CA5101-Mathematical Foundations of Computer Science |
MATRIX ALGEBRA |
Matrices – Rank of Matrix – Solving System of Equations – Eigen Values and Eigen
Vectors – Inverse of a Matrix – Cayley Hamilton Theorem |
BASIC SET |
Basic Definitions – Venn Diagrams and set operations – Laws of set theory – Principle
of Inclusion and Exclusion – Partitions – Permutation and Combination – Relations –
Properties of relations – Matrices of relations – Closure operations on relations –
Functions – Injective – Surjective and Bijective functions - Induction |
MATHEMATICAL LOGIC |
Propositions and logical operators – Truth table – Propositions generated by set –
Equivalence and Implication – Basic laws – Some more connectives – Functionally
complete set of connectives – Normal forms – Proofs in Propositional calculus –
Predicate calculus
|
GRAPHS AND TREES |
Graphs – Types of Graphs – Connectedness – Euler Graphs – Hamiltonian Graphs –
Trees - Undirected graphs – Directed graphs – Spanning trees – Algorithm for finding
shortest spanning trees.
|
LATTICES |
Partial order relation – Posets – Hasse diagram – Lattices – Special Lattices – Boolean
algebra. |
Text Books |
1. Trembley and Manohar R, “Discrete Mathematical Structures with Applications
to Computer Science”, Tata McGraw Hill, 2009. |
Reference Books |
1. Narasingh Deo, “Graph Theory with Applications to Engineering and computer
science”, Prentice Hall of India, New Delhi,2007.
2. Kenneth H.Rusen “Discreate Mathematics and its Applications”, Sixth Edition,
Tata McGraw Hill, 2007. |