Discrete Mathematics

ノート、クイズ、ブログや工学のコースのための離散数学の動画。

Notes,quiz,blog and videos of discrete mathematics for engineering courses . Mostly topics are covered with diagrams which make easy to learn.it almost cover all important topics which are given below

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