Topic # 3 mathematics as a science

Mathematics is an activity which has as its purpose the formulation and understanding of a complete model of the universe. Mathematics as a science is a collection of branches. They are arithmetic, algebra, geometry, trigonometry and others. Ancient Egyptians used arithmetic and geometry more than 5,000 years ago to measure out plots of land and to build pyramids with great accuracy. Arithmetic deals with numbers and calculating. Addition, subtraction, multiplication, and division are its main operations. Geometry is concerned with lines, angles, figures and solids. Greeks such as Euclid worked out most of the general principles of geometry, called theorems, about 2,500 years ago. Algebra is a kind of mathematical shorthand that uses symbols to stand for unknown quantities. It was developed by the Arabs less than 1,200 years ago. Arithmetic, geometry, and algebra are the foundations of mathematics.

Mathematicians divide mathematics into pure and applied mathematics. Pure mathematics is an investigation of mathematical theories and ideas. The study of the whole numbers, the development of the number theory and the theory of equations are examples of pure mathematics. Applied mathematics deals with the application of mathematical theories to the problems in different branches of science. The work in cybernetics is an outstanding example of applied mathematics. Another example of applied mathematics is statistics, which uses the theory of probability as a tool and allows the description, analysis, and prediction of phenomena.

Mathematics is the language of science. Engineers, physicists and other scientists use mathematics in their research to prove their ideas and theories.

Topic # 4 famous scientists (claude elwood shannon)

Claude Elwood Shannon was born in 1916 in Petoskey, Michigan, and died in 2001. He was an American electrical engineer and mathematician. He was the founder of practical digital circuit design theory. Especially he was famous for his contribution to information science and he has been called “the father of information science”.

In 1932 he entered the University of Michigan, where he took a course that introduced him to the works of George Boole. He graduated from the University in 1936 with two bachelor’s degrees, one in electrical engineering and one in mathematics. Then he began his graduate study at the Massachusetts Institute of Technology devoting much time to the elaboration of differential analyzer, analog computer.

While studying the complicated circuits of the differential analyzer, Shannon saw that Boole’s concepts could be used to great utility. Shannon proved that Boolean algebra and binary arithmetic could be used to simplify the arrangement of the electromechanical relays. Shannon’s work was considered to be the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II.

During World War II Shannon worked at Bell Labs elaborating fire-control systems and cryptography. To commemorate his achievements, after the breakup of the Bell system, the part of Bell Labs was named in his honor.

In 1948 Shannon published “A Mathematical Theory of Communication”. This work was devoted to the problem of how best to encode the information a sender wants to transmit. Shannon developed information entropy as a measure for the uncertainty in a message. Another notable paper “Communication Theory of Secrecy Systems” was published in 1949. This work was a contribution to the development of the mathematical theory of cryptography.

In 1956 Shannon came to the Massachusetts Institute of Technology to join its faculty and to conduct work in the Research Laboratory of Electronics. He continued to work at the Massachusetts Institute of Technology till 1978.

Shannon’s contribution to science is great. The whole digital revolution started with him.