Charles Babbage's Contributions To Mathematics

Charles Babbage is a famous mathematician in British and a member of the Royal Society.He was a Lucasian Chair of Mathematics at the University of Cambridge,and he helped to establish the Analytical Society,the Cambridge Astronomical Society and the British Society for the Advancement of Science.He invented the Difference Machine and the Analysis Machine,so he is called the Ancestor of Computer.He has achieved fruitful results in the fields of Function Calculus,Plane Geometry,Games of Chance and Notation.Based on the study of a large number of relevant original documents and research documents,this dissertation discusses Babbage's contribution to mathematics by taking his representative work in the fields of Function Calculus,Plane Geometry,Games of Chance and Notation as examples.This dissertation discusses and summarizes his mathematical contributions.At the same time,this dissertation analyzes Babbage's life experience and his work and contribution in the introduction of Leibniz Calculus notation and the establishment of the Analytic Society.So that people can have a clearer understanding of his mathematical thoughts and achievements.The main results and conclusions are as follows:1.Babbage's legendary life experiences are explored.He loved mathematics since childhood and liked to explore new things.He received a bachelor's degree from Trinity College of Cambridge University and a master's degree from Peter College.He was a Lucasian Chair of Mathematics at Cambridge University and a member of the Royal Society.He helped to establish the London Statistical Society,the British Association for the Advancement of Science,the Astronomical Society and the Analytical Society.2.This dissertation introduces Babbage's innovative work in Function Calculus,and combs the development process of function equation.His most important work in this field is to give the method of solving the equation of order function and solve the problem of function equation with two variables.He also explained the essential problem of Function Calculus and defined the special and general solutions.3.This dissertation discusses Babbage's idea of using algebraic method to deal with plane geometry problems.He proved several general theorems of Stewart by trigonometric series and added some new properties of circles.Then,it introduces his work of restoring Euclid's indefinite problem.4.This dissertation expounds Babbage's exploration Games of Chance.This dissertation mainly introduces his three methods of exploring Games of Chance,and how he used mathematical methods to prove the profit and loss of game participants with a series of examples.5.This dissertation analyzes Babbage's work on the reform of Notation.He believes that the symbolic problem is one of the most important problems in mathematics.Good symbols promote the rapid development of mathematics,while complex symbols hinder the development of mathematics.Therefore,in the early stage of his career,he was very actively involved in the symbol reform.6.Investigated Babbage's contribution as a science organizer.He introduced the Leibniz's calculus into Britain,and combined it with Newton's flow arithmetic,which provided a reference for the representation of calculus.Together with his friends,he established a scientific organization,the Analytical Society,which provided a place for students to exchange and study at Cambridge University and promoted communication and cooperation among students.Through the study of Babbage's achievements in different of mathematics fields,we can not only better understand his mathematical contributions,but also better grasp his mathematical thoughts.Through the study of his contribution as a scientific organizer,we can better understand his life achievements.