an oracle for a problem in NP), and in fact it is complete for that class.

Reference:
http://en.wikipedia.org/wiki/Function_problem