Chapter 1: Mathematical Logic & Propositions
Propositions, logical connectives, truth tables, logical equivalence, tautologies, contradictions and valid arguments.
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UNIVERSITY MATHEMATICS · ORIGINAL COURSE RESOURCE
Discrete Mathematics
Complete Course Notes · Solved Exercises · Concepts & Applications
Structured university notes for AD/ADP, BS Mathematics, BSCS, BSIT, Software Engineering and related programmes.
COMPLETE LEARNING JOURNEY
Logic, proof, structures, counting and computation
This complete resource develops the reasoning tools used throughout mathematics, computer science and software engineering. Each chapter connects definitions with methods, examples and problem-solving practice.
CHAPTER-BY-CHAPTER CONTENT
Complete 20-chapter syllabus
Use the chapter list to move directly to the topic you need.
Chapter 2: Predicate Logic, Quantifiers & Rules of Inference
Predicates, universal and existential quantifiers, nested quantifiers, free and bound variables, inference rules and validity.
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Chapter 3: Mathematical Reasoning & Methods of Proof
Direct proof, contrapositive, contradiction, counterexamples, cases, existence and uniqueness proofs.
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Chapter 4: Set Theory, Cardinality & Countability
Set operations, power sets, Cartesian products, partitions, cardinality, countable and uncountable sets.
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Chapter 5: Relations, Equivalence Relations, Partial Orders & Lattices
Properties of relations, closures, equivalence classes, posets, Hasse diagrams, lattices and Boolean lattices.
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Chapter 6: Functions, Sequences, Summations & Discrete Structures
Injective, surjective and bijective functions, inverse functions, sequences, sums and structural representation.
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Chapter 7: Mathematical Induction, Strong Induction & Recursion
Ordinary and strong induction, recursive definitions, structural induction and recursive algorithms.
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Chapter 8: Algorithms, Correctness & Computational Complexity
Algorithm specification, pseudocode, loop invariants, correctness, efficiency, growth rates and Big-O analysis.
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Chapter 9: Number Theory & Modular Arithmetic
Divisibility, primes, greatest common divisors, Euclidean algorithm, congruences, inverses and applications.
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Chapter 10: Counting Principles, Permutations & Combinations
Product and sum rules, permutations, combinations, binomial coefficients, pigeonhole principle and inclusion-exclusion.
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Chapter 11: Advanced Combinatorics
Binomial identities, principle of inclusion-exclusion, distributions, arrangements and combinatorial arguments.
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Chapter 12: Recurrence Relations & Divide-and-Conquer
Linear recurrences, characteristic roots, iteration, substitution, recursion trees and divide-and-conquer analysis.
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Chapter 13: Generating Functions
Ordinary generating functions, coefficient extraction, recurrence solving and combinatorial applications.
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Chapter 14: Discrete Probability
Sample spaces, conditional probability, independence, Bayes' theorem, random variables, expectation and variance.
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Chapter 15: Graph Theory
Graphs and multigraphs, degree sequences, paths, cycles, connectivity, Euler and Hamilton concepts and planar graphs.
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Chapter 16: Graph Algorithms, Coloring, Matching & Network Optimization
Graph traversal, shortest paths, spanning trees, coloring, matching, flows and network optimization.
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Chapter 17: Trees, Traversals & Spanning Trees
Rooted and ordered trees, binary trees, traversals, expression trees, spanning trees and minimum spanning trees.
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Chapter 18: Boolean Algebra, Logic Gates & Circuit Minimization
Boolean identities, canonical forms, logic gates, switching circuits, Karnaugh maps and minimization.
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Chapter 19: Formal Languages, Automata & Models of Computation
Alphabets, strings, grammars, finite automata, regular languages, machines and computational models.
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Chapter 20: Advanced Topics in Discrete Mathematics
A connected review of discrete structures, algorithms, proof strategies and applications across mathematics and computing.
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