Discrete Mathematics Notes PDF Free Download – Computer Science Engineering

Discrete Mathematics Notes: Discrete Mathematics Handwritten Notes PDF If you are looking for Discrete Mathematics handwritten notes PDF, then you have come to the right place. This is where you will find free and downloadable notes for the topic.

Discrete Mathematics handwritten notes PDF are incredibly important documents for the study of this subject. All the students who wish to pursue careers in programming and computer science must use the discrete mathematics handwritten notes PDF to their full advantage.

These Lecture Notes will help you in your exams by providing you with efficient notes and will also help ease some nervousness and anxiety that may arise from the need to do well in exams.

  • Discrete Mathematics reference books
  • Discrete Mathematics curriculum
  • List of Discrete Mathematics important questions
  • FAQs about Discrete Mathematics
  • Conclusion

Introduction to Discrete Mathematics Handwritten Lecture Notes PDF

Discrete Mathematics is an important subject in the fields of mathematics and computer science. It is differentiated from continuous mathematics, such that the numbers are starkly different from each other. They can be used to create various programs, algorithms and software, and is also used in the field of cryptography and for proving theorems.

Discrete structures in mathematics can be either finite or infinite, depending on its properties. Also, combinatorics or combinations, set theory, logic statements and graphs are all important components of discrete mathematics.

Here are some notes for Discrete Mathematics:

  • Discrete Mathematics Handwritten Notes PDF
  • Discrete Mathematics Handwritten Lecture Notes
  • Lecture Notes on Discrete Mathematical Structures
  • Notes for Discrete Mathematics – DMS
  • Discrete Mathematics Note PDF Download

BSc Computer Science Discrete Mathematics Handwritten Notes PDF – Free Download

Computer Science is the subject of study which incorporates discrete mathematics to the fullest. It is one of the most important subjects in Computer Science because Discrete Mathematics is what we use to formulate many components:

  • Algorithms
  • Programming languages
  • Various software
  • Set theory
  • Logical statements
  • Graph theory
  • Computability

Discrete Mathematics Reference Books

Reference books are some of the best tools to utilise for our studies because they have not only important questions and answers but also accurate notes to refer to when studying.

Discrete Mathematics reference books are of utmost importance to students, especially those who are pursuing computer science. The subject can be confusing, but discrete mathematics reference books take the confusion away by providing discrete mathematics handwritten notes as well as printed notes for the subject.

The following is a list of the best reference books available out there for the preparation of students for Discrete Mathematics studies.

  • Introduction to Counting & Probability by David Patrick
  • Intermediate Counting & Probability by David Patrick
  • Elements of Discrete Mathematics by C.L. Liu
  • Discrete Mathematics and Application by Kenneth Rosen
  • Concrete Mathematics by Ronald Graham, Donald Knuth and Oren Patashnik
  • Discrete Mathematical Structures with applications to Computer Science by J.P. Tremblay and R. Manohar
  • Graph Theory by Frank Harary
  •  The Art of Computer Programming (Vol. 1) by Donald Knuth
  • Combinatorial Problems and Exercises by Laszlo Lovasz
  • Discrete Combinatorial Mathematics Applied Introduction by Grimaldi
  • A Course in Combinatorics by van Lint and Wilson
  • An Invitation to Discrete Mathematics by Jiri Matousek & Jaroslav Nesetril
  • Introduction to Discrete Mathematics by S.V. Yablonsky
  • Discrete Mathematics with Applications by Susanna Epp

Discrete Mathematics Curriculum

The best way to do any kind of work is first to formulate a skeleton or a structure for the work you would like to do. This same concept carries over to when we have to study or prepare for an examination. It is best to create a structure of study before we start studying and to do this, it is important to know the Discrete Mathematics curriculum like the back of your hand.

The following is the unit-wise and topic-wise curriculum for the subject Discrete Mathematics.

