Mathematics in the 19th 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 19th CenturyCarl Friedrich Gauss Adrien Marie Legendre Bernhard Bolzano

What is it???

Intermediate Value Theorem/

Bolzano-Weierstrass Theorem

Remember from Calculus I we took last semester…

Mathematicians in the 19th CenturyCarl Friedrich Gauss Adrien Marie Legendre Bernhard Bolzano

Augustin-Louis Cauchy Niels Henrik AbelKarl Theodor Wilhelm Weierstrass

George Riemann

Knowledge prevalent during the 19th 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 19th CenturyTwo remarkable developments:

Non-Euclidian geometry

Abstract algebra

Progress in the later half of the 19th Century:

Set theory

Later in the early 20th century:Creation of axiomatics and the logical foundations

Conclusion

The 19th Century was devoted to the efforts of establishing a firm, logical foundation based on the shaky super structure erected in the 18th century

ReferencesLakshmikantham 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