Application of Discrete Mathematics in CSE
- 3. MEMBERS OF OUR GROUP 1. A. N. M. JuBaer-162-15-7850 2. MD Imrul Hasan Ashik -162-15-7723 3. MD.Shahbuddin Emon-162-15-7789 4. Tanvir Hossen Bappy-162-15-7706.
- 4. TOPIC OF OUR PRESENTATION:-- APPLICATION OF DISCRETE MATHMATICS IN CSE
- 5. What is Discrete Mathematics ? Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from each other. Integers ,rational numbers, automobiles, houses, people etc. are all discrete objects.
- 6. Theoretical Computer Science Theoretical computer science includes areas of discrete mathematics relevant to computing. Theoretical computer science also includes the study of various continuous computational topics.
- 7. Information Theory: Information theory involves the quantification of information. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. Here a simple cirlce of continous topics-
- 8. Mathematical logic: Logic is the study of the principles of valid reasoning and inference. The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software.
- 9. Set theory: Set theory is the branch of mathematics that studies sets, which are collections of objects. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets (including finite sets) are the main focus.
- 10. Graph theory: Graph theory, the study of graphs and networks, is often considered part of combinatorics. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. There are also continuous graphs like--
- 11. Discrete probability theory: Discrete probability theory deals with events that occur in countable sample spaces. Discrete probability distributions can be used to approximate continuous ones and vice versa. For highly constrained situations like dice or calculating the probability of events is basically enumerative.
- 12. Number theory: Number theory is concerned with the properties of numbers in general, particularly integers. Boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions in algebraic coding theory.
- 13. Trees: Trees are used to represent data that has some hierarchical relationship among the data elements. Here is a simple diagram of a tree—
- 14. Topology: Although topology is the field of mathematics that formalizes and generalizes the intuitive notion. See topological graph theory,discrete topological space, finite topological space, topology .
- 15. CONCLUSIONS We emphasize the essential role that mathematics plays in the development of computer science both for the particular knowledge and for the reasoning skills associated with mathematical maturity.