Teaching Reform and Practice on Course Construction of Discrete Mathematics

Discrete mathematics studies the respective structures,laws and interrelationships of different discrete quantities,which has a wide range of applications in computer science and software engineering.It has the characteristics of research,practice and innovation.The teaching goals of the course of discrete mathematics include not only the understanding and mastery of knowledge,but also the study of methodology.However,current teaching mechanism has limitations in outdated course contents,rare real project examples and nonscientific scoring modes.This paper attempts to think about the course construction of discrete mathematics to improve the teaching effects and cultivate students’practical ability.

On Relationships Between Semi- antichains andUnichain Coverings in Discrete Mathematics

The paper explores the relationships between the largest cardinality of a semi antichain and the smallest cardinality of its unichain covering on the direct product space induced by two partially ordered sets,through studying on partially ordered sets. A sufficient condition under which they are equal is obtained.

Towards Connecting Discrete Mathematics and Software Engineering

To enhance training in software development,we argue that students of software engineering should be exposed to software development activities early in the curriculum.This entails meeting the challenge of engaging students in software development before they take the software engineering course.In this paper,we propose a method to connect courses in the software engineering curriculum by setting comprehensive development projects to students in prerequisite courses for software development.Using the Discrete Mathematics(DM)course as an example,we describe the implementation of the proposed method and teaching practices using several practical and comprehensive projects derived from topics in discrete mathematics.Detailed descriptions of the sample projects,their application,and training results are given.Results and lessons learned from applying these practices show that it is a promising way to connect courses in the software engineering curriculum.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

ON THE STABILITY OF THE SOLUTION TO A GONORRHEA DISCRETE MATHEMATICAL MODEL

In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the rationality of the model is ex-plained in a theoretic way.

On the Defining Equations of Protein’s Shape from a Category Theoretical Point of View

This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins, rather than on the proteins themselves. Knowledge of category theory is not required as mathematical notions are defined concretely. In this paper, proteins are represented as closed trajectories (i.e., loops) of flows of triangles. The relations between proteins are defined using the fusion and fission of loops of triangles, where allostery occurs naturally. The shape of a protein is then described with quantities that are measurable with unity elements called “unit loops”. That is, protein’s shape is described with the loops that are obtained by the fusion of unit loops. Measurable loops are called “integral”. In the approach, the unit loops play a role similar to the role “1” plays in the set Z of integers. In particular, the author considers two categories of loops, the “integral” loops and the “rational” loops. Rational loops are then defined using algebraic equations with “integral loop” coefficients. Because of the approach, our theory has some similarities to quantum mechanics, where only observable quantities are admitted in physical theory. The author believes that this paper not only provides a new perspective on protein engineering, but also promotes further collaboration between biology and other disciplines.

离散数学课程建设(英文)

Many students find great difficulty in the formal programming modules taught in almost every computing science degree.These modules,often taught in later years,rely on some mathematical abilities that seem beyond many students.This paper describes two new modules in years I and II of the curriculum that are helping students to prepare for the formal programming courses.These modules are algorithmic problem solving and discrete mathematics for computing science and are now running in two third-level institutions in Ireland.This paper also shows the impact that these new modules have had on the students in question.

A Mathematical Theory of Big Data

This article presents a cardinality approach to big data,a fuzzy logic-based approach to big data,a similarity-based approach to big data,and a logical approach to the marketing strategy of social networking services.All these together constitute a mathematical theory of big data.This article also examines databases with infinite attributes.The research results reveal that relativity and infinity are two characteristics of big data.The relativity of big data is based on the theory of fuzzy sets.The relativity of big data leads to the continuum from small data to big data,big data-driven small data analytics to become statistical significance.The infinity of big data is based on the calculus and cardinality theory.The infinity of big data leads to the infinite similarity of big data.The proposed theory in this article might facilitate the mathematical research and development of big data,big data analytics,big data computing,and data science with applications in intelligent business analytics and business intelligence.

Research on cubic polynomial acceleration and deceleration control model for high speed NC machining

To satisfy the need of high speed NC (numerical control) machining, an acceleration and deceleration (acc/dec) control model is proposed, and the speed curve is also constructed by the cubic polynomial. The proposed control model provides continuity of acceleration, which avoids the intense vibration in high speed NC machining. Based on the discrete characteristic of the data sampling interpolation, the acc/dec control discrete mathematical model is also set up and the discrete expression of the theoretical deceleration length is obtained furthermore. Aiming at the question of hardly predetermining the deceleration point in acc/dec control before interpolation, the adaptive acc/dec control algorithm is deduced from the expressions of the theoretical deceleration length. The experimental result proves that the acc/dec control model has the characteristic of easy implementation, stable movement and low impact. The model has been applied in multi-axes high speed micro fabrication machining successfully.