Introduction to Mathematics is an introductory course for majors in mathematical disciplines and is the basis for subsequent professional foundation and specialized courses. This course aims at the professional quality education of students, and aims to give them a more comprehensive understanding of the relevant knowledge of mathematical disciplines. Systematic introduction to the origin, development and status of the discipline of mathematics, its role and status, and the links and differences between other related disciplines. To enable students to understand the main curriculum, study content, study and research methods and future development direction of the major.
Mathematical Analysis is an important basic theory course required for students of mathematics and applied mathematics, information and computational science, which is opened for training the builders of socialist modernization. Through the course, students can master to the basic definitions, theorems and calculation skills of the calculus of functions of one element. It plays a vital role in the formation of good mathematical quality of students and the subsequent course of study. In particular, this course can cultivate students' abstract thinking ability, logical thinking ability, spatial imagination ability and independent learning ability, and then will use the knowledge learned to analyze and solve problems.
Analytical Geometry is based on the secondary school plane analytic geometry and three-dimensional geometry, and introduces vector algebra as a tool to establish a spatial coordinate system in three-dimensional space, so as to establish the inner connection between algebra and space geometry, and achieve the purpose of using algebraic methods to solve geometric problems. Students will be able to use vector algebra as a tool to establish the equations of spatial lines and planes by the scale-frame method; master the position relations of lines and planes and the calculation of geometric quantities; master the derivation of the equations of special surfaces and be able to use the plane truncation method to inscribe the geometric properties of surfaces; the general theory of quadratic curves (surfaces).
Higher Algebra is a basic course for mathematics and applied mathematics majors and information and computing science majors. Through the teaching of this course, students will master determinants and matrices and the use of them to solve systems of linear equations. In addition, it develops students' understanding of the concepts of linear spaces and linear mappings. This course strengthens students' ability to solve systems of linear equations.
Discrete Mathematics is a mathematical discipline that studies the structure of discrete quantities and their interrelationships, and is an important branch of modern mathematics, as well as the basis for subsequent professional foundation courses and specialized courses. This course aims at the professional quality education of students, and aims to give them a more comprehensive understanding of the relevant knowledge of discrete mathematics. The main content of this course includes mathematical logic, set theory, algebraic systems, graph theory and other four aspects. Through the study of this course, students will understand and master some basic concepts, basic ideas and basic methods in discrete mathematics, cultivate and improve students' abstract thinking and logical reasoning ability, and gain the ability to solve practical problems.
Ordinary Differential Equations is the most fundamental mathematical theory and method for studying the laws of motion, evolution and change of things, objects and phenomena in natural and social sciences. Many principles and laws in the fields of physics, chemistry, biology, engineering, aerospace, medicine, economics, and finance can be described as appropriate ordinary differential equations. Ordinary Differential Equations is one of the professional foundation courses of the Department of Mathematics, and it is also one of the important compulsory and backbone courses for students of all majors in the Department of Mathematics, and it is the basis of subsequent courses in mathematical physical equations, dynamical systems, optimal control theory, mathematical models, mathematical economics, financial mathematics, biological mathematics, economic mathematics, numerical solution of differential equations, etc. It has been playing an important and special role in the process of training talents in mathematical disciplines .
Operations Research is an interdisciplinary study of applied mathematics and formal sciences, often used to solve complex problems in real life, in particular to improve or optimize the efficiency of existing systems. Operations Research is an important disciplinary foundation course required for undergraduate students in industrial engineering and logistics engineering, and is a course set up to train students to master the basic ideas, basic knowledge, basic theories and basic methods of operations research. Through the study of this course, students will initially understand and master the basic principles and methods of operations research, train students to establish the idea of optimization, master the method of modeling typical practical problems, master the basic calculation method of solving problems, and initially have the basic ability to carry out the optimization of practical management problems.
Algorithms and Data Structures is a professional foundation course for Information and Computing Science majors. It mainly introduces the representation of data structures such as linear tables, stacks and queues, binary trees and trees, graphs, dictionaries and the implementation of related algorithms and their applications. This course aims at the professional quality education of students, so that students can learn to analyze and study the general characteristics of data objects and processing methods of computer processing, master the implementation of various common data structures and their algorithms, organize data effectively, design efficient algorithms, and write high-quality programs.
