Discrete Mathematics is a branch of mathematics that is concerned with “discrete” mathematical structures instead of “continuous”. Discrete mathematical structures include objects with distinct values like graphs, integers, logic-based statements, etc. In this tutorial, we have covered all the topics of Discrete Mathematics for computer science like set theory , recurrence relations, group theory, and graph theory.
Discrete Mathematics deals with mathematical structures involving distinct values, such as graphs, integers, and logic-based statements. It’s essential for computer science and problem-solving1.
This Discrete Mathematics Tutorial and taken a giant leap towards mastering the fundamental concepts that will propel you to greatness in the world of software engineering and beyond. By applying the concepts learned in this tutorial to practice problems and real-world examples.
GeeksforGeeks Like Article -->Prerequisite - Solving Recurrences, Different types of recurrence relations and their solutions, Practice Set for Recurrence Relations The sequence which is defined by indicating a relation connecting its general term an with an-1, an-2, etc is called a recurrence relation for the sequence. Types of recurrence relations First order Recurrence relat
4 min read Elementary Matrices | Discrete MathematicsPrerequisite : Knowledge of Matrices & Identity Matrix Introduction :A matrix is a collection of numbers arranged in a row-by-row and column-by-column arrangement. The elements of a matrix must be enclosed in parenthesis or brackets.Example - The 3 * 3 matrix means a matrix with 3 rows & 3 columns with a total of 9 elements. (3*3 = 9) Ident
3 min read Discrete Mathematics - GATE CSE Previous Year QuestionsSolving GATE Previous Year's Questions (PYQs) not only clears the concepts but also helps to gain flexibility, speed, accuracy, and understanding of the level of questions generally asked in the GATE exam, and that eventually helps you to gain good marks in the examination. Previous Year Questions help a candidate practice and revise for GATE, whic
4 min read Functions in Discrete MathematicsFunctions are an important part of discrete mathematics. This article is all about functions, their types, and other details of functions. A function assigns exactly one element of a set to each element of the other set. Functions are the rules that assign one input to one output. The function can be represented as f: A ⇢ B. A is called the domain
9 min read Boolean Ring in Discrete MathematicsDiscrete mathematics is one of the subfields of mathematics that deals with discrete and separate elements using algebra and arithmetic. It is considered to be one of the fundamental branches of computer science and includes the studies of combinatorics, graphs, and logic. One of those concepts is the Boolean ring which is used in different practic
7 min read Discrete Mathematics | Representing RelationsPrerequisite - Introduction and types of Relations Relations are represented using ordered pairs, matrix and digraphs: Ordered Pairs - In this set of ordered pairs of x and y are used to represent relation. In this corresponding values of x and y are represented using parenthesis. Example: <(1, 1), (2, 4), (3, 9), (4, 16), (5, 25)>This represent sq
2 min read Types of Sets in Discrete MathematicsA set in discrete mathematics is a collection of distinct objects, considered as an object in its own right. Sets are fundamental objects in mathematics, used to define various concepts and structures. In this article, we will discuss Types of Sets in Discrete Structure or Discrete Mathematics. Also, we will cover the examples. Let's discuss one by
13 min read Peano Axioms | Number System | Discrete MathematicsThe set of natural numbers is axiomatically defined below. G. Peano, an Italian mathematician, and J. W. R. Dedekind, a German mathematician, are credited with these axioms. These axioms aim to prove the existence of one natural number before defining a function to create the remaining natural numbers, known as the successor function. Peano AxiomsA
12 min read Types of Proofs - Predicate Logic | Discrete MathematicsThe most basic form of logic is propositional logic. Propositions, which have no variables, are the only assertions that are considered. Because there are no variables in propositions, they are either always true or always false.Example - P: 2 + 4 = 5. (Always False) is a proposition.Q: y * 0 = 0. (Always true) is a proposition.The majority of math
14 min read Principal Ideal Domain (P.I.D.) | Discrete MathematicsAlgebraic Structure: A non-empty set G equipped with 1 or more binary operations is called an algebraic structure.Example - (N,+) where N is a set of natural numbers and(R, *) R is a set of real numbers. Here ' * ' specifies a multiplication operation.RING : An algebraic structure that sets the processing of two binary operations simultaneously is
11 min read Prime Numbers in Discrete MathematicsPrime numbers are the building blocks of integers, playing a crucial role in number theory and discrete mathematics. A prime number is defined as any integer greater than 1 that has no positive divisors other than 1 and itself. Understanding prime numbers is fundamental to various mathematical concepts and applications, including cryptography, codi
9 min read Discrete Mathematics - Applications of Propositional LogicA proposition is an assertion, statement, or declarative sentence that can either be true or false but not both. For example, the sentence "Ram went to school." can either be true or false, but the case of both happening is not possible. So we can say, the sentence "Ram went to school." is a proposition. But, the sentence "N is greater than 100" is
11 min read Hypergraph Representation | Discrete MathematicsA hypergraph is a graph in which hyperedges (generalized edges) can connect to a subset of vertices/nodes rather than two vertices/nodes.The edges (also known as hyperedges) of a hypergraph are arbitrary nonempty sets of vertices. A k-hypergraph has all such hyperedges connecting exactly k vertices; a normal graph is thus a 2-hypergraph (as one edg
7 min read PDNF and PCNF in Discrete MathematicsPDNF (Principal Disjunctive Normal Form)It stands for Principal Disjunctive Normal Form. It refers to the Sum of Products, i.e., SOP. For eg. : If P, Q, and R are the variables then (P. Q'. R) + (P' . Q . R) + (P . Q . R') is an example of an expression in PDNF. Here '+' i.e. sum is the main operator. You might be confused about whether there exist
