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IT235 Discrete Structure

Discrete Structure notes

10 chapter notes, in syllabus order. Each starts with the key points.

Unit 1 · 6 hrs

Discrete Math Basics & Logic Gates: Propositions, Connectives & Truth TablesUnit 1 of Discrete Structure introduces the foundational concepts of discrete mathematics and logic, covering propositions, logical connectives, truth tables, and their applications in computing and problem-solving. This note explains how to construct and evaluate logical statements, analyze truth tables, and apply log15 min read

Unit 2 · 8 hrs

Sets, Relations, Functions & ProofsUnit 2 of Discrete Structure covers set theory (operations, power sets, Cartesian products), relations (equivalence, partial orders), functions (injective/surjective), and proof techniques (direct, contradiction, induction) with real-world applications in databases, networks, and algorithms.13 min read

Unit 3 · 6 hrs

Functions, Induction: Definitions, Proofs, and Real-World ModelsUnit 3 of Discrete Structure covers functions (types, properties, and inverses) and mathematical induction (principles, proofs, and applications), with visuals for injectivity, surjectivity, and recursive structures, plus real-world ties to eSewa transactions, Daraz order queues, and Ncell billing.11 min read

Unit 4 · 6 hrs

Counting Principles, Permutations, Combinations & Advanced TechniquesUnit 4 of Discrete Structure covers fundamental counting principles (addition, multiplication, inclusion-exclusion), permutations and combinations (with/without repetition), advanced combinatorial identities, and real-world applications in scheduling, probability, and algorithm design.7 min read

Unit 5 · 6 hrs

Sequences, Recurrence Relations & Binomial Theorem: Definitions, Solving, and ApplicationsUnit 5 of Discrete Structure covers arithmetic/geometric sequences, recurrence relations (linear homogeneous/non-homogeneous), characteristic equations, binomial theorem expansions, and combinatorial proofs—with real-world ties to loan amortization, algorithm analysis, and probability models.7 min read

Unit 6 · 8 hrs

Graph Theory Basics: Definitions, Models, Paths & ConnectivityUnit 6 of Discrete Structure introduces graphs as mathematical models of networks, covering vertices, edges, degrees, types (directed/undirected, weighted/unweighted), graph representations (adjacency matrix/list), and basic properties like paths, cycles, and connectivity—essential for analyzing real-world systems like13 min read

Unit 7 · 6 hrs

Graph Traversal, Trees & Applications: DFS, BFS, Trees, Spanning TreesUnit 7 of Discrete Structure covers graph traversal algorithms (DFS and BFS), tree structures (binary trees, spanning trees), their applications in real-world systems, and how to analyze and compare them for efficiency and use cases.10 min read

Unit 8 · 6 hrs

Sorting Algorithms & Complexity: Analysis, Comparison & Real-World ImpactUnit 8 of Discrete Structure covers fundamental sorting algorithms (Bubble, Selection, Insertion, Merge, Quick, Heap), their time/space complexity, and Big-O analysis—with real-world applications in Nepalese apps like eSewa, Daraz, and Ncell, plus exam-focused comparison tables and step-by-step traces.13 min read

Unit 9 · 4 hrs

Number Theory: Divisibility, Primes, Congruences & CryptographyUnit 9 of Discrete Structure covers divisibility rules, prime numbers, greatest common divisors (GCD), modular arithmetic, and applications in cryptography—essential for secure transactions, error detection, and algorithm design.8 min read

Unit 10 · 4 hrs

Graph Matching, Coloring, and Advanced PathsUnit 10 of Discrete Structure explores advanced graph theory concepts—matching (perfect, maximum), graph coloring (chromatic number, greedy algorithms), and advanced path problems (Eulerian/Hamiltonian cycles)—with real-world applications in scheduling, network design, and optimization.9 min read