HISTORY OF PROBABILITY

Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment of dice began with the work of Cardano, Pascal and Fermat between the 16th and 17th century.

Probability is distinguished from statistics; see history of statistics. While statistics deals with data and inferences from it, (stochastic) probability deals with the stochastic (random) processes which lie behind data or outcomes.

             ANALYTIC  GEOMETRY

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space(three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

                 GEOMETRY

What is the history of geometry?

Geometry was documented by the Sumerian civilization around 5,000 years ago; it was used by them in setting out temples (look up Gilgamesh). The Egyptians also studied and applied a sophisticated knowledge of geometry. In building Stonehenge, around 2,500 BC Neolithic surveyors also used survey methods based on geometric principals.

What is geometry?

         Geometry is the mathematical study and reasoning behind shapes and planes in the universe. Geometry compares shapes and structures in two or three dimensions or more. Geometry is the branch of mathematics that deals with the deduction of the properties, measurements of points…

                          ALGEBRA

Answer pops out

      The power of algebra isn't in coding statements about the physical world. Computer scientist and author Mark Jason Dominus writes on his blog, The Universe of Discourse: "In the first phase you translate the problem into algebra, and then in the second phase you manipulate the symbols, almost mechanically, until the answer pops out as if by magic." While these manipulation rules derive from mathematical principles, the novelty and non-sequitur nature of "turning the crank" or "plugging and chugging" has been noticed by many students and professionals alike.