CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Set Theory

- Sets, Venn diagrams, Operations on Sets
- Laws of set theory, Power set and Products
- Partitions of sets, The Principle of Inclusion and Exclusion

200.00 Logic

- Propositions and logical operations, Truth tables
- Equivalence, Implications
- Laws of logic, Normal Forms
- Predicates and Quantifiers
- Mathematical Induction

300.00 Relations, Digraphs and Lattices

- Relations, Paths and Digraphs
- Properties and types of binary relations
- Manipulation of relations, Closures, Warshall’s algorithm
- Equivalence and partial ordered relations
- Posets and Hasse diagram
- Lattice

400.00 Functions and Pigeon Hole Principle

- Definition and types of functions:- Injective, Surjective and Bijective
- Composition, Identity and Inverse
- Pigeon-hole principle

500.00 Generating Functions and Recurrence Relations

- Series and Sequences
- Generating functions
- Recurrence relations
- Recursive Functions:- Applications of recurrence relations e,g, Factorial, Fibonacci, Binary search, Quick Sort etc.

600.00 Graphs and Subgraphs

- Definitions, Paths and circuits:- Eulerian and Hamiltonian
- Planer graphs, Graph coloring
- Isomorphism of graphs
- Subgraphs and Subgraph isomorphism

700.00 Trees

- Trees and weighted trees
- Spanning trees and minimum spanning tree
- Isomorphism of trees and sub trees
- Prefix codes

800.00 Algebraic Structures

- Algebraic structures with one binary operation:- semigroup, monoids and groups
- Product and quotient of algebraic structures
- Isomorphism, Homomorphism and Automorphism
- Cyclic groups, Normal subgroups
- Codes and group codes