Write your own proofs in set theory and discrete mathematics

doi:10.5860/choice.44-0358

Discrete Mathematics into K-11 and K-12 Grade Education

Journal of University of Shanghai for Science and Technology ◽

10.51201/jusst/21/05150 ◽

2021 ◽

Vol 23 (05) ◽

pp. 319-324

Author(s):

Mr. Balaji. N ◽

◽

Dr. Karthik Pai B H ◽

Keyword(s):

Set Theory ◽

Mathematical Reasoning ◽

Mathematical Induction ◽

Discrete Mathematics ◽

College Classrooms ◽

Underlying Principle ◽

Education Study ◽

Strongly Connected ◽

Proof Techniques ◽

K 12

Discrete mathematics is one of the significant part of K-11 and K-12 grade college classrooms. In this contribution, we discuss the usefulness of basic elementary, some of the intermediate discrete mathematics for K-11 and K-12 grade colleges. Then we formulate the targets and objectives of this education study. We introduced the discrete mathematics topics such as set theory and their representation, relations, functions, mathematical induction and proof techniques, counting and its underlying principle, probability and its theory and mathematical reasoning. Core of this contribution is proof techniques, counting and mathematical reasoning. Since all these three concepts of discrete mathematics is strongly connected and creates greater impact on students. Moreover, it is potentially useful in their life also out of the college study. We explain the importance, applications in computer science and the comments regarding introduction of such topics in discrete mathematics. Last part of this article provides the theoretical knowledge and practical usability will strengthen the made them understand easily.

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User-Centric Design for Mathematical Web Services

Advances in Human-Computer Interaction ◽

10.1155/2014/436980 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Adlin Sheeba ◽

Chandrasekar Arumugam

Keyword(s):

User Interface ◽

Web Services ◽

Web Service ◽

Set Theory ◽

Rapid Development ◽

Discrete Mathematics ◽

Virtual Keyboard ◽

Application Logic ◽

User Centric ◽

Sophisticated User

A web service is a programmatically available application logic exposed over the internet and it has attracted much attention in recent years with the rapid development of e-commerce. Very few web services exist in the field of mathematics. The aim of this paper is to seamlessly provide user-centric mathematical web services to the service requester. In particular, this paper focuses on mathematical web services for prepositional logic and set theory which comes under discrete mathematics. A sophisticated user interface with virtual keyboard is created for accessing web services. Experimental results show that the web services and the created user interface are efficient and practical.

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ORDER AND ORDERING IN DISCRETE MATHEMATICS AND INFORMATICS

Ukrainian Journal of Information Technology ◽

10.23939/ujit2021.03.037 ◽

2021 ◽

Vol 3 (1) ◽

pp. 37-43

Author(s):

V. K. Ovsyak ◽

◽

O. V. Ovsyak ◽

J. V. Petruszka ◽

◽

...

Keyword(s):

Mathematical Logic ◽

Graph Theory ◽

Set Theory ◽

Operator Algebra ◽

Proof Theory ◽

Cartesian Product ◽

Object Oriented ◽

Discrete Mathematics ◽

Program Execution ◽

System Of Algorithmic Algebras

The available means of ordering and sorting in some important sections of discrete mathematics and computer science are studied, namely: in the set theory, classical mathematical logic, proof theory, graph theory, POST method, system of algorithmic algebras, algorithmic languages of object-oriented and assembly programming. The Cartesian product of sets, ordered pairs and ordered n-s, the description by means of set theory of an ordered pair, which are performed by Wiener, Hausdorff and Kuratowski, are presented. The requirements as for the relations that order sets are described. The importance of ordering in classical mathematical logic and proof theory is illustrated by the examples of calculations of the truth values of logical formulas and formal derivation of a formula on the basis of inference rules and substitution rules. Ordering in graph theory is shown by the example of a block diagram of the Euclidean algorithm, designed to find the greatest common divisor of two natural numbers. The ordering and sorting of both the instructions formed by two, three and four ordered fields and the existing ordering of instructions in the program of Post method are described. It is shown that the program is formed by the numbered instructions with unique instruction numbers and the presence of the single instruction with number 1. The means of the system of algorithmic algebras, which are used to perform the ordering and sorting in the algorithm theory, are illustrated. The operations of the system of algorithmic algebras are presented, which include Boolean algebra operations generalized to the three-digit alphabet and operator operations of operator algebra. The properties of the composition operation are described, which is intended to describe the orderings of the operators of the operator algebra in the system of algorithmic algebras. The orderings executed by means of algorithmic programming languages are demonstrated by the hypothetical application of the modern object-oriented programming language C#. The program must contain only one method Main () from which the program execution begins. The ARM microprocessor assembly program must have only one ENTRY directive from which the program execution begins.

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The use of discrete mathematics algorithms in technological design

MATEC Web of Conferences ◽

10.1051/matecconf/202032903082 ◽

2020 ◽

Vol 329 ◽

pp. 03082

Author(s):

Nina Glinskaya ◽

Isabella Belonovskaya

Keyword(s):

Decision Making ◽

Graph Theory ◽

Structural Optimization ◽

Set Theory ◽

Traveling Salesman ◽

Discrete Mathematics ◽

Mechanical Processing ◽

Mathematics Methods ◽

Decision Making Processes ◽

Technological Processing

The article examines the possibility of the formalization of the main stages of a detail mechanical processing using discrete mathematics methods. There are examples of using the graph theory for modeling practically all the stages of the development of processing technology. For structural optimization of technological process it is offered to use the problem of the traveling salesman. The choice of technological bases may be carried out both with using the graph theory and the set theory. The article makes a conclusion about the effectiveness of discrete mathematics methods for the formalization of decision making processes during technological processing.

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