ITE3822 · SEM 6
Discrete Mathematics
Offline study guides — one per week, built from the lecture notes and lecture videos. Green bar = sections you marked as understood.
Exam practicePast papers with worked answersReal exam questions from previous years, fully solved, plus which topics come up most.
Week 01The Foundations — Predicate Logic, Quantifiers & Direct ProofsPredicates and propositional functions, compound expressions, ∀ / ∃ / ∃!, negating quantifiers, translating English into logic, and constructing direct proofs.
Week 02Sets & Set OperationsSet terminology and notation, the number systems, equality, subsets and proper subsets, disjoint sets, Venn diagrams, union, intersection, complement and difference, set laws, De Morgan's laws, and inclusion–exclusion.
Week 03FunctionsDefinition of a function, domain, codomain and range, finding domains, one-to-one (injective), onto (surjective) and bijective functions, inverses, and composition.
Week 04Sequences & SummationsSequence notation, geometric and arithmetic progressions, strings, finding formulas for sequences, Σ notation and its laws, the geometric series theorem, infinite series, double sums, and the standard closed forms.
Week 05MatricesMatrices to represent data, size, square and equal matrices, rows, columns and entries, addition, multiplication and its algorithm, non-commutativity, identity, powers, transpose, symmetric matrices, and zero–one matrices (join and meet).
Week 06Number Theory & CryptographyDivisibility and its theorem, the division algorithm (div and mod), congruence modulo m, congruence classes, primes and composites, the fundamental theorem of arithmetic, and Caesar's cipher.
Week 07Mathematical Induction & RecursionThe principle of mathematical induction (basis step, inductive step, inductive hypothesis), four fully worked proofs, the well-ordering property, and recursively defined sequences and functions (factorial, powers, sums, Fibonacci).
Week 08Counting — Product & Sum Rules, Permutations & CombinationsWhy counting matters, the product rule, the sum rule, inclusion–exclusion for counting, tree diagrams, combinations ⁿCᵣ, and permutations with and without repetition.
Week 09Relations & Their PropertiesBinary relations as subsets of A × B, arrow diagrams and tables, functions as relations, relations on a set, reflexive, symmetric and transitive properties, and equivalence relations.
Week 10n-ary Relations & Relational Databasesn-ary relations, domains and degree, the relational data model, records and fields, primary and composite keys, extension vs intension, and the selection, projection and join operators.
Week 11Graphs & Graph ModelsWhat a graph is, the Königsberg bridge problem, finite vs infinite graphs, the six graph types (simple, multigraph, pseudograph, simple directed, directed multigraph, mixed), and graph models for social, information, transport and tournament problems.
Week 12Trees & Applications of TreesCircuits and trees, forests, the unique-path theorem, rooted trees and family terminology, subtrees, ordered and binary trees, and binary search trees with the insertion algorithm.
Week 13Decision Trees, Tree Traversal & Spanning TreesDecision trees as maps of choices and outcomes (drawing, evaluating with expected values, pros and cons), preorder and postorder traversal of ordered rooted trees, and spanning trees with their use in IP multicasting.
★Mixed practice exam
20 random questions drawn from all 13 weeks (154 in the bank). Every attempt is a new mix — a good way to test whole-subject knowledge before the exam.