**Master Degree Program of Mathematics and Information Science Institute**

The institute of mathematics and information science offers the master degree program. There are three professors and six associate professors who are involved in this master degree program. Their researches mainly focus on the theories and technologies of mathematical problems in the information science, the modeling and simulation of complex systems, cryptography theory and technology. They directed and completed four natural science foundations of China and many provincial or ministerial scientific research projects, and they published about one hundred papers which were indexed by SCI and some of other famous databases. Some of distinctive and innovative researches have been made. The directions of our master degree program of mathematics and information science are introduced briefly as follows:

1、The mathematical problems in the information science: This direction focuses on the theories and their applications of partial differential equations and image processing. The researches include elliptic partial differential equations，parabolic partial differential equations and some of other partial differential equations related with image processing. Based on these partial differential equations, the models of image processing are built. These models are used to study the theories and technologies of image processing, including the image reconstruction, segmentation, filter, recognition, resampling, enhancement, statistical analysis, classification, and so on.

2、The modeling and simulation of complex systems: This direction focuses on theoretical research and applied research related to computation and simulation of nonlinear systems, including the theory and application of nonlinear partial differential equation, solution theory, symbolic calculation and approximate solution of nonlinear systems. The analysis, simulation and calculation of nonlinear systems are made by using the method of qualitative analysis.

3、Cryptography theory and technology：This direction focuses on the mathematic theories on cryptography, construction of cryptography algorithms, provable security theories and formal security analysis, the applications on cryptography protocol, quantum cryptography theory and its applications on information security, and so on.

*Courese offered in this program are as follows:*

Cryptography Theory and Technology

Credit: 3

Credit hours: 60

Course number: 080004

This course is an obligatory specialized course for the information and computing science. Its goal is to make the postgraduate students master and understand some basic concepts and algorithms of cryptography, including some frequently used encryption and decryption principles, authentication theories, and some common digital signature algorithms and their security analysis. This course involves block cipher, stream cipher, public encryption, digital signature, hash function, key setup and its management, identification, authentication theory and technology, PKI technology, and so on. The postgraduate students should master the basic concepts, basic theories and methods of cryptography and preliminary master their realizationtechnologies, so that they can prepare for the informatizationdemand of the society and serve for the society.

**Digital Signature Principle and Technology**

Credit: 2

Credit hours: 40

Course number: 080005

This course is an elective specialized course for the information and computing science. Its goal is to make the postgraduate students master the theories and their applications of digital signatures. This course involves the algorithms of digital signatures, RSA signature, Rabin signature, DSA signature, DSS signature, ElGamal signature, Schnorr signature, and quantum signature, the security analysis of digital signatures, and so on.

**Mathematical Methods of Information Security**

Credit: 2

Credit hours: 40

Course number: 080002

This course is an obligatory specialized course for the information and computing science. Its goal is to make the postgraduate students master the number theory and basic algebra knowledge of cryptography, and master their concepts and methods. This course involves division of integers, congruence modulo, quadratic residue, primitive root and index, group, ring, field, and the structure of finite group. This course can lay solid foundations for the study of cryptography and the application of the technologies. This course is also the pre-course of digital signature principle and technology.

**Functional Analysis**

This course is separated into five parts. In the first, we mainly concern complete metric spaces and contract map theorems. In the second, we discuss the geometry of Banach space, and the bounded linear operators and bounded linear functionals on the Banach space. In the third, we hit the variational principle, orthogonal decomposition, orthonormal base, Riesz representation theorem and the conjugate operators in the Hilbert space. The last two parts contain the four basic principles in Banach space, and the theory on the spectrum of operators.

**Matrix theory**

Credit: 2

Class hours: 40

Course number:

Matrix theory is a basic course of the professions of computer and communication engineering, mechanical and electrical engineering and electric and information engineering. In this course, the basic concepts, basic theories and basic methods and their applications of linear space and linear transformation, norm, matrix analysis and matrix decomposition will be taught systematically.

Partial differentialequation

**Partial differential equation**

Partial differential equationis a major course and an important branch in modern mathematics, which plays an important role in many subjects especially in physics, fluiddynamics etc. It can establish the mathematics model, give the theoretical analysis and the explanation of the objective phenomenon, and solve the practical problems.

**Methods and Simulation of Mathematical Physics**

Methods and Simulation of Mathematical Physicsis the compulsory course ofZhengzhou University of Light Industryof information and computing science.Compared withthe traditional teachingcourse of methods of mathematical physics,this course isto strengthenthe computer simulation programming practicecontent.The coursesystem has four main parts:foundation of mathematical physics,mathematical physicalequations,specialfunction,the computer simulationprogrammingpractice --mathematical model.

Methods and Simulation of Mathematical Physics(Second Edition)is planning materials of facing the twenty-first Centuryhigher education undergraduatecurriculum.

The system describesFourier transform and Laplace transform,various methodsof mathematical physics equations,special functions andcomputer simulationprogramming practice. It hasguiding significance to thecultivation of thinking ability andpracticeability of programming. Basedon the depth and breadth,giving full consideration to themodernhigh-tech frontierdiscipline domain knowledgecontent, we have formed the theoretical systemand computermethods of mathematical physics which has frontierdiscipline characteristic simulationcombining

**NumericalAnalysis**

Credits: 3

Hours: 48 hours all for lessons +6 hours for practice exercise

Course ID: 1023109

The course of numerical analysis has function interpolation and approximation, solving equations, eigenvalue and eigenvector calculations, and numerical solution of differential equation. There are not only theories but also numerical experiments in numerical analysis. It provides the reliability method and theory of the calculation in scientific and engineering.

**Modern software engineering**

Credits：2

Period：40

Course id: 100123

We mainly introduce the concept of software engineering, software engineering principle and method of the typical technology in software engineering. Our students can master the methods of developing high-quality software by studying the procedure-oriented software development method and the object-oriented software development method.

Students are able to know how to make software metrics and management by means of studying the process of software development and technology of process management.

**Probability and Mathematical Statistics**

Institute：College of Mathematics and Information Science

Credits：

Hours：48

Course Code：

Course Description：

Probability and Mathematical Statistics is a basic course of Master graduate students. It’s very useful in the engineering technology, scientific research, economic management, and many other fields. The purpose of this course is to enable the students to master the basic concept of Probability and Mathematical Statistics, the basic theory and method. At the same time, we will train the students' consciousness and ability of using the knowledge to solve the practical problems.

**Optimization**

Course Code：991010

Credits/ Hours：2.0/40

Optimization is to study the mathematical theories and methods of the optimal selection for decision making problems. Optimization theories and methods are widely used in the automation area. The main subjects include the basics of optimization theory, linear programming, non-linear programming, and modern meta-heuristic algorithms for combinatorial optimization problems.