AMERICAN MATHEMATICS

Sergey NikolaevRuslan Pakhomov

CONTENT

• Historical information.

• Story about the mathematician.

• Mathematical Prize.

• Entertaining puzzles and interesting facts.

HISTORICAL INFORMATION

•A huge contribution to world culture, as well as in the development of mathematics and astronomy have pre-Columbian civilization living in Central America.

MAYA

• Maya - a civilization of Central America, known for its literature, art, architecture , and mathematical and astronomical systems. Began to form in era (2000 BC. E . - 250 AD. E . ) . Maya built cities of stone , many of which were abandoned long before the arrival of Europeans , and others were inhabited since . Calendar developed by the Maya, and used other peoples of Central America. Used hieroglyphic writing system , partially deciphered . Survived numerous inscriptions on monuments . Created an efficient system of agriculture , have profound knowledge in the field of astronomy.

• Maya were able to calculate the time of any particular system. Fixing time is made possible by a combination of written and thorough astronomical knowledge. In addition, the Mayans used "tzolkin" or "tonalamatl" - counting system based on numbers 20 and 13.

• The Mayas existed and its scoring system , applied in everyday life. Maya counting system based not on the familiar decimal system , and widespread in Mesoamerican cultures of 20 . Origins lie in the method of account when applied not only ten fingers, but ten toes. In this structure existed in the form of four blocks of five digits , which corresponded to the five fingers of the hands and feet . Also interesting is the fact that the Maya existed designation zero , which was schematically represented as empty shells of oysters or snails . Designation zero also applied to denote infinity. Since zero is needed in many mathematical operations , but at the same time in ancient Europe was unknown, scientists suggest today that the Maya had a highly developed culture with a good level of education.

• Mayan figures - positional record based on the value twenty system (base 20) used in the pre-Columbian Maya civilization of Mesoamerica.

MAYAN FIGURES WERE MADE UP OF THREE ELEMENTS: ZERO (SIGN SEASHELLS), UNIT (DOT) AND FIVE

(HORIZONTAL LINE). FOR EXAMPLE, 19 WAS WRITTEN AS FOUR DOTS IN A HORIZONTAL ROW ABOVE THREE

HORIZONTAL LINES. NUMBER MORE THAN 19 WRITTEN VERTICALLY UPWARDS AT 20 DEGREES.

• For example:

• 32 written as (1) (12) = 1 × 20 + 12

• As 429 (1) (1) (9) = 400 × 1 + 1 × 20 + 9

• As 4805 (12) (0) (5) = 12 × 400 + 20 × 0 + 5

• To write numbers from 1 to 19, sometimes also used images of deities. These figures are used rarely, remaining only a few monumental stelae.

• In the "long count" Mayan calendar was used by 20 species hexadecimal number system, in which the second category could include the numbers from 0 to 17, then to the third category was added unit. Thus, a unit of the third category is not meant 400, and 18 × 20 = 360, which is close to the number of days in a solar year.

AMERICAN MATHEMATICIANS

NORBERT WIENER

• Norbert Wiener - American scientist , an outstanding mathematician and philosopher , founder of cybernetics and artificial intelligence theory .

• Norbert Wiener was born into a Jewish family . Maternal grandparents , Bertha Kahn, were natives of Germany.

• In 4 years Wiener already been admitted to the parent library , and 7 years later he wrote his first scientific treatise on Darwinism . Norbert never really did not learn in high school. But 11 years of age he entered the prestigious Taft College, from which he graduated with honors in three years with a Bachelor of Arts.

• In 18 years, Norbert Wiener received his Ph.D. in mathematical logic at Cornell and Harvard Universities . At the age of nineteen Dr. Wiener was invited to the chair of mathematics at MIT.

• In 1913, young Wiener begins its journey in Europe, listening to lectures and Russell Hardy in Cambridge and Hilbert in Göttingen . After the start of the war, he returned to America. During his studies in Europe, the future "father of cybernetics " had to try his hand as a journalist okolouniversitetskoy newspapers , test yourself on the pedagogical field , a couple of months to serve as an engineer at the plant.

