The Papyrus Rhind is the source of most of modern knowledge about mathematics in Ancient Egypt
Introduction
Mathematics (sometimes shortened to maths or math), is the study of numbers, shapes and patterns. Mathematicians are people who learn about and discover such things in mathematics. Mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use mathematics. Today, mathematics is needed in many jobs. Business, science, engineering, and construction need some knowledge of mathematics.
Mathematicians solveproblems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true is just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from other kinds of thinking.
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A directed graph
Graph theory is a field of mathematics about graphs. A graph is an abstract representation of: A number of points are connected by lines. Each point is usually called a vertex (more than one are called vertices), and the lines are called edges. Graphs are a tool for modelling relationships. They are used to find answers to a number of problems.
Graph theory is an important part of mathematics and computer science. To many such problems, exact solutions do exist. Many times however, they are very hard to calculate. Therefore, very often, approximations are used. There are two kinds of such approximations, Monte-Carlo algorithms and Las-Vegas algorithms.
Graphs are normally represented by two different sets, typically set a graph G would be represented as the collection of the sets V and E. The set V is a discrete set containing all vertices of the graph. The set E is a binary set, whose pairwise elements are elements of set V. Each pair in set E represents an edge connecting two vertices. If any two nodes have an edge between them, then the graph is called the complete graph.
Illustration of the Pythagorean theorem. The sum of two sqares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple).
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