Mathematics in the 19 th Century D. Manoj Reddy 29 March 2010

Ponder over these questions??? + What do you know about Mathematics and its history? + How did Mathematics come about as we know of it today? + What were the great ideas during the 1800’s? + Who were the famous personalities in Mathematics during this time period?

Outline Different Mathematicians during this time period Knowledge prevalent at that time Major mathematical ideas being developed by these famous Mathematicians

This is what Wordle had to say…

Mathematicians in the 19 th Century Carl Friedrich GaussAdrien Marie LegendreBernhard Bolzano

What is it??? Intermediate Value Theorem/ Bolzano-Weierstrass Theorem Remember from Calculus I we took last semester…

Mathematicians in the 19 th Century Carl Friedrich GaussAdrien Marie LegendreBernhard Bolzano Augustin-Louis CauchyNiels Henrik Abel Karl Theodor Wilhelm Weierstrass George Riemann

Knowledge prevalent during the 19 th Century Acquainted with the following topics: Trigonometry, Analytical Geometry, Calculus, Theory of Numbers, Theory of Equations, Probability, Differential Equations and Analytical Mechanics Largely spent time in exploiting the powerful methods of Calculus to a diversity of problems

Revolutionary Mathematical Developments in the 19 th Century Two remarkable developments: Non-Euclidian geometry Abstract algebra Progress in the later half of the 19 th Century: Set theory Later in the early 20 th century: Creation of axiomatics and the logical foundations

Conclusion The 19 th Century was devoted to the efforts of establishing a firm, logical foundation based on the shaky super structure erected in the 18 th century References Lakshmikantham V., Leela S., Devi J. V. (2005). The Origin and History of Mathematics. Cambridge Scientific Publishers: UK. McElroy T. (2005). A to Z of Mathematicians. VB Techbooks: USA