• Since 1919, Wiener became a lecturer in the Department of Mathematics at MIT.

• In 1926 he married Margaret Engerman .

• Before World War II Wiener became a professor at Harvard , Cornell , Columbia , at Brown , University of Gottingen , got into his own undivided ownership department at the Massachusetts Institute , has written hundreds of articles on the theory of probability and statistics, series and Fourier integrals , potential theory and number theory , the generalized harmonic analysis .

• A few months before the death of Norbert Wiener was awarded the Academic Gold Medal, the highest award for a man of science in America. At a solemn meeting dedicated to this event, President Johnson said, "Your contribution to science is surprisingly versatile, your opinion is always been original, you awesome symbiosis incarnation of pure and applied mathematics scholar." Total Wiener received five awards for scientists, Norbert Wiener, died March 18, 1964 in Stockholm.

JOHN VON NEUMANN.

• John von Neumann - Hungarian- American mathematician of Jewish origin , who made important contributions to quantum physics , quantum logic , functional analysis, set theory , computer science , economics and other branches of science.

• Janos , or just Yanchi , was unusually gifted child . Already in the 6 years he could share in the mind two eight-digit number and talk with his father on the Greek. Janos always interested in mathematics , numbers and logic nature of the world. In eight years, he was well versed in the mathematical analysis . In 1911 he entered the Lutheran Gymnasium .

• Von Neumann received his Ph.D. in mathematics (with elements of experimental physics and chemistry ) at the University of Budapest in '23 . Simultaneously, he studied chemical engineering in Zurich, Switzerland ( Max von Neumann believed mathematics profession insufficient to ensure a sustainable future for his son ) . From 1926 to 1930 John von Neumann was a lecturer in Berlin.

• In 1930, von Neumann was invited to a teaching position at the American Princeton University .

• In 1937 von Neumann became a U.S. citizen . In 1938 he was awarded the M. Bocher for his work in the field of analysis .

• In 1957 von Neumann became ill with cancer bone may caused by radiation exposure in atomic bomb tests in the Pacific Ocean or . A few months after diagnosis von Neumann died in severe agony. Cancer also hit his brain , depriving it almost possible to think.

ALONZO CHURCH

• Alonzo Church - distinguished American mathematician and logician who made significant contributions to the foundations of computer science. Received a bachelor's degree from Princeton University in 1924 and his Ph.D. in 1927 under the leadership of Oswald Veblen. Church became professor of mathematics at Princeton in 1929.

• Church remained a professor of mathematics at Princeton until 1967, after which he moved to California. Among other things, its system of lambda calculus formed the basis for functional programming languages .

CLAUDE ELWOOD SHANNON

• Claude Elwood Shannon - American engineer and mathematician , his works are a synthesis of mathematical ideas with concrete analysis of extremely complex problems of their technical realization .

• He is the founder of information theory , which has found application in modern high-tech communication systems. Shannon made a huge contribution to the theory of probability schemes , automata theory and the theory of control systems - science included in the term " cybernetics" . In 1948 he proposed the use of the word " bit " to refer to the smallest unit of information.

• Claude Shannon was born April 30, 1916 in Petotski , Michigan , USA. The first sixteen years of his life Claude held at the Gaylord , Michigan, where in 1932 he finished secondary school Gaylord .

• In 1932, Shannon was enrolled in the University of Michigan .

• From 1950 to 1956, Shannon engaged in the creation of logical machines , thus continuing initiatives Turing and von Neumann . Shannon retiring at the age of fifty in 1966 , but he continues to advise the company Bell. In 1985, Claude Shannon and his wife Betty attends International Symposium on Information Theory in Brighton. Shannon did not attend long enough international conferences, and at first it did not even know . At the banquet, Claude Shannon gave a short speech just three balls and then gave hundreds and hundreds of autographs bewildered by his presence the scientists and engineers who defended the queue length , experiencing vibrant feelings towards the great scientist , comparing it to Sir Isaac Newton.

• Claude Shannon died on February 24, 2001 .

