Download Discrete Mathematics PDF
You can download the Discrete Mathematics PDF for free using the direct download link given at the bottom of this article.
| File name | Discrete Mathematics PDF |
| No. of Pages | 62 |
| File size | 1.2 MB |
| Date Added | Aug 18, 2022 |
| Category | Education |
| Language | English |
| Source/Credits | Drive Files |
Discrete Mathematics Overview
Discrete mathematics is the study of mathematical structures that can be considered “discrete” rather than “continuous”. Objects studied in discrete mathematics include integers, graphs, and statements in logic.
Examples of structures that are discrete are combinations, graphs, and logical statements. Discrete structures can be finite or infinite.
Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.
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. Information theory has a lot of mathematics surrounding it, including things such as: analog signals, analog coding, analog encryption.
Logic
Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness. For example, in most systems of logic Peirce’s law (((P→Q)→P)→P) is a theorem. For classical logic, it can be easily verified with a truth table. The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software. The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false.
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas.
Combinatorics
Combinatorics studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects – e.g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae.
Graph theory
Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. Graphs are one of the prime objects of study in discrete mathematics.
Number theory
Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing.
Algebraic structures
Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages.
