The term “mathematics” originated from the Greek word “mathema” which means knowledge. The subject Mathematics comprises the study of different branches namely number theory, algebra, mathematical analysis, permutation and combination, mathematical logic, calculus, topology etc. Archimedes, who is the father of Mathematics lived between 287 BC – 212 BC. The birthplace of Archimedes was Syracuse, a Greek island of Sicily. He was assisting King Hiero II of Syracuse in resolving problems related to Mathematics and helping in expanding the king’s dynasty and his army.
A few notable innovations of Archimedes are as follows:
- method of exhaustion to find the area occupied by the shapes
- how spheres and cylinders are related?
- applications of prime numbers
- Archimedes’ Principle
- Development of the concept of infinity
- The law of equilibrium of fluids
- The Quadrature of the Parabola
- Computation of measurement of a circle
- The Sand Reckoner
- Loculus of Archimedes or Archimedes’ Box is a dissection puzzle that resembles a Tangram and many more.
As a token of appreciation towards the contributions made by Archimedes to the field of Science and for the outstanding achievement in Mathematics, “Fields Medal” is named after him. He was assassinated by a Roman soldier in 212 BC.
The word matrix was devised by an English mathematician named James Sylvester in the 19th century. The answer to the question of what is a matrix in math can be found here. A rectangular arrangement of numbers in the form of rows and columns is termed as a matrix. Various operations can be performed on matrices depending on the order of them. The number of rows and columns present in a matrix defines its order. The different types of matrices include:
- Square matrix: same number of rows and columns
- Diagonal matrix: All the numbers outside the principal diagonal are zero.
- Identity matrix: the elements on the principal diagonal are 1 and the rest of the elements are 0.
- Symmetric matrix: A matrix that is equal to its transpose.
- Skew-symmetric matrix: A matrix that is equal to the negative of its transpose.
- Orthogonal matrix: a square matrix with the numbers whose columns and rows contain orthogonal unit vectors.
The applications of matrices are as follows.
- The payoff matrix determines the payoff for two players in game theory and economics, depending on the given set of alternatives that are chosen by the players.
- The basic notion of graph theory depends on the concept of the adjacency matrix of a finite graph.
- The square matrices whose rows are probability vectors are termed as Stochastic matrices where the numbers are positive and sum up to 1.
- Stochastic matrices are used in defining the Markov chains with finitely many states.
- Linear transformations and the symmetries associated with it are important topics and are useful in modern physics.
- Geometrical optics involve the use of matrices.
- The idea of traditional mesh and nodal analysis in electronics guide to a group of linear equations that can be explained using a matrix.
The uses of matrices have wide applicability. Few of them are listed above for reference.