The picture of the first grade math handwritten newspaper is neat and beautiful.

Beautiful Mathematics Handwritten Newspaper

Content of mathematical manuscript: Expounding the conceptual structure of mathematics.

Many mathematical objects, such as numbers, functions and sets, have internal structures. The structural properties of these objects are discussed in groups, rings, bodies and other abstract systems that are themselves objects. This is the field of abstract algebra. Here is a very important concept, that is, vector, which is extended to vector space and studied in linear algebra. The study of vector combines three basic fields of mathematics: quantity, structure and space. Vector analysis extends it to the fourth basic field, namely change.

space

The study of space originated from Euclidean geometry. Trigonometry combines space and numbers and contains a very famous Pythagorean theorem. Now the research on space is extended to high-dimensional geometry, non-Euclidean geometry and topology. Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold. Algebraic geometry has the description of geometric objects such as polynomial equation solution set, which combines the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.

basis

In order to understand the basis of mathematics, mathematical logic and set theory are developed. Cantor (1845- 19 18), a German mathematician, initiated the set theory and boldly put forward the important ideas. Infinite? In order to provide a solid foundation for all branches of mathematics, and its own content is quite rich, March put forward the idea of "real infinity" and made inestimable contributions to the future development of mathematics.

Set theory gradually penetrated into all branches of mathematics at the beginning of the 20th century, and became an indispensable tool in analytical theory, measurement theory, topology and mathematical science. At the beginning of the 20th century, mathematician Hilbert spread Cantor's thought in Germany, which was called set theory? A mathematician's paradise? And then what? The most magical product of mathematical thought? . British philosopher Russell praised Cantor's work as? The greatest job that this era can boast about? .

logic

Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. As far as it is concerned, it is the origin of Godel's second incompleteness theorem, which is perhaps the most widely circulated achievement in logic. Modern logic is divided into recursion theory, model theory and proof theory, which are closely related to theoretical computer science.

sign

Perhaps China's ancient arithmetic is one of the earliest symbols used in the world, which originated from divination in Shang Dynasty.

Most of the mathematical symbols we use today were invented after16th century. Before that, mathematics was written in words, which was a hard procedure that would limit the development of mathematics. Today's symbol makes mathematics easier for people to operate, but beginners are often afraid of it. It is extremely compressed: several symbols contain a lot of information. Like music notation, today's mathematical symbols have clear grammar and information codes, so it is difficult to write them in other ways.

Mathematical manuscript: the relationship between mathematics and national defense in World War II, and what role did mathematicians play in the Allied victory?

Feng? Neumann was a top mathematician in the 20th century, and he was also the first developer of computer programs and memories. He made two major contributions to the manufacture of American atomic bombs:

One is to help Los Alamos find a mathematical method. ? Math? Refers to the use of fast computer simulation to calculate the explosion process and explosive power of atomic bombs.

The second is to study explosive bombs, that is, to bind some bombs with atomic bombs and emit greater power.

Ulan is a Polish mathematician. After he fled from Europe to America, he took part in the Manhattan Project. In order to simulate the nuclear experiment, he invented the Monte Carlo calculation method.

Andrei Andrey Kolmogorov, a great mathematician in the former Soviet Union, put forward the theory of stationary stochastic process in World War II. Wiener, an American mathematician, put forward the filtering theory, which can eliminate noise interference and process the information obtained by radar.

British mathematician Turing was the first person to design a universal digital computer. In World War II, together with some excellent mathematicians, he finally solved the mystery of German cipher. American cryptanalysts also cracked Japanese cryptanalysis at 1940? The secret of purple? Password.

1942 the Japanese navy failed to raid midway island. One of the important reasons is that the United States deciphered the intelligence of Japan's attack on Midway Island. 1943 In April, using the deciphered information, the United States laid Isoroku Yamamoto's landline, which became a wonderful page in the history of cryptography.

In modern wars, the role of mathematics is more prominent. In terms of weapons, there are contests between advanced weapons such as nuclear weapons and long-range cruise missiles. There is a contest between secrecy, decryption, interference and anti-interference in information. In terms of countermeasures, there are contests in strategy, tactics and weapons preparation. Each item is closely related to mathematics.

The nuclear reaction process is carried out at high temperature and high pressure, and the huge energy of nuclear explosion is released in microseconds. It is difficult to measure the subtle process inside the nuclear explosion in the nuclear test, and only some comprehensive effect data can be obtained. Through the mathematical model of nuclear reaction process, numerical calculation can give detailed images, quantitative data and interaction of various factors and mechanisms in the explosion process. After joining the Comprehensive Nuclear-Test-Ban Treaty, it is more important to simulate nuclear tests by numerical calculation.

Regarding cruise missiles, the People's Liberation Army Daily wrote in a report about the power of mathematics. One equation improves the quality of satellite images by 30%, and one formula changes the informed mode of an army. ? Rich in information? Encryption? With what? Decryption? As they say, this is a confrontation? The magic is one foot high and the road is ten feet high? . And the performance of this kind of resistance is based on mathematical theory. For example, most public key algorithms are based on difficult problems with high computational complexity, and it takes a lot of time to get the answer on high-speed computers. These methods usually come from number theory. For example, RSA comes from integer factorization problem, DSA comes from discrete logarithm problem, and elliptic curve cryptography, which has developed rapidly in recent years, is based on elliptic curve related mathematical problems.