Unit

Topics

Sets and Sequences: Data Models

  • Finite sets
  • Power sets
  • The cardinality of finite sets
  • Cartesian Product
  • Properties of sets
  • Vector implementation of sets

Describing Sets:  Logic & Proofs

  • Introduction to logic
  • Propositional logic
  • Truth tables
  • Deduction
  • Resolution
  • Predicates & Quantifiers
  • Infinite sets
  • Countable & Uncountable sets
  • Cantor’s diagonalisation
  • Mathematical Induction
    • Weak induction
    • Strong induction

Relational Structures on Sets: Relations & Graphs

  • Relations
  • Equivalence Relations
  • Functions
  • Bijection
  • Binary relations & Graphs
  • Basics of Trees
  • Posets & Lattices
  • Hasse Diagrams
  • Boolean Algebra

Sizes of Sets: Counting & Combinatorics

  • Counting
  • Sum & Product Rule
  • Principle of Inclusion Exclusion
  • Pigeon Hole Principle
  • Counting by Bijections
  • Double Counting
  • Linear Recurrence Relations – Methods of Solutions
  • Generating Functions
  • Permutations & counting

Structured Sets : Algebraic Structures

  • Structured sets with respect to binary operations
  • Groups
  • Semigroups
  • Monoids
  • Rings
  • Fields
  • Vector Spaces
  • Bases

List of Discrete Mathematics Important Questions

While studying, one of the most important parts of preparing to the best of our abilities is looking at the important questions for the subject. Similarly, when preparing for an exam for Discrete Mathematics, looking at Discrete Mathematics important questions is vital for the best level of preparation.

We understand how necessary it is to look at Discrete Mathematics important questions. Thus, for your benefit, we have listed down some Discrete Mathematics important questions for you to utilise to the maximum.

Graphical questions about the Euler path or Euler circuit

  1. Find the Euler path or an Euler circuit, if it exists, from the given graphs that follow.
  2. Establish an isomorphism between the 2 following graphs.

Proofs

  1. State and prove Lagrange’s theorem.
  2. State and prove Cayley’s representation theorem.
  3. State and prove the fundamental theorem of a group homomorphism.
  4. State and prove the isotonic property, distributive inequality and modular inequality.
  5. Prove that if a graph H has not more than two vertices of odd degree, then there can be an Euler path in G.
  6. State and prove De Morgan’s Laws in lattices and Boolean Algebra.
  7. In a distributive lattice, prove that the complement of an element, if it exists, is unique.
  8. In Boolean algebra, show that ab1+ a1b=0 if and only if a=b.
  9. Use mathematical induction to prove that n3+2n is divisible by 3 for all integers n1.
  10. State and prove the pigeonhole principle.
  11. State and prove the generalized pigeonhole principle.

FAQs about Discrete Mathematics Notes

Question 1.
What is Discrete Mathematics?

Answer:
Discrete Mathematics is a subject of study which is incredibly pertinent in the subject of Computer Science. Discrete Mathematics focuses on graphs, combinatorics, sets, logical statements, etc. It uses logical notions to mathematically define and reason with fundamental data types and structures that are used to formulate algorithms, systems, software, etc.

Question 2.
What are the best Discrete Mathematics reference books?

Answer:
There are various Discrete Mathematics reference books that students can refer to. The best books out of these which most students prefer to refer to are “Discrete Mathematics and Application” by Kenneth Rosen and “Concrete Mathematics” by Ronald Graham, Donald Knuth and Oren Patashnik.

Question 3.
What are the basic units which are studied in the Discrete Mathematics course?

Answer:
The basic units which are part of the Discrete Mathematics course are as follows:

  • Sets & Sequences : Data Models
  • Describing Sets: Logic & Proofs
  • Relational Structures on Sets: Relations & Graphs
  • Sizes of Sets: Counting & Combinatorics
  • Structured Sets: Algebraic Sets

Question 4.
What are some of the Discrete Mathematics important questions?

Answer:
There are various Discrete Mathematics important questions that pertain to graphical questions as well as questions where proofs are required. Here are some Discrete Mathematics important questions:

  1. State and prove Lagrange’s theorem.
  2. In a distributive lattice, prove that the complement of an element, if it exists, is unique.
  3. Establish an isomorphism between the 2 following graphs.
  4. State and prove the isotonic property, distributive inequality and modular inequality.

Other important questions about Discrete Mathematics have been listed above.

Conclusion

To conclude, we would like to let you know that the Discrete Mathematics Handwritten Notes PDF will be beneficial for you. They have been compiled with the utmost care for the student to do exceptionally well in their exams. It is always useful to have some extra help with studying, especially during the preparations for examinations. Hopefully, our provided Discrete Mathematics Handwritten Notes PDF have been helpful for you to learn. Do download them free of cost and utilise them in the best way possible.

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