I. Introduction to the theme
Applied mathematics is two disciplines under the first-level mathematics discipline, which mainly studies mathematical theories or methods with practical background or application prospect. It takes the applied basic theories of various branches of mathematics as the research object, and also studies mathematical problems in the fields of physics, mechanics, petroleum development, geological exploration, information, economy, finance, management, etc., including the basic theoretical research of applied mathematics, establishes new mathematical theories, methods and mathematical models, and applies mathematical methods to solve practical problems.
Tutor of applied mathematics 15, including 9 professors and 5 doctors. Mainly engaged in optimization theory and application, nonlinear differential equations, mathematical physics, mathematical methods of petroleum engineering, graphic image processing and data mining.
Second, the training objectives
Graduate students majoring in applied mathematics have a solid foundation in mathematics, have the ability to independently carry out scientific theoretical research or solve practical problems, can achieve theoretical or practical results in a certain research direction, can solve mathematical problems in practical production such as physics, mechanics, petroleum, geology, economy, finance, management, etc., can establish mathematical models and solve problems they have learned, can skillfully read foreign literature and books of their major, and can engage in teaching, scientific research or other related courses after graduation.
Third, the main research direction:
1, optimization theory and application
This paper mainly studies the theory and numerical algorithm of nonlinear optimization, stochastic optimization and fuzzy optimization, the optimization technology of oil and gas pipeline network and other oilfield mathematical optimization problems.
2. Nonlinear differential equations
This paper mainly studies the existence, uniqueness, positive solutions and multiple solutions of various boundary value problems of nonlinear differential equations, and the eigenvalue theory of nonlinear differential equations.
3. Mathematical physics
This paper mainly studies related problems in mathematical physics, and establishes new theories and methods to deal with these problems, including the integrability of classical and quantum systems and the construction of solutions, functional integration theory and its application in quantum field theory and statistical mechanics, integral geometric methods for some geometric probability problems, the construction of random processes, the mathematical basis of non-equilibrium statistical mechanics, geometric analysis, renormalization method and seepage theory.
4. Mathematical methods of petroleum engineering
This paper studies the theory and method of applied mathematics in petroleum engineering, mainly studying the theory and method of solving partial differential equations in modern well testing theory in petroleum engineering and reservoir numerical simulation.
5. Graphic image processing
This paper mainly studies the analysis and processing of digital images, including compression, interpolation, feature extraction and image segmentation, registration, fusion, enhancement, recovery and retrieval of medical images, and mathematical problems related to image processing.
6. Applied statistics
It mainly studies machine learning and data mining, information statistics, economic and financial statistical analysis, biomedical statistical analysis and so on.
Fourth, the subject literature reading catalogue
1. Log list
1) Siam Review
2) communication between pure mathematics and applied mathematics
3) Mathematical physics communication
4) Journal of Physics A- Mathematics and Theory
5) Journal of Mathematical Physics
6) Yearbook of Mathematical Statistics
7) Progress in Applied Mathematics
8) Applied Mathematics and Calculation
9) Applied Mathematics and Optimization
10) Mathematics Journal
Journal of applied mathematics
12) applied mathematics and mechanics
13) application probability statistics
Journal of Mathematical Physics
Journal of operational research
16)
2. List of teaching materials and works
1) Liu, lecture notes on infinite dimensional analysis (edited by himself)
2) Liu's Lecture Notes on Algebra (edited by himself)
3) Selected Lectures on Mathematical Problems and Methods in Statistical Physics and Quantum Field Theory (edited by Liu)
4) Liu Lecture on Analytic Inequality, Geometric Inequality and Probability Inequality (edited by himself)
5) Wang Mingliang, Nonlinear Evolution Equation and Soliton, Lanzhou University Press, 1990.
6) Guo Dajun, Functional Methods for Nonlinear Ordinary Differential Equations, Shandong Science and Technology Press, 2005.
7) Arnold, translated by Qi, Mathematical Methods of Classical Mechanics (4th Edition), Higher Education Press, 2006.
8) Author 8) Okden, translated by Tan Yongji, Applied Partial Differential Equations, Science Press, 2008.
9) Santaro, Integral Geometry and Geometric Probability, Nankai University Press, 199 1.
10) translated by Wu Xindong and others and translated by Li Deng. , Ten Algorithms of Data Mining, Tsinghua University Publishing House, 20 13.
1 1) New progress series of foreign oil and gas exploration and development
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