1. Josiah Blaisdell, Valentin Moreau, Rémy Groux, Marion Saulcy
Augustin Louis Cauchy
Josiah Blaisdell, Valentin Moreau,
Rémy Groux, Marion Saulcy

2. I) The socio-economic context
II) His personal life
III) His mathematical contribution

3. I) The socio-economic context
1789 : the Storming of the Bastille
1792 – 1804 : French First Republic, separated in 3 parts :
The National Convention ( )
the Directory ( )
the Consulate ( )
: First French Empire

4. 1815-1830 : Bourbon Restoration
: July Monarchy
: Second French Republic
: Second French Empire

5. II) His personal life 1789 : birth of Augustin-Louis CAUCHY.
1805 : he placed second to the entrance examination (and he was admitted) to the Ecoles Polytechniques.
1807 : School for Bridges and roads.
1810 : graduated in civil engeneering with highest honor.
1812 : loose interest in engeneering, being attracted by abstract mathematics.
1815 : teach mathematics in Polytechniques.
1816 : Cauchy was appointed to take place in the Academy of science.
1818 : Cauchy maried Aloïse de BURE.

6. 1830 : Cauchy leave the country
1833 : Cauchy go to Prague to teach at the Duke of Bordeau (grandson of Charles X)
1838 : come back in Paris .
: elected but not approved to take place in the Bureau des longitudes.
1849 : teach mathematical astronomy at the Faculté des sciences.
1857: death of August-Louis CAUCHY.

7. Contributions In Algebra
Cauchy Matrix
Cauchy Determinant of Cauchy Matrix
If the elements xs and ys are distinct then the determinant can be found quickly.
Group theory

8. Contributions in Analysis
Stressed the importance of rigor
“Infinitessimally small” quantities used to describe change.
Precursor to calculus.
Cauchy-Schwarz Triangle Inequality
Inner product and length
Cauchy Sequence
Used to construct the real line
Cours d‘Analyse
Cauchy-Riemann Conditions

9. Cauchy-Schwartz Inequality
Motivation: How can we go about assigning a length, or norm, to any vector in Rn?
Simple Examples:

10. Cauchy-Schwartz Inequality
Stating the inequality:
Or, using the dot product:

11. Cauchy-Schwarz Inequality
First show that the inequality holds when one of the vectors is the zero vector.
Notice that:

12. Conclusion