## Graph (mathematics)

In mathematics, a graph is used to show how things are connected. The things being connected are called vertices, and the connections among them are called edges. If vertices are connected by an edge, they are called adjacent. The degree of a ver ...

## Graph theory

Graph theory is a field of mathematics about graphs. A graph is an abstract representation of: a number of points that are connected by lines. Each point is usually called a vertex, and the lines are called edges. Graphs are a tool for modelling ...

## Chinese postman problem

The Chinese postman problem is a mathematical problem of graph theory. It is also known as route inspection problem. Suppose there is a mailman who needs to deliver mail to a certain neighbourhood. The mailman is unwilling to walk far, so he want ...

## Five color theorem

The Five color theorem is a theorem from Graph theory. It states that any plane which is separated into regions, such as a map, can be colored with no more than five colors. It was first stated by Alfred Kempe in 1890, and proved by Percy John He ...

## Graph coloring

Graph coloring is the name for a number of problems from graph theory. These problems are concerned with coloring the vertices of a graph, given certain conditions. A simple problem in this context might look for the minimal number of colors need ...

## Nearest neighbour algorithm

Nearest neighbour algorithms is a the name given to a number of greedy algorithms to solve problems related to graph theory. This algorithm was made to find a solution to the travelling salesman problem. In general, these algorithms try to find a ...

## Ramsey theory

The Ramsey theory is named after the British mathematician and philosopher Frank Ramsey. It is a branch of mathematics that studies the conditions under which order must appear.

## Crelles Journal

Crelles Journal, or just Crelle, is a journal that was published monthly for mathematical articles. It was founded by August Leopold Crelle in 1826 in Berlin. The full German title is Journal fur die reine und angewandte Mathematik. Crelle edited ...

## Rhind Mathematical Papyrus

The Rhind papyrus in the British Museum is the best example of Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian. He bought the papyrus in 1858 in Luxor, Egypt. It was found during illegal excavations in or nea ...

## Logic

Logic is the study of reasoning. The rules of logic let philosophers make valid logical deductions about the world. Logic helps people decide whether something is true or false. Logic is often written in syllogisms, which are one type of logical ...

## Abduction (logic)

Abduction is the kind of practical logic which answers questions of the type "how did this come about?". It produces answers which are not guaranteed to be correct. Consider the observation that the lawn is wet in the morning. How did that happen ...

## Absolute truth

Absolute truth is something that is true at all times and in all places. It is something that is always true no matter what the circumstances. It is a fact that cannot be changed. For example, there are no round squares. There are also no square ...

## Analogy

An analogy is a comparison between two things that are similar in some way. When you draw an analogy between two different things, you are comparing them because you want to make a concept easier to understand. "In general but not always, such ar ...

## Connotation

Today the word has different meanings, but it is always used for the contrast of a word or phrase with its primary, literal meaning known as a denotation. That can be an implied value judgement or feelings. It is often useful to avoid words with ...

## Deductive reasoning

Deduction is one of the two main types of reasoning. The other is induction. In deduction, we apply a general rule to a particular case. Deductive arguments are attempts to show that a conclusion must follow from a set of premises or hypotheses. ...

## Definite description

In logic, a definite description is a term of the form the. It is used to describe something. This is more difficult than it first appears, because: There must be exactly one such person or thing. The thing or person talked about must exist. Unfo ...

## Denotation

In order to understand fully the difference between denotation and connotation in the media studies and semiotics uses it is necessary to become familiar with some examples: :

## Dilemma

A dilemma is a problem with at least two solutions or possibilities. None of the solutions are practically acceptable; a person in this position has been traditionally described as being impaled on the horns of a dilemma, neither horn being comfo ...

## Evil

Evil means something which is morally bad or wicked. It is the opposite of good. People may say that an action which hurts people or breaks certain rules such as the Ten Commandments is evil. A person or a group that does evil things may also be ...

## Exclusive disjunction

Exclusive disjunction is a logic operation on two values. It is often represented by the symbol ⊻ {\displaystyle \veebar }. It will be true, if exactly one of the two values is true. Otherwise, it will be false. This also means that the result of ...

## Existence quantifier

In mathematics and logic, the existence quantifier is a quantifier used to state that a proposition is true for at least one element in the universe of discourse. The existence quantifier is commonly written as ∃ {\displaystyle \exists }, and is ...

## First order logic

First order logic is a type of logic which is used in certain branches of mathematics and philosophy. First order logic enables the definition of a syntax which is independent of the mathematical or logical terms. In first order logic, reasoning ...

## If and only if

In logic and mathematics, if and only if is a logical operator denoting a logical biconditional. It is often used to conjoin two statements which are logically equivalent. In general, given two statement A and B, the statement "A if and only if B ...

## Implication (logic)

Implication is a logical operation. It is the relationship between statements that holds true when one logically "follows from" one or more others. While a statement of the form "if P then Q is often written as P → Q {\displaystyle P\to Q}, the a ...

## Inclusive disjunction

Inclusive disjunction is a logic operation. It normally takes two truth values as inputs and returns one truth value as output. It is false when both inputs are false, but is true otherwise. It is written with the symbol ∨ {\displaystyle \lor }. ...