THE AMERICAN PRIZE FOR MATHEMATICS.

•We now turn to the story and bonuses established by the United States for achievements in the field of mathematics. Most distinguished and honorable award is considered established for the solution of problems of the Millennium.

• Objectives Goals constitute seven mathematical problems identified as "important classical problems whose solution has been found for many years ." Solution for each of these problems the Clay Institute offered a prize of one million U.S. dollars. Announcing the award , the Clay Institute drew a parallel with the list of Hilbert's problems , presented in 1900, and have a significant impact on the mathematicians of the XX century . Of the 23 most Hilbert problems have been solved , and only one - Riemann hypothesis - entered the list of the millennium bug .

• As of July 2011 , only one of the seven Millennium Challenge Account ( Poincaré conjecture ) is solved . The prize was awarded for its decision to Russian mathematician G. J. Perelman , who, however , refused the award .

•Also in America, awarded "Gold Medal scientist" - the highest award for a man of science in America. And "National Medal of Science" - it is also an honorary award.

THE FIELDS MEDAL IS MADE OF 14 CARAT GOLD (583 SAMPLES). ON THE FRONT SIDE -

LATIN INSCRIPTION: «TRANSIRE SUUM PECTUS MUNDOQUE POTIRI» («TRANSCEND THEIR HUMAN LIMITATIONS AND CONQUER THE

UNIVERSE"), AND THE IMAGE OF ARCHIMEDES. AND ON THE BACK: «CONGREGATI EX TOTO ORBE MATHEMATICI OB SCRIPTA INSIGNIA

TRIBUERE» («MATHEMATICS, GATHERED FROM AROUND THE WORLD, HONORING OUTSTANDING CONTRIBUTION TO

KNOWLEDGE").? AMOUNT OF THE CASH AWARD IS RELATIVELY SMALL - 15 000

CANADIAN DOLLARS.

DISCOVERIES IN THE FIELD OF MATHEMATICS.

• Church famous for developing the theory of the lambda calculus, following his famous article in 1936 in which he revealed the existence of the so-called. "Unsolvable problems." This article preceded the famous study of Alan Turing on the halting problem, which also demonstrated the existence of problems, unsolvable mechanical means.

• Claude Shannon created a machine that could play chess, long before the creation of Deep Blue. In 1952, Shannon has created a learning machine find a way out of the maze.

• Also, he was a developer of the first commercial radio control toys, which was produced in the 50s in Japan. He also developed a device that could add a Rubik's Cube, a mini computer for a board game Hex, which is always defeated opponent mechanical mouse that could find a way out of the maze. He also realized the idea of a comic machine «Ultimate Machine».

ENTERTAINING PUZZLES.

•The three painters had a brother John and John's brothers were not. How could this happen?

•Answer: The painters were sisters

IS THE BEST CHESS PLAYER THE BEST MUSICIAN

AMONG MUSICIANS OF CHESS?

•Answer: No, not necessarily.

INTERESTING FACTS.

• The number 37 has many curious properties. So, multiplied by 3 and multiples of 3 (to 27 inclusive), it gives works depicting any one figure:

• 37 × 3 = 111;

• 37 × 6 = 222;

• 37 × 9 = 333;

• 37 × 12 = 444;

• 37 × 15 = 555;

• 37 × 18 = 666;

• 37 × 21 = 777;

• 37 × 24 = 888;

• 37 × 27 = 999.

• Artwork by multiplying 37 by the sum of its digits is equal to the sum of the cubes of the same digits, ie:

• 37 × (7 + 3) = 33 + 73 = 370.

• If the number 37 to take the sum of the squares of its digits and subtract this amount from the product of the same figures, we again obtain 37:

• (32 + 72) - 3 × 7 = 37.

• Interesting properties of the number 9 are often used in arithmetic. For example it is easy to see that if we write any two-digit number, and then write the same number of digits in reverse order and take the difference obtained numbers, this difference is always divided into 9.

• eg

• 72 - 27 = 45;

• 92 - 29 = 63;

• 63 - 36 = 27

• etc.