Logic: Logic- Prepositional – Predicates and Quantifiers. Sets – Functions – Counting: Basics of Counting- The Pigeonhole Principle- Inclusion-Exclusion Principle, Permutations and Combinations. Relations: Relations and their Properties- Representing Relations- Closure of Relations- Equivalence and partial order Relations.

Matrices: Linear Systems of Equations- Rank of a Matrix- Linear dependence. Solutions of Linear Systems: Existence- Uniqueness- General Form- Eigen values- Eigen vectors- Symmetric- Skew-Symmetric and Orthogonal Matrices. Complex Matrices: Hermitian- Skew Hermitian- Unitary- Similarity of Matrices (Definition and Examples only)-Diagonalization.

Introduction to Vector Space – Subspaces, Linear Independence, Basis and Dimension Graph Theory: Definition, walk, path, trails, connected graphs, regular and bipartite graphs, cycle and circuits. Tree and rooted tree. Spanning trees – Eccentricity of a vertex radius and diameter of a graph. Central graphs – Centre (s) of a tree. Hamiltonian and Eulerian graph, planar graphs Groups: Finite fields and Error correcting/detecting codes

1. Rosen K. H., “Discrete Mathematics and its Applications”, Seventh Edition, Tata McGraw-Hill, New Delhi, 2007.
2. Grimaldi R. P., “Discrete and Combinatorial Mathematics”, Fifth Edition, Pearson Education Asia, New Delhi, 2008.
3. E Kreyszig, “Advanced Engineering Mathematics”, Tenth Edition, John Wiley and Sons, 2010. 4. Carl D. Meyer, “Matrix Analysis and Applied Linear Algebra, SIAM, 2000.