## Inductive reasoning

Induction is one of the main forms of logical reasoning. The other is deduction. In induction, we find a general rule by using a large number of particular cases. For example, watching water in many different situations, we can conclude that wate ...

## Inference

Inference is a process of deriving new knowledge, given existing knowledge, and a number of rules. In logic, there are three different forms: Induction. In a car, the brake is used; the car slows down; therefore: using the brake will slow down th ...

## INUS condition

INUS condition stands for an i nsufficient, but n ecessary part of an u nnecessary but s ufficient condition. John Mackie introduced the term in the 1960s. Mackie uses the example of a house burning: There was an electric short circuit that cause ...

The law of non-contradiction is a rule of logic. It states that if something is true, then the opposite of it is false. For example, if an animal is a cat, the same animal cannot be not a cat. Or, stated in logic, if +p, then not -p, +p cannot be ...

## Law of the excluded middle

The law of the excluded middle is a simple rule of logic. It states that for any proposition, there is no middle ground. Every proposition is either true or false. For example, "Ginger is a cat" affirms the fact that Ginger is a cat. If it is tru ...

## Logic programming

Logic programming is using mathematical logic to write computer programs. There are specialized programming languages where the user can directly enter logical statements. Probably the best-known of these languages is called Prolog. Alonzo Church ...

## Logical equivalence

In logic and mathematics, two statements are logically equivalent if they can prove each other, or have the same truth value under all circumstances. In propositional logic, two statements are logically equivalent precisely when their truth table ...

## Logical quantifier

In logic, a quantifier is a way to state that a certain number of elements fulfill some criteria. For example, every natural number has another natural number larger than it. In this example, the word "every" is a quantifier. Therefore, the sente ...

## Natural deduction

Natural deduction is a branch of mathematical logic developed in Poland in the 1920s and 30s. It is meant to express inference rules closely related to the "natural" way of reasoning. Spurred on by a series of seminars in Poland in 1926 by Lukasi ...

## Oxymoron

An oxymoron is a term for a figure of speech. It is made up of two or more words that seem to be opposite to each other, or actually are opposite. For example, the words "Wise fool", "Warm freezer", "Legal murder" all have two words. In each one, ...

## Premise

A premise is a statement which an argument claims will justify a conclusion. The proof of a conclusion depends on both the truth of the premises and the validity of the argument.

## Proposition

A proposition is a term in philosophy and logic. It is a statement which has a truth value, meaning it can be proved to be true or false. For a proposition to be valid, it must be possible to prove the proposition is either true or false. Many te ...

## Propositional logic

Propositional logic is a formal system in mathematics and logic. Other names for the system are propositional calculus and sentential calculus. The system is made of a set of propositions. Each proposition has a truth value, being either true or ...

## Relevance

Relevance is the idea that one topic may be useful to another topic: so consider the second topic when considering the first. The concept of relevance is studied in many fields, including cognitive sciences, logic, and information science. It is ...

## Syllogism

A syllogism is a deduction. It is a kind of logical argument in which one proposition is inferred from two or more others. The idea is an invention of Aristotle. In the Prior Analytics, Aristotle defines the syllogism as "a discourse in which, ce ...

## Tautology (logic)

A tautology can also be a figure of speech In propositional logic, a tautology is a propositional formula that is always true, and is sometimes denoted by the symbol ⊤ {\displaystyle \top }. In other words, a tautology cannot be wrong. For exampl ...

## Truth

The truth is what is true. It may be everything that is true or just a part of it. It may also be a statement that is true: a truth. Things or statements that are not true are untrue or false. True things exist ; false things do not. Aristotle sa ...

## Truth value

In logic, the truth value of a logical statement says how much it is true. Usually, the truth value can only be "true" or "false". For example, "The car is red" is true when the car is red, and false when it is not. The "true" truth value is ofte ...

## Universal quantifier

In mathematics and logic, the universal quantifier is a quantifier used to state that a proposition applies to all elements in the universe of discourse. An example that uses this quantifier would be the proposition "All men are mortal". Usually, ...

## Validity

Validity is an idea that is used in everyday language and in logic. In ordinary language it means correct or in the right form. An argument is valid if it seems appropriate, well-grounded and can be defended. A contract is valid if it is enforcea ...

## Logarithmic scale

A logarithmic scale is a scale used when there is a large range of quantities. Common uses include earthquake strength, sound loudness, light intensity, spreading rates of epidemics, and pH of solutions. It is based on orders of magnitude, rather ...

## Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli, who called i ...

## Curve fitting

Curve fitting is constructing a mathematical function which best fits a set of data points. Curve fitting may involve either interpolation or smoothing. Using interpolation requires an exact fit to the data. With smoothing, a "smooth" function is ...

## Interpolation

In many domains of science, measurements are done. If these measurements are drawn in a graph, they will be shown as simple unconnected points. Such data are called data points, or discrete. Handling and analysis of the data is easier, if it can ...

## Least squares

Least squares is the name of a procedure in mathematics, to construct a function from a number of observed values. The basic idea is to construct the function in such a way that the sum of the difference between the observed value and its data po ...