One Hundred Interesting Mathematical Calculations, Number 9: Archive Entry From Brad DeLong's Webjournal
One Hundred Interesting Mathematical Calculations, Number 9 One Hundred Interesting Mathematical Calculations, Number 9: False Positives Suppose that we have a test for a disease that is 98% accurate: if one has the disease, the test comes back "yes" 98% of the time (and "no" 2% of the time), and if one does not have the disease, the test comes back "no" 98% of the time (and "yes" 2% of the time). Suppose further that 0.5% of people--one out of every two hundred--actually has the disease. Your test comes back "yes." Suppose just for ease of calculation that we have a population of 10000, of whom 50--one in every two hundred--have the disease. If you test "no" you can be very happy indeed: there is only one chance in 9752 that you are the unlucky guy who had the disease and yet tested negative. If you test "yes" you are less happy. From John Allen Paulos's Innumeracy .
John von Neumann
John von Neumann (/vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian and later American pure and applied mathematician, physicist, inventor, polymath, and polyglot. He made major contributions to a number of fields,[2] including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.[3] He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory[2][4] and the concepts of cellular automata,[2] the universal constructor, and the digital computer. . and
FIBONACCI
"...considering both the originality and power of his methods, and the importance of his results, we are abundantly justified in ranking Leonardo of Pisa as the greatest genius in the field of number theory who appeared between the time of Diophantus [4th century A.D.] and that of Fermat" [17th century] R.B. McClenon [13]. [Numbers in square brackets refer to REFERENCES at the end of this article.] 1. During the twelfth and thirteenth centuries, many far-reaching changes in the social, political and intellectual lives of people and nations were taking place. By the end of the twelfth century, the struggle between the Papacy and the Holy Roman Empire had left many Italian cities independent republics. Among these important and remarkable republics was the small but powerful walled city-state of Pisa which played a major role in the commercial revolution which was transforming Europe. Pisa today is best known for its leaning tower (inclined at an angle of about 161/2o to the vertical).
Ludwig Boltzmann
Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion). Biography[edit] Childhood and education[edit] Boltzmann was born in Vienna, the capital of the Austrian Empire. Boltzmann studied physics at the University of Vienna, starting in 1863. Academic career[edit] In 1869 at age 25, thanks to a letter of recommendation written by Stefan,[1] he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. Ludwig Boltzmann and co-workers in Graz, 1887. In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. Final years[edit] Physics[edit]
Loi de Poisson
Un article de Wikipédia, l'encyclopédie libre. La loi de Poisson a été introduite en 1838 par Siméon Denis Poisson (1781–1840), dans son ouvrage Recherches sur la probabilité des jugements en matière criminelle et en matière civile[2]. Le sujet principal de cet ouvrage consiste en certaines variables aléatoires N qui dénombrent, entre autres choses, le nombre d'occurrences (parfois appelées « arrivées ») qui prennent place pendant un laps de temps donné. Si le nombre moyen d'occurrences dans cet intervalle est λ, alors la probabilité qu'il existe exactement k occurrences (k étant un entier naturel, k = 0, 1, 2, ...) est où e est la base de l'exponentielle (2,718...)k! On dit alors que X suit la loi de Poisson de paramètre λ. Calcul de p(k)[modifier | modifier le code] Ce calcul peut se faire de manière déductive en travaillant sur une loi binomiale de paramètres (T; λ/T). Il peut aussi se faire de manière inductive en étudiant sur l'intervalle [0; T] les fonctions On note Remarques : et
Andreï Kolmogorov
Un article de Wikipédia, l'encyclopédie libre. Andreï Nikolaïevitch Kolmogorov Andreï Nikolaïevitch Kolmogorov (en russe : Андрей Николаевич Колмогоров ; 25 avril 1903 à Tambov - 20 octobre 1987 à Moscou) est un mathématicien soviétique et russe dont les apports en mathématiques sont considérables. Biographie[modifier | modifier le code] Enfance[modifier | modifier le code] Kolmogorov est né à Tambov en 1903. Kolmogorov fut scolarisé à l'école du village de sa tante, et ses premiers efforts littéraires et articles mathématiques furent imprimés dans le journal de l'école. Carrière[modifier | modifier le code] Après avoir terminé ses études secondaires en 1920, il suit les cours à l'Université de Moscou et à l'institut Mendeleïev. Après la fin de ses études supérieures en 1925, il commence son doctorat auprès de Nikolaï Louzine, qu’il termine en 1929. La même année, il devient directeur de l'Institut de mathématiques de l'université de Moscou. Contributions[modifier | modifier le code]
