Module1
Mathematical Logic – Statements, connectives – Well formed formulas – Tautologoies – Equivalance of formulas – Duality law Tautological implications – Normal forms – the theory of inference for the statement – Calculus – validity, Consistency, Theorem proving – the predicate calculus – Inference Theory of the predicate calculus.
Mathematical Logic – Statements, connectives – Well formed formulas – Tautologoies – Equivalance of formulas – Duality law Tautological implications – Normal forms – the theory of inference for the statement – Calculus – validity, Consistency, Theorem proving – the predicate calculus – Inference Theory of the predicate calculus.
Module 2
Number Theory: Prime and Relatively prime numbers – Modular arithmetic – Fermat’s and Euler’s Theorems – Testing for Primability – Euclids Algorithm – Discrete Logarithms
Relations & Functions – Properties of binary relations – Equivalance relations and partitions – Functions and pigeon hole principle.
Number Theory: Prime and Relatively prime numbers – Modular arithmetic – Fermat’s and Euler’s Theorems – Testing for Primability – Euclids Algorithm – Discrete Logarithms
Relations & Functions – Properties of binary relations – Equivalance relations and partitions – Functions and pigeon hole principle.
Module 3
Algebraic systems – general properties – Lattices as a partially ordered set – some properties of lattices – lattices as algebraic systems – sub lattices – direct product – homomorphism – some special lattices.
Algebraic systems – general properties – Lattices as a partially ordered set – some properties of lattices – lattices as algebraic systems – sub lattices – direct product – homomorphism – some special lattices.
Module 4
Discrete Numeric Functions & generating Functions, Recurrence relations – Manipulations of Numeric functions – generating functions – Recurrence relations – Linear recurrence relations with constant coefficients – Homogeneous solutions – Particular solutions – Total solutions – solutions by the method of generating functions.
Discrete Numeric Functions & generating Functions, Recurrence relations – Manipulations of Numeric functions – generating functions – Recurrence relations – Linear recurrence relations with constant coefficients – Homogeneous solutions – Particular solutions – Total solutions – solutions by the method of generating functions.
Module 5
Graph Theory: Basic concept of graphs, subgraphs, connected graphs, Paths, Cycles, Multigraph and Weighted graph – Trees – spanning trees.
Graph Theory: Basic concept of graphs, subgraphs, connected graphs, Paths, Cycles, Multigraph and Weighted graph – Trees – spanning trees.
References
1. Elements of Discrete Mathematics – C.L.Lieu, McGraw Hill.
2. Discrete mathematical structures with applications to Computer Science – J.P. Trembly, R. Manohar, McGraw Hill.
3. Discrete Mathematics – Richard Johnsonbaugh, Pearson Education Asia
4. Discrete Mathematical Structures – Bernard Kolman, Robert C. Bushy, Sharon Cutler Ross, PHI
5. A first look at Graph Theory – John Clark & Derek Allan Holton, Allied Publishers
6. Cryptography and network security principles and practice – William Stallings, Pearson Education Asia
2. Discrete mathematical structures with applications to Computer Science – J.P. Trembly, R. Manohar, McGraw Hill.
3. Discrete Mathematics – Richard Johnsonbaugh, Pearson Education Asia
4. Discrete Mathematical Structures – Bernard Kolman, Robert C. Bushy, Sharon Cutler Ross, PHI
5. A first look at Graph Theory – John Clark & Derek Allan Holton, Allied Publishers
6. Cryptography and network security principles and practice – William Stallings, Pearson Education Asia
mg university b.tech syllabus s3 computer science engg S3