Matematica applicata e Informatica

1. Matematica applicata e Informatica Introduzione Sviluppi della teoria della probabilità e statistica Nascita dei calcolatori Nuove applicazioni della matematica e calcolatori

2. Introduzione Successivamente alla seconda guerra mondiale la matematica ha avuto radicali cambiamenti. La teoria degli insiemi e la teoria della probabilità sono state tra le protagoniste di queste innovazioni. Tra gli studiosi di maggior spicco si possono ricordare: Kolmogorov, matematico russo che ha maggiormente influenzato lo sviluppo della probabilità. F. Galton studioso dei fenomeni di regressione; Von Neumann pioniere nell’uso dei metodi matematici in economia; N. Wienner con la sua “Cibernetica”, che mette in relazione la macchina con l’uomo

3. Sviluppi della teoria della probabilità e statistica La probabilità e la statistica strettamente collegate tra di loro hanno avuto nel nostro periodo uno notevole sviluppo in dipendenza anche dell’espansione dei calcolatori. Kolmogrov, matematico russo che ha maggiormente influenzato lo sviluppo della probabilità. Ha pubblicato “General Theory of Measure and Probability Theory”. I suoi studi contribuirono all’applicazione della probabilità alla fisica, chimica e biologia e alla cibernetica. Francis Galton, studioso di fenomeni legati alla regressione. Newmann, pubblicò “Theory of Games and Economic Behavior “, dove introdusse la Teoria dei giochi. Norbert Wiener, fu il pioniere della Teoria della comunicazione statistica, collaborò con ingegneri e neurobiologi dando inizio alla “cibernetica” (lo studio del controllo e comunicazione negli animali e nelle macchine)

4. Nascita dei calcolatori Il padre dei sofisticati calcolatori dei nostri giorni è ritenuto sia Charles Babbage. Progettò nel 1833 una “Macchina delle differenze”. Questa macchina aveva la stessa flessibilità degli attuali calcolatori con esclusione della velocità. Poteva eseguire tutte le operazioni aritmetiche attraverso una macchina regolata da leve. Seguendo le idee di Babbage nel 1939 si iniziò a costruire Mark 1 una macchina elettromeccanica. Seguì quindi nel 1944 la costruzione di un calcolatore completamente elettronico, fra gli scienziati impegnati come consulenti vi era anche J. Von Neumann. Da allora ci sono stati progressi molto rapidi e i calcolatori di quel periodo sono divenuti pezzi da museo.

5. Nuove applicazioni della matematica e calcolatori Grazie all’avvento dei calcolatori ad alta velocità di elaborazione, problemi che superavano le umane capacità dei matematici sono stati risolti. L’amplificazione delle possibilità di calcolo ha dato origine a nuove applicazioni della matematica quali: programmazione lineare, ricerca operativa, teoria dei giochi. Alcuni studiosi di particolare rilievo furono: Von Neumann uno dei primi studiosi che applicò la matematica per lo studio dell’economia e delle scienze sociali, famoso è il suo libro “ Theory of Games and Economic Behaviour” N. Wienner che con la sua pubblicazione “Cibernetica” diede avvio allo studio del controllo e della comunicazione negli uomini.

6. Bibliografia C. B. Boyer, Storia della matematica,A. Mondadori Editore

7. Appendice Kolmogrov, a Russian mathematician, had a major influence on the development of probability. He published “General Theory of Measure and Probability Theory” (1929) in which he introduced a unique theory of probability built on basic properties from measure theory. This was expanded in 1933 and translated into English as Foundations of the Theory of Probability (1950). He is also responsible for thoroughly expanding the principles of stochastic processes in “Analytical Methods of Probability Theory”. His Kolmogrov equations contributed greatly to the advancement of the applications of probability theory in physics, chemistry, civil engineering, and biology. He also studied Markov chains, which influenced dynamic systems as well as other areas of mathematics, and stationary processes, which has statistical importance in cybernetics.

8. Francis Galton an Englishman and first cousin to Charles Darwin. He published a work entitled Meteorgraphica (1863), which analyzed multivariate data using graphical methods, while working on weather patterns. Galton is also known for his applications of statistics in other sciences and experimenting with fitting data to normal curves and graphing data in order to determine whether to it should be considered together. Through his experimentation with graphing data, he discovered the inverse normal cumulative distribution function. Galton used measurable qualities to draw inferences on immeasurable qualities of a sample of the population in Hereditary Genius. He found a connection between regression and the bivariate normal distribution and used this relationship to prove that heredity had an influence on one’s intelligence. He called this connection reversion. His major breakthrough was his realization that the addition of independent normal distributions was a normal distribution, and that this idea could be applied to the combining of multivariate data. Galton’s work opened the door to the study of correlation, and he is referred to as one of the very first statisticians.

9. Newmann was born in Hungary but later moved to Washington D.C. He became a professor at Princeton University and is primarily remembered for his work on “rings of operators”, which is now referred to as Nuemann algebras. He also had a hand in the creation of the hydrogen bomb during WWII. Neumann and Oskar Morgenstern, an economist, coauthored the book, Theory of Games and Economic Behavior (1944), in which he introduced the topic of game theory. This book addressed competitive situations in which the actions of players at each turn are taken into consideration and consequently have an impact on the path of the next turn. Neumann concluded that for the most part when games involved only two parties, there was really nothing to gain by playing.

10. Norbert Wiener (1894-1964) worked in pure mathematics, but also used mathematics to pioneer statistical communication theory, and in collaboration with engineers and neurobiologists originated and elaborated the field of "cybernetics" (the study of "control and communication in the animal and the machine"). Wiener's work in the 1940s, related to cybernetics, constitutes one of the roots of modern "cognitive science." After World War II, anticipating the social and philosophical significance of cybernetic technologies, Wiener developed an important prescient philosophy of technology incorporating humane values. Nearly all his work shows the mark of a highly original mind.

11. Charles Babbage (1791-1871) The calculating engines of English mathematician Charles Babbage (1791-1871) are among the most celebrated icons in the prehistory of computing. Babbage’s Difference Engine No.1 was the first successful automatic calculator and remains one of the finest examples of precision engineering of the time. Babbage is sometimes referred to as "father of computing." The Charles Babbage Foundation took his name to honor his intellectual contributions and their relation to modern computers. Biographical note Charles Babbage was born in London on December 26, 1791, the son of Benjamin Babbage, a London banker. As a youth Babbage was his own instructor in algebra, of which he was passionately fond, and was well read in the continental mathematics of his day. Upon entering Trinity College, Cambridge, in 1811, he found himself far in advance of his tutors in mathematics.

12. Babbage co-founded the Analytical Society for promoting continental mathematics and reforming the mathematics of Newton then taught at the university. In his twenties Babbage worked as a mathematician, principally in the calculus of functions. He was elected a Fellow of the Royal Society in 1816 and played a prominent part in the foundation of the Astronomical Society (later Royal Astronomical Society) in 1820. It was about this time that Babbage first acquired the interest in calculating machinery that became his consuming passion for the remainder of his life. In 1821 Babbage invented the Difference Engine to compile mathematical tables. On completing it in 1832, he conceived the idea of a better machine that could perform not just one mathematical task but any kind of calculation. This was the Analytical Engine (1856), which was intended as a general symbol manipulator, and had some of the characteristics of today’s computers.