Multivariate Statistical Analysis for science students, including: matrix algebra; random vectors; multivariate normal distribution; discriminant analysis; cluster analysis; principal component analysis; factor analysis; SPSS software applications.
Fuzzy Mathematics and its Applications: Modern mathematics has important applications in many fields such as information processing, artificial intelligence, engineering science and technology, management decision making, etc. Among them, the wide application of uncertain mathematical theories such as fuzzy sets and rough sets is an important feature. This course focuses on the basics of fuzzy mathematics and rough set theory, and introduces their practical applications in detail with several application topics (including fuzzy comprehensive evaluation, fuzzy cluster analysis, industrial control, intelligent control of robots, fuzzy decision making, and the application of rough sets in knowledge simplification, decision support, fault diagnosis, data mining, etc.).
Functions of Real Variables is one of the important basic courses in analysis for mathematics and applications, and is a further development of the Riemann integral in mathematical analysis. The core of this course is the theory of measure and Lebesgue integral, mainly including the theory of bases of infinite sets, measurable sets, measurable functions, the definition of Lebesgue integral, Lusin's theorem and Egoroff's theorem, Fubini's theorem and Tonelli's theorem, Lebesgue differentiation theorem, the fundamental theorem of Lebesgue integral, etc.
Mathematical Physics Equations introduces three typical types of mathematical physics equations, namely, fluctuation equations, heat conduction equations, and reconciliation equations. It includes the derivation of the equations, the methods of solving various definite solution problems, such as the separation of variables method, the Fourier transform method, the energy integration method, etc., and the discussion of the nature of the solutions.
Numerical Analysis is the study of how to use computers and other tools to find numerical solutions to mathematical problems. In scientific research and engineering technology, the problem of solving mathematical models is often encountered. However, in many cases, it is often very difficult to obtain the exact solution to a model problem. Therefore, it is necessary to study the approximate solutions of various mathematical problems. Numerical Analysis is devoted to the study of a class of approximate solutions to various mathematical problems, starting from a set of original data and performing finite step operations according to defined rules of operations to finally obtain an approximate solution of the problem in numerical form and satisfying accuracy requirements.
Stochastic Processes is a branch of stochastic mathematics, which studies the statistical regularity of the evolution of random phenomena in the objective world. The theory of stochastic processes arose at the beginning of the 20th century and was developed gradually due to the needs of physics, biology, communication and control, and management science. The theory of stochastic processes provides mathematical tools for the study of a large number of complex random phenomena, and it has a wide range of applications in both natural and social sciences. A stochastic process is a totality or set of random variables that depend on the variation of the time parameter t. It can also be called the totality and set of sample functions.
Professional Literature Reading and Writing is a required professional practical course for mathematics and applied mathematics majors and information and computational science majors. Professional Literature Reading and Writing is an important training method for students to synthesize their knowledge system and enhance their cognitive ability.
Mathematical Modeling is a discipline that studies how to transform real-life problems into mathematical problems and analyze and solve the transformed problems with mathematical theories and computer software. This course mainly introduces the basic ideas of mathematical modeling, the methods of mathematical modeling and computer solution techniques, as well as several examples of mathematical models of different categories.
As a general education elective course, Mathematical Modeling Practical Training enables students to understand the important application of mathematical knowledge in practice through mathematical modeling application examples. The mathematical knowledge used in this general education course is familiar to the students, including the primary mathematics in secondary school. The main contents are: introduction to mathematical modeling and primary models; advanced mathematical modeling cases; equation modeling and solution methods; linear algebra modeling cases; probability theory and mathematical statistics models; optimization models. The course also arranges experiments to study the commonly used mathematical modeling software.
The course of Calculus mainly introduces the basic definitions, theories and computation skills about infinite sequence and series, vectors and It is a part of fundamental mathematical courses and is a necessary foundation for most students. It is a part of fundamental mathematical courses and is a necessary foundation for most Economic Management and Science and Engineering courses.
