1 and1In the second half of the 9th century, the Bibiburg school headed by Chebyshev appeared.
The Petersburg School is also called Chebyshev School. /kloc-Many famous mathematicians in the second half of 0/9th century and the first half of this century, such as Colding, Markov, Lyapunov, Ronoy, stech Loff and krylov, all belong to this school.
Soviet mathematicians Victor Noguera and Bernstein are the direct successors of this school, and many of them are students of Chebyshev, the founder of this school.
Chebyshev was born in Okadovo, 184 1 graduated from Moscow University, 1847 served as an associate professor at Petersburg University. Worked in Petersburg University until 1882. He published more than 70 scientific papers in his life, covering number theory, probability theory, function approximation theory, integral calculus and so on. He proved beltran formula, prime number distribution theorem of natural sequence, general formula of law of large numbers and central limit theorem. He not only attaches importance to pure mathematics, but also attaches great importance to the application of mathematics.
Chebyshev has two outstanding students, Lyapunov and Markov. The former is famous for studying the stability theory of differential equations, while the latter is famous for Markov processes. They carried forward Chebyshev's idea of integrating theory with practice.
Lyapunov is an outstanding representative of the Petersburg School founded by Chebyshev. His achievements involve many fields, especially probability theory, differential equations and mathematical physics. In probability theory, he founded the characteristic function method, which achieved a breakthrough in the research method of limit theorem of probability theory. The characteristic of this method is to keep all the information of the distribution law of random variables, provide a one-to-one correspondence between the convergence properties of characteristic functions and the convergence properties of distribution functions, and give a simpler and more rigorous proof than Chebyshev and Markov central limit theorems. He also used this theorem to scientifically explain why many random variables encountered in practice obey normal distribution for the first time. His contributions to probability theory are mainly published in his papers "A Probability Theorem in 1900" and "A New Form of Probability Limit Theorem in 190 1". His method has been widely used in modern probability theory. ? Lyapunov is the founder of the theory of motion stability of ordinary differential equations. 1884 completed the paper "On the Stability of Ellipsoid Shape of Rotating Liquid Equilibrium", 1888 published "On the Stability of Finite Freedom Mechanical System". In particular, his doctoral thesis "General Problems of Motion Stability" in 1892 is a classic, in which the Lyapunov function method for solving nonlinear ordinary differential equations, also known as the direct method, is creatively proposed, which links the stability of the solution with the existence of a function with special properties (now called Lyapunov function) and the derivative of this function along the trajectory with certain properties about time. It is precisely because this method has obvious geometric intuition and concise analytical skills that it is easy to be mastered by practitioners and theoretical workers, so it has been widely used and developed in many scientific and technological fields, and laid the foundation for the stability theory of ordinary differential equations, which is also an important means of qualitative theory of ordinary differential equations.
2. After the 20th century, the Moscow School rose and made great contributions to the function theory. Its founders are Ye Golov and Jin Lu.
Ye Golov's theorem on measurable function, which was proved by Ye Golov in 19 1 1, is the origin of Russian real variable function theory, which is included in any textbook of real complex number theory.
Jin Lu (1883- 1950) is the core figure of the Moscow school of mathematics. 1906 graduated from Moscow university and stayed on as a teacher. Jin Lu is one of the pioneers and founders of modern real variable function theory. He was one of the founders of descriptive function theory and found a more complex set-shadow set. And put forward many related speculations. In addition, he has also made achievements in analytic function theory, differential geometry, differential equations and other fields.
Jin Lu is a student in yegorov. 19 15 years, his doctoral thesis "Integral and Trigonometric Series" became the starting point for the future development of Moscow School. Since the 1920s, Moscow School has replaced France as the first in the world.