Other university all, Computer Engineering , Discrete Mathematics Syllabus

214441: Discrete Mathematics

Unit I Sets And Propositions 
Sets: Sets, Combinations of Sets, Venn Diagram, Finite and Infinite Sets, Countable Sets, Multisets,
Principle of Inclusion and Exclusion, Mathematical Induction.
Propositions: Propositions, Logical Connectives, Conditional and Bi-conditional Propositions, Logical
Equivalence, Validity of Arguments by using Truth Tables, Predicates and Quantifiers, Normal forms.
Applications of Sets and Propositions.

Unit II Combinatorics And Discrete Probability

Combinatorics: Rules of Sum and Product, Permutations, Combinations.
Discrete Probability: Discrete Probability, Conditional Probability, Bayes Theorem, Information and
Mutual Information, Applications of Combinatorics and Discrete Probability.

Unit III Graph Theory
Graphs: Basic Terminologies, Multi-Graphs, Weighted Graphs, Sub Graphs, Isomorphic graphs,
Complete Graphs, Regular Graphs, Bipartite Graphs, Operations on Graphs, Paths, Circuits, Hamiltonian
and Eulerian graphs, Travelling Salesman Problem, Factors of Graphs, Planar Graphs, Graph Colouring.
Trees: Tree Terminologies, Rooted Trees, Path Length in Rooted Trees, Prefix Codes, Spanning Trees,
Fundamental Cut Sets and Circuits, Max flow –Min Cut Theorem (Transport Network).
Applications of Graph Theory.

Unit IV Relations And Functions 
Relations: Properties of Binary Relations, Closure of Relations, Warshall’sAlgorithm, Equivalence
Relations, Partitions, Partial Ordering Relations, Lattices, Chains and Anti Chains.
Functions: Functions, Composition of Functions, Invertible Functions, Pigeonhole Principle, Discrete
Numeric Functions.
Recurrence Relations: Recurrence Relation, Linear Recurrence Relations with Constant Coefficients,
Total Solutions, Applications of Relations and Functions.

Unit V Introduction To Number Theory
Divisibility of Integers: Properties of Divisibility, Division Algorithm, Greatest Common Divisor GCD and its Properties, Euclidean Algorithm, Extended Euclidean Algorithm, Prime Factorization Theorem,
Congruence Relation, Modular Arithmetic, Euler Phi Function, Euler’s Theorem, Fermat's Little
Theorem, Additive and Multiplicative Inverses, Chinese Remainder Theorem.

Unit VI Algebraic Structures
Algebraic Structures: Introduction Semigroup, Monoid, Group, Abelian Group, Permutation Groups,
Cosets, Normal Subgroup, Codes and Group Codes, Ring, Integral Domain, Field.
Applications of Algebraic Structures.

Text Books:

1. C. L. Liu and D. P. Mohapatra, “Elements of Discrete Mathematics”, 4th Edition, McGraw-Hill
2. Kenneth H. Rosen, “Discrete Mathematics and its Applications”, & 7th edition, McGraw-Hill

Reference Books:

1. Bernard Kolman, Robert C. Busby, Sharon Cutler Ross, “Discrete mathematical structures”, 6th edition, Prentice Hall of India
2. Edgar G. Goodaire, Michael M. Parmenter, “Discrete Mathematics with Graph Theory”, 3rd Edition, Pearson Education
3. Tremblay J. S., “Discrete mathematical structures with application”, 3rdEdition, Tata McGraw Hill
4. Lipschutz Seymour, “Discrete mathematics”, 4th Edition, Tata McGraw-Hill
5. Johnsonbaugh Richard, “Discrete Mathematics”, 7th edition, Pearson
6. Biggs Norman L, “Discrete mathematics”, 6th edition, Oxford
7. David M. Burton, “Elementary Number Theory”, &7th Edition, McGraw-Hill