Discrete Mathematics

It is designed swipe based for engineering student of all streams to learn discrete mathematics. It almost cover all important topics which are covered chapter wise. Chapter 1 Set Theory, Relation, Function, Theorem Proving Techniques 1. Set Theory 2. countable and uncountable sets 3. Venn Diagrams 4. proofs of some general identities on sets Relation in Venn Diagrams 5. types of relation 6. composition of relations 7. Equivalence relation 8. Partial ordering relation 9. one-to-one Function 10. into and onto function 11. Inverse Functions 12. Pigeonhole Principle Chapter 2 Algebraic Structures 1. Algebraic structures 2. Abelian group 3. Subgroups 4. cyclic group 5. Homomorphism and isomorphism of Groups 6. Rings and Fields Chapter 3 Propositional Logic 1. Proposition 2. Conditional Statements 3. Truth Tables of Compound Propositions 4. Logic and Bit Operations 5. PROPOSITIONAL EQUIVALENCES 6. Logical Equivalences 7. Constructing New Logical Equivalences 8. Predicates 9. Quantifiers 10. Infinite States and Infinite State Transitions 11. Finite state machines as language recognizers Chapter 4 Graph Theory 1. Introduction of graphs 2. Basic Terms of Graph Theory 3. Planer graphs 4. multigraph 5. isomorphic Graph 6. paths, cycles, trails, and circuits 7. Shortest paths 8. Eulerian and Hamiltonian paths and circuits 9. Graph coloring 10. chromatic number 11. Homomorphism and isomorphism of Groups Chapter 5 Posets, Hasse Diagram and Lattices 1. Posets, Hasse Diagram 2. ordered set 3. Hasse diagrams 4. isomorphic ordered set 5. well ordered set 6. properties of Lattices 7. bounded and complemented lattices 8. Combinatorics 9. Permutation and combination 10. Binomial Theorem 11. Introduction to Recurrence Relation and Recursive algorithms 12. Linear recurrence relations with constant coefficients 13. Homogeneous solutions