Discrete Mathematics Tutorial Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report 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. Recent Articles on Discrete Mathematics!Mathematical LogicLearn propositional and predicate logic, equivalences, proofs, and rules of inference for logical reasoning.Introduction to Propositional LogicApplications of Propositional LogicPropositional and Predicate LogicPropositional EquivalencesNormal and Principle FormsPredicates and QuantifiersNested Quantifiers TheoremRules of InferenceIntroduction to ProofsSets and RelationsUnderstand set theory, operations, relations, functions, and equivalence relations with real-world applications.Set TheoryTypes of SetsSet OperationsRough Set TheoryFunctionsSequence and SummationsRepresentations of Matrices and Graphs in RelationsTypes of RelationClosure of Relation and Equivalence RelationsMathematical InductionExplore counting techniques, permutations, combinations, generating functions, and probability concepts.Mathematical InductionBasics of CountingPascal's IdentityPigeonhole PrinciplePermutations and CombinationsGeneralized Permutations and CombinationsGenerating FunctionsInclusion-Exclusion PrincipleDiscrete Probability TheoryBoolean AlgebraStudy Boolean functions, algebraic theorems, properties, and methods for minimizing Boolean expressions.Boolean FunctionsBoolean Algebraic TheoremProperties of Boolean AlgebraNumber of Boolean FunctionsMinimization of Boolean FunctionsOptimizationLearn linear programming, simplex algorithm, and PERT for solving optimization problems.Linear Programming Graphical Solution For Linear ProgrammingSimplex AlgorithmPERT Ordered Sets & LatticesUnderstand partially ordered sets, Hasse diagrams, and lattice theory in mathematical structures.Partially Ordered SetsElements of POSETHasse DiagramsLatticesProbability TheoryDive into probability axioms, conditional probability, and common distributions like Poisson, normal, and exponential.Basic Concepts of ProbabilityProbability AxiomsProperties of ProbabilityConditional ProbabilityBayes' TheoremUniform DistributionExponential DistributionNormal DistributionPoisson DistributionGraph TheoryExplore graph types, algorithms (like Dijkstra’s and DFS), and applications in problem-solving and optimization.Introduction to GraphBasic Terminology of a GraphTypes of a GraphWalks, Trails, Paths, and CircuitsGraph Distance componentsCut-Vertices and Cut-EdgesBridge in GraphIndependent setsShortest Path Algorithms [Dijkstra's Algorithm]Application of Graph TheoryGraph Traversals[DFS]Graph Traversals[BFS]Characterizations of TreesPrim's Minimum Spanning Tree Kruskal's Minimum Spanning TreeHuffman Codes Tree TraversalsTraveling Salesman ProblemSpecial GraphStudy Eulerian and Hamiltonian graphs, including algorithms and problems like the Traveling Salesman Problem.Bipartite Graphs Independent Sets and CoveringEulerian graphsEulerian graphs- Fleury’s algorithmEulerian graphs- Chinese-Postman-Problem HamiltonMatchingLearn about matching in graphs, approximation algorithms, and optimization techniques.Matching- Basics, Perfect, BipartiteApproximation AlgorithmsVertex ColoringsExplore graph colorings, chromatic numbers, and algorithms like Greedy Coloring for graph theory.Chromatic Numbers, Greedy Coloring AlgorithmEdge ColoringVizing TheoremPlanar Graph- Basics, Planarity TestingDirected Graphs- Degree CentralityDirected Graphs- Weak ConnectivityDirected Graphs- Strong Components Directed Graphs- Eulerian, Hamilton Directed GraphsDirected Graphs- Tarjans' Algorithm To Find Strongly Connected ComponentHandshaking in Graph TheoremGroup TheoryUnderstand the basics of groups, subgroups, isomorphisms, and structures like rings and fields.Groups, Subgroups, Semi GroupsIsomorphism, HomomorphismAutomorphismRings, Integral domains, FieldsQuick LinksAccess last-minute notes and quizzes to reinforce your learning in discrete mathematics.Last-Minute Notes (LMNs)Quizzes on Discrete MathematicsConclusionThis 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. Comment More infoAdvertise with us Next Article Matrices A abhishek1 Follow Improve Article Tags : Computer Subject Engineering Mathematics Discrete Mathematics Similar Reads Engineering Mathematics Tutorials Engineering mathematics is a vital component of the engineering discipline, offering the analytical tools and techniques necessary for solving complex problems across various fields. Whether you're designing a bridge, optimizing a manufacturing process, or developing algorithms for computer systems, 3 min read Linear AlgebraMatricesMatrices are key concepts in mathematics, widely used in solving equations and problems in fields like physics and computer science. 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According to this theorem, the expression (a + b)n where a and b are any numbers and n is a non-negative integer. It can be expanded into the sum of terms involving powers of a and 15+ min read Finding nth term of any Polynomial SequenceGiven a few terms of a sequence, we are often asked to find the expression for the nth term of this sequence. While there is a multitude of ways to do this, In this article, we discuss an algorithmic approach which will give the correct answer for any polynomial expression. Note that this method fai 4 min read CalculusLimits, Continuity and DifferentiabilityLimits, Continuity, and Differentiation are fundamental concepts in calculus. 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Cauchy's Mean Value theorem is also called the Extended Mean Value Theorem or the Second Mean Value Theorem.According 7 min read Taylor SeriesA Taylor series represents a function as an infinite sum of terms, calculated from the values of its derivatives at a single point.Taylor series is a powerful mathematical tool used to approximate complex functions with an infinite sum of terms derived from the function's derivatives at a single poi 8 min read Inverse functions and composition of functionsInverse Functions - In mathematics a function, a, is said to be an inverse of another, b, if given the output of b a returns the input value given to b. Additionally, this must hold true for every element in the domain co-domain(range) of b. In other words, assuming x and y are constants, if b(x) = 3 min read Definite Integral | Definition, Formula & How to CalculateA definite integral is an integral that calculates a fixed value for the area under a curve between two specified limits. 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Relationship between Independent and dependent variab 6 min read Practice QuestionsLast Minute Notes - Engineering MathematicsGATE CSE is a national-level engineering entrance exam in India specifically for Computer Science and Engineering. It's conducted by top Indian institutions like IISc Bangalore and various IITs. In GATE CSE, engineering mathematics is a significant portion of the exam, typically constituting 15% of 15+ 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 h 4 min read Like