Josiah Blaisdell, Valentin Moreau, Rémy Groux, Marion Saulcy

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Presentation transcript:

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

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

I) The socio-economic context 1789 : the Storming of the Bastille 1792 – 1804 : French First Republic, separated in 3 parts : The National Convention (1792-1795) the Directory (1795-1799) the Consulate (1799-1804) 1804-1815 : First French Empire

1815-1830 : Bourbon Restoration 1830-1848 : July Monarchy 1848-1851 : Second French Republic 1851-1870 : Second French Empire

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.

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 . 1839-1843 : 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.

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

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

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

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

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

Conclusion