Subject Code & Name: MA25C14 – Discrete Mathematics
Regulation: R-2025
Semester: III (Third Semester)
Branch: B.E. Computer Science and Engineering (CSE) / B.Tech. Information Technology (IT) / B.Tech. Artificial Intelligence and Data Science (AI&DS) / B.Tech. Computer Science and Business Systems (CSBS) / B.E. Computer and Communication Engineering (CCE) / B.E. Computer Science and Engineering (Data Science) (CSE(DS)) / B.E. Computer Science and Engineering (Internet of Things) (CSE(IoT)) / B.E. Computer Science and Engineering (Cyber Security) (CSE(Cyber)) / B.E. Computer Science and Engineering (Artificial Intelligence and Machine Learning) (CSE(AI&ML))
Credits / L-T-P: 4 Credits | L-T-P: 3-1-0
Course Objectives
- To introduce foundational concepts of set theory, relations, functions, and recurrence relations relevant to modeling data and algorithmic structures.
- To explain principles of propositional and predicate logic, Boolean algebra, and lattice theory for reasoning and decision-making in AI systems.
- To present core ideas of graph theory and its applications to analyze and optimize networks, data structures, and intelligent systems.
Full Unit-wise Syllabus
Unit I – Set Theory, Relations and Functions
Set theory – inductive definition of sets and proof by induction – Peano postulates – Relations – equivalence relations and partitions. Functions – Type of functions: Injective, surjective and bijective functions – Composition of functions – Inverse functions – Permutation functions – Recurrence relations – Solving linear recurrence relations.
Activities: Create and present Venn diagrams to illustrate union, intersection. Categorize real-world mappings such as student-to-email ID, username-to-password, as injective, surjective, or bijective using role-play or sorting tasks.
Unit II – Logic
Propositions – Logical operators – Normal forms – Rules of inference – Consistency and inconsistency – Propositional logic – Proofs – Predicates – Quantifiers – Universe of discourse – Logical equivalences and implications for quantified statements – Rules of specification and generalization – Validity of arguments.
Activities: Conduct a truth table building competition for compound propositions using logical operators.
Unit III – Boolean Algebra and Lattice Theory
Partial ordering – Posets – Lattices as Posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra – Sub Boolean Algebra – Boolean Homomorphism.
Activities: Draw Hasse diagrams for lattices from a given set and identify sublattices and lattice operations.
Unit IV – Graph Theory
Graphs – Types of graphs – Matrix representation of graphs – Graph isomorphism – Walk – Path – Cycles – Eulerian graphs – Hamiltonian graphs – Planar graphs – Euler formula – Shortest path algorithm: Dijkstra's algorithm.
Activities: Implement Dijkstra's algorithm to find the shortest path in a weighted AI decision graph.
Course Outcomes (COs)
- CO1: Understand the concepts of sets, Functions, Recurrence Relations, Logic, Boolean algebra and graph theory.
- CO2: Apply principles of logic, functions, Boolean algebra, lattices, recurrence relations, and graph theory to solve real world engineering problems.
- CO3: Employ discrete mathematical structures such as relations, recurrence relations, logical statements, lattices and graphs to analyze engineering problems.
- CO4: Model engineering problems and provide discrete mathematics based solutions.
Assessment Pattern (Quick Note)
- Weightage: Continuous Assessment 40% | End Semester Examinations 60%
- Internal methodology: Assignments (20%), Solution to application-oriented problems using software (20%), Solving Competitive Examination questions (20%), Internal Examinations (40%)
Source: Official Anna University – B.E. Computer Science and Engineering R-2025 Syllabus
Last Updated: September 2026
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