I. Brief Introduction
Mathematics is a science of quantitative relation and space form in a rather wide natural phenomenon and social phenomenon. The essential feature shows as the summarized common principles from the side of natural phenomenon quantities to predict the future development and positively leads people to learn and change the reality. As the base of every scientific subject, it works as a thinking bank in natural, social and engineering technology. Besides, it also acts as an important tool in economic construction and technical progress. As a whole, mathematics is a wide spread, specifically divided and mass applied scientific system.
Mathematics is a first degree authorized subject. Applied mathematics was authorized as master’s degree in 2003, basic mathematics realized in 2005 and mathematics in 2010. Self-evaluation right of professor title was authorized in 2002. In 2007 applied mathematics was rated as Key Subjects at the Provincial Level . Now this department owns 76 full-time teachers among whom are 9 professors, 14 associate professors, 6 doctoral supervisors, 19 master supervisors, 30 doctoral degree teachers, 2 members of Shanxi Province “one hundred talents plan”, 2 of governmental subsidy, 2 winners of Huo Yingdong advanced youth teacher award, 2 members of Shanxi Province high level experts, 1 member of Ministry of Education new era talents, 4 provincial leading teachers, 13 university masters, each 2 members of academic leading youth in Shanxi Province, Shanxi Province excellent scientific workers and Shanxi Province 333 talents project of new century academic and technology leaders, 1 national master, 5 executive members of the provincial above institution and last 4 editorial members in domestic and abroad journals.
Since 2007, our college has undertook 42 scientific programs worth 5 million including 9 National Science Foundation and 30 provincial or ministry level project. Academically, more than 700 articles have been published, accounting 200 SCI, 10 pieces in mathematical first area, 1 in J. R. Soc. Interface and 1 collected into the “Hundred of the most international influential Chinese academic theses in 2008”. There are also 3 monograph, 4 awards in technology awards above provincial level and 1 first award in national science.
II. Educational Objectives
This subject aims to cultivate high-level mathematical talents with a good mastery of subject theory, future direction and sturdy practice ability in further scientific research of one particular direction. We are devoted to help students hold a solid professional knowledge and relative software and shape individual theory research ability or cooperation ability in a team to tackle real problems. Proficiently master a foreign language is an essential skill for students to study further on the professional foreign literature. Obviously a proficient skill of Chinese weighs as important as a foreign language. After all these training programs, students can be ensured a good advantage in profession hunting in fields like education, scientific research and practical works.
III. Education Duration
This subject is set only for postgraduates with academic master degree in three years. Graduate course and theses completion takes up the same credit. Courses should be completed in the first year and the theses completion program should be achieved in 1.5 year at least (before graduation). It will ask for a strict examination for both advance thesis defense and postpone thesis defense.
IV. Research Interests
As a rapid burgeoning inter discipline in 20s century, basic theories and research methods in bio-mathematics have exposed great influence to the current development of this subject and gained a wide application in all relative fields.
Main research directions are: mathematical modeling and analyze of population dynamics and infectious disease dynamical system; differential coefficient equation and stability theory and its application; reaction diffusion equation traveling waves and delay differential equation theories and application; discrete dynamical system theory and relevant application; cellular automata application in ecological and epidemic; species and epidemic dynamical system pattern formation mechanism and complex network node dynamical system. In recent years, researches are most conducted in fields of real life epidemic dynamics model, Internet information (virus) diffusion, product information diffusion, data visualization software exploitation in information recommendation and geographical information system which have produced a series of original achievements winning a wide-spread influence in domestic and abroad.
By the algebraic representation (adjacency matrix, Laplacian matrix, incidence matrix) of building composite structures (graphs, composite designs etc.), this subject combines with applied algebra (theory of matrices and group theory) at same time to do researches in topological properties in combined structures or apply topological properties in combined structures to study matrix algebraic properties.
Specific directions are nonnegative matrix composition theory, sign pattern matrix qualitative theory and digraphs composite structure theory which are the core contents of combinatorics study. Close relation with algebra, algorithm theory and other branches enables it gain a wide application in economic mathematics, computer science and biology.
III. Scientific Computing in Engineering
Many scientific mathematical problems also exist in engineering. This subdivision study the spacial allocation, parameters optimum design and error analysis of information reconstruction and accurate measurement and virtual experiment platform basing on the imaging information process theory. Key researches are laid on the propagation rules in ray, voice, ultrasonic and infrared ray mediums, projected image analytic algorithm, iterative algorithm convergence and fast implementation and images feature extraction and reinforcement.
This subject is based on the practical resolve in engineering process, so keeps a close cooperation with Shanxi Province non-destructive testing center. Using lgebra, geometry, partial differential equation, functional analysis, mathematics of randomness and optimization theory, more theory study conducted in the real life practice.
IV. Modern Optimization Technique and Application
Main researches are neural network optimization algorithm, genetic algorithm, particle swarm optimization and simulated annealing algorithm. These algorithm are mostly applied in the difficult optimum situations. Due to the independence quality from gradient information, this direction is the best choice in large-scale complex problems where traditional methods don’t work out.
Artificial neural network, as one direction of this subject, is defined as the most rapid developing research field. Close related with the practical resolution is the second direction to design and realize the practical algorithm. According to the application of neutral network, researches are concentrated on neural network, elastic neutral network, structural optimum calculation application of self-organization features and BP neutral network application in function approximation, stock market prediction and epidemic prediction.
V. Nonlinear Differential Equation Theory and Application
Research directions are existence, uniqueness, stablity, asymptotic, oscillations, periodic solution and boundary value problem of nonlinear ordinary differential equation, functional differential equation and impulsive differential equation solution; branch theories and dynamic geometric theory.
Improvements have been made in directions of periodic solution existence in nonlinear impulsive differential equation, global asymptotic stability under threshold conditions and its branch studies, global asymptotic stability in self-feedback high dimensional delay differential equations and epidemic dynamic models, functional differential equation and existence, stability and oscillations of impulsive differential equation solutions.
VI. Nonlinear Functional Analysis and Application
Researches of this subject are topological degree theory in infinite dimensional spaces, partial ordering critical point theory, operator semi-group and application of these theories to discuss the global structures of nonlinear integral equation and differential equation solution existence and positiveness. Meanwhile, iterative sequence and error estimate of approximate solutions offer further research background as well.
VII. Partial Differential Equation
Main research direction is the nonlinear hyperbolic partial differential equation well posedness theory including global existence of classical solution, asymptotic behavior, division phenomenon and division formation mechanism of global solutions and solution span.
VIII. Applied Probability and Statistics
Mostly focusing on the probability theory, mathematical statistics and multivariate statistical analysis, this subject tends to the practical use of theories and resolve real problems for creative researches.