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

</div> <div jsname="WJz9Hc" style="display:none">Ia direka sapu berasaskan untuk pelajar kejuruteraan semua aliran untuk belajar matematik diskret. Ia hampir meliputi semua topik penting yang dilindungi bab bijak.

Bab 1 Set Theory, Perhubungan, Fungsi, Teorem Membuktikan Teknik

1. Teori Set

2. set terbilangkan dan tak terbilangkan

3. Rajah Venn

4. bukti beberapa identiti umum pada set Perhubungan di Venn Diagram

5. jenis hubungan

6. komposisi hubungan

7. Kesetaraan berhubung

8. berhubung separa pesanan

9. satu-sama-satu Fungsi

10. ke dalam dan ke fungsi

11. songsang Fungsi

12. Pigeonhole Prinsip

Bab 2 algebra Struktur

1. struktur algebra

2. kumpulan Abelian

3. Subkumpulan

4. Kumpulan kitaran

5. homomorphism dan isomorfisma daripada Kumpulan

6. Cincin dan Fields

Bab 3 usulan Logik

1. Usul

2. Penyata Bersyarat

3. Jadual Kebenaran Usul Kompaun

4. Logik dan Bit Operasi

5. persamaan yang usulan

6. persamaan yang logik

7. Membina persamaan yang logik Baru

8. predikat

9. pengkuantiti

10. Infinite Syarikat dan Infinite Peralihan Negeri

11. Mesin negeri terhingga sebagai recognizers bahasa

Bab 4 Teori graf

1. Pengenalan graf

2. Terma-terma Asas Teori graf

3. graf Planer

4. multigraph

5. Graph isomorfik

6. laluan, kitaran, denai, dan litar

7. laluan Terpendek

8. Euler dan Hamiltonian laluan dan litar

Pewarna 9. Graph

10. bilangan kromatik

11. homomorphism dan isomorfisma daripada Kumpulan

Bab 5 Posets, Hasse Rajah dan kekisi

1. Posets, Hasse Rajah

2. mengarahkan menetapkan

3. gambar rajah Hasse

4. isomorfik mengarahkan menetapkan

5. juga mengarahkan menetapkan

6. sifat kekisi

7. kekisi disempadani dan dilengkapi

8. Kombinatorik

9. Pilihatur dan gabungan

10. Teorem binomial

11. Pengenalan kepada berulangnya Perhubungan dan Recursive algoritma

12. Linear hubungan jadi semula dengan pekali malar

13. penyelesaian yang seragam</div> <div class="show-more-end">