Everyone

Arvind Kumar

Ice Cream Sandwich

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

Discrete Mathematics

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