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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

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.

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

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The courses available here are completely online and, thus, offer the flexibility to one to complete the course within his/her time. The course duration mentioned in the course syllabus would be printed on the course certificate. However, the user can finish the course in lesser time as well.

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There are Multiple Choice Questions (MCQs) asked in the exam to complete the course. The number of questions varies for different courses.

The minimum passing marks percentage for each course is 50%. Only once the user passes the exam, he/she is eligible for the Certificate.

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Discrete Structure