4 min read Discrete Mathematics | Hasse DiagramsHasse Diagram A Hasse diagram is a graphical representation of the relation of elements of a partially ordered set (poset) with an implied upward orientation. A point is drawn for each element of the partially ordered set (poset) and joined with the line segment according to the following rules: If p<q in the poset, then the point correspondin
10 min read Four Color Theorem and Kuratowski’s Theorem in Discrete MathematicsThe Four Color Theorem and Kuratowski's Theorem are two fundamental results in discrete mathematics, specifically in the field of graph theory. Both theorems address the properties of planar graphs but from different perspectives. In this article, we will understand about Four Color Theorem and Kuratowski’s Theorem in Discrete Mathematics, their de
14 min read Arguments in Discrete MathematicsIntroduction to Arguments in Discrete MathematicsIn discrete mathematics, an argument refers to a sequence of statements or propositions intended to determine the validity of a particular conclusion. The study of arguments in this context is crucial because it forms the basis for logical reasoning, which is essential in areas like computer science,
10 min read Discrete Maths | Generating Functions-Introduction and PrerequisitesDiscrete Maths | Generating Functions-Introduction and PrerequisitesPrerequisite - Combinatorics Basics, Generalized PnC Set 1, Set 2 Definition: Generating functions are used to represent sequences efficiently by coding the terms of a sequence as coefficients of powers of a variable (say) [Tex]\big x [/Tex]in a formal power series. Now with the fo
5 min read Mathematics | Probability Distributions Set 2 (Exponential Distribution)The previous article covered the basics of Probability Distributions and talked about the Uniform Probability Distribution. This article covers the Exponential Probability Distribution which is also a Continuous distribution just like Uniform Distribution. Introduction - Suppose we are posed with the question- How much time do we need to wait befor
5 min read Mathematics | Unimodal functions and Bimodal functionsUnimodal Function : A function f(x) is said to be unimodal function if for some value m it is monotonically increasing for x≤m and monotonically decreasing for x≥m. For function f(x), maximum value is f(m) and there is no other local maximum. See figure (A) and (B): In figure (A), graph has only one maximum point and rest of the graph goes do
2 min read Mathematics | Indefinite IntegralsAntiderivative - Definition :A function ∅(x) is called the antiderivative (or an integral) of a function f(x) of ∅(x)' = f(x). Example : x4/4 is an antiderivative of x3 because (x4/4)' = x3. In general, if ∅(x) is antiderivative of a function f(x) and C is a constant.Then, ' = ∅(x) = f(x). Indefinite Integrals
4 min read Mathematics | Generating Functions - Set 2Prerequisite - Generating Functions-Introduction and Prerequisites In Set 1 we came to know basics about Generating Functions. Now we will discuss more details on Generating Functions and its applications. Exponential Generating Functions - Let [Tex]h_0, h_1, h_2, . h_n, . [/Tex]e a sequence. Then its exponential generating function,
3 min read Mathematics | Rings, Integral domains and FieldsPrerequisite - Mathematics | Algebraic Structure Ring - Let addition (+) and Multiplication (.) be two binary operations defined on a non empty set R. Then R is said to form a ring w.r.t addition (+) and multiplication (.) if the following conditions are satisfied: (R, +) is an abelian group ( i.e commutative group) (R, .) is a semigroup For any th
7 min read Mathematics | Renewal processes in probabilityA Renewal process is a general case of Poisson Process in which the inter-arrival time of the process or the time between failures does not necessarily follow the exponential distribution. A counting process N(t) that represents the total number of occurrences of an event in the time interval (0, t] is called a renewal process, if the time between
2 min read Definite Integral | MathematicsDefinite integrals are the extension after indefinite integrals, definite integrals have limits [a, b]. It gives the area of a curve bounded between given limits. [Tex]\int_^F(x)dx [/Tex], It denotes the area of curve F(x) bounded between a and b, where a is the lower limit and b is the upper limit. Note: If f is a continuous function defined
1 min read Application of Derivative - Maxima and Minima | MathematicsThe Concept of derivative can be used to find the maximum and minimum value of the given function. We know that information about and gradient or slope can be derived from the derivative of a function. We try to find a point which has zero gradients then locate maximum and minimum value near it. It is of use because it can be used to maximize profi
3 min read Mathematics | Problems On Permutations | Set 2Prerequisite - Permutation and Combination, Permutations | Set 1 Formula's Used : P(n, r) = n! / (n-r)! Example-1 : How many words can be formed from the letters of the word WONDER, such that these begin with W and end with R? Explanation : If we fix W in the beginning and R at the end, then the remaining 4 letters can be arranged in 4P4 ways. Thus
3 min read Gamma Distribution Model in MathematicsIntroduction : Suppose an event can occur several times within a given unit of time. When the total number of occurrences of the event is unknown, we can think of it as a random variable. Now, if this random variable X has gamma distribution, then its probability density function is given as follows. [Tex]f(x) = \frac<1> x^
2 min read Engineering Mathematics - GATE CSE Previous Year QuestionsSolving GATE Previous Year's Questions (PYQs) not only clears the concepts but also helps to gain flexibility, speed, accuracy, and understanding of the level of questions generally asked in the GATE exam, and that eventually helps you to gain good marks in the examination. Previous Year Questions help a candidate practice and revise for GATE, whic
4 min read Mathematics | Graph Theory Basics - Set 1A graph is a data structure that is defined by two components : A node or a vertex.An edge E or ordered pair is a connection between two nodes u,v that is identified by unique pair(u,v). The pair (u,v) is ordered because (u,v) is not same as (v,u) in case of directed graph.The edge may have a weight or is set to one in case of unweighted graph.Cons
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