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