Augustin Louis Cauchy: Socio-Economic Context, Personal Life, Mathematical Contributions
Augustin Louis Cauchy, a prominent mathematician, lived during significant historical periods in France. He made noteworthy contributions in algebra and analysis, emphasizing rigor and introducing concepts in calculus. From his early education to his marriage, from teaching to journeying abroad, Cauchy's life was filled with academic achievements and career milestones. His works in group theory, Cauchy matrices, and determinants, alongside his advancements in analysis, showcase his lasting influence in the field of mathematics.
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Presentation Transcript
Augustin Louis Cauchy Josiah Blaisdell, Valentin Moreau, R my Groux, Marion Saulcy
I) The socio-economic context II) His personal life III) His mathematical contribution
I) The socio-economiccontext 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) Hispersonallife 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 Alo se 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 Facult 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:
