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### What you'll get

• Govt. Verified Certification
• Job Credibility
• Certification Valid for Life

### Exam details

• Mode of Exam : Online
• Duration : 1 Hour
• Multiple Choice Questions are asked
• No. of Questions are asked : 50
• Passing Marks : 25 (50%)
• There is no negative marking

### Course Content

Total: 84 lectures
• Set Notation and Relations
• Basic Set Operations
• Cartesian Products and Power Sets
• Binary Representation of Positive Integers
• Summation Notation and Generalizations
• Basic Counting Techniques - The Rule of Products
• Permutations
• Partitions of Sets and the Law of Addition
• Combinations and the Binomial Theorem
• Propositions and Logical Operators
• Truth Tables and Propositions Generated by a Set
• Equivalence and Implication
• The Laws of Logic
• Mathematical Systems and Proofs
• Propositions over a Universe
• Mathematical Induction
• Quantifiers
• A Review of Methods of Proof
• Methods of Proof for Sets
• Laws of Set Theory
• Minsets
• The Duality Principle
• Basic Definitions and Operations
• Special Types of Matrices
• Laws of Matrix Algebra
• Matrix Oddities
• Basic Definitions
• Graphs of Relations on a Set
• Properties of Relations
• Matrices of Relations
• Closure Operations on Relations
• Definition and Notation
• Properties of Functions
• Function Composition
• The Many Faces of Recursion
• Sequences
• Recurrence Relations
• Some Common Recurrence Relations
• Generating Functions
• Graphs - General Introduction
• Data Structures for Graphs
• Connectivity
• Traversals: Eulerian and Hamiltonian Graphs
• Graph Optimization
• Planarity and Colorings
• What Is a Tree?
• Spanning Trees
• Rooted Trees
• Binary Trees
• Operations
• Algebraic Systems
• Some General Properties of Groups
• Greatest Common Divisors and the Integers Modulo n
• Subsystems
• Direct Products
• Isomorphisms
• Systems of Linear Equations
• Matrix Inversion
• An Introduction to Vector Spaces
• The Diagonalization Process
• Some Applications
• Linear Equations over the Integers Mod 2
• Posets Revisited
• Lattices
• Boolean Algebras
• Atoms of a Boolean Algebra
• Finite Boolean Algebras as n-tuples of 0’s and 1’s
• Boolean Expressions
• A Brief Introduction to Switching Theory and Logic Design
• Monoids
• Free Monoids and Languages
• Automata, Finite-State Machines
• The Monoid of a Finite-State Machine
• The Machine of a Monoid
• Cyclic Groups
• Cosets and Factor Groups
• Permutation Groups
• Normal Subgroups and Group Homomorphisms
• Coding Theory, Group Codes
• Rings, Basic Definitions and Concepts
• Fields
• Polynomial Rings
• Field Extensions
• Power Series

### Description

Discrete structure to discrete mathematics is a tool of computer science for logic and it also contains the basics theorems related to functions and sets. This is used in computer science for designing the application and program for the users. This is one of the vital terms that one needs to know who is interested in data science. The discrete mathematical structure course will help you to deal with complex puzzles that you will face in corporate life.

In this course, we have included the introduction to discrete structure from the basics and you will reach up to intermediate modules.

• You will learn how to think and write mathematically.
• The concepts are covered with real examples that will help you to learn effectively.
• You will understand De Morgan's law in logic and learn theories for better understanding.
• Also, in this program, you will have a complete understanding of using a variety of mathematical statements.
• The candidate will learn about trees, grammar, relations, and other functions in detail.

If you are a student or a candidate who belongs to a tech background, then you have an interest in mathematics. Then if you take admission in this course, this will build up your strong mathematical skills. By the end of the program you will be able to create real-world programs, also you will have critical problem-solving skills.

If you have an interest in data science or want to be a professional who belongs to this field, then this certificate course pushes you a lot. This course is suitable for data science and mathematics students who want to get enhanced knowledge.