Number Theory / Modular Arithmetic

Engineering Mathematics Volume-1

What you'll learn
In this course all fundamentals and advance Concepts of Number Theory/Modular Arithmetic are covered..
The fundamental Concepts like, Calculation of GCD value, Euclidean algorithm, Extended Euclidean algorithm etc. are covered.
The advance Concepts like Diophantine Equation, Chinese Remainder, Euler's Theorem, Little Fermat's Theorem, Prime Factor, Legendre and Jacobi symbol, etc.
After Completion of this Course learner will be able to apply the core and fundamental concepts of number theory as per the need of application.
Requirements
No Prerequisite required, because all prerequisites are covered in lecture only.
Description
This contains all Fundamentals and Advance concepts of Number Theory/Modular Arithmetic.This Course is designed in such a way that anybody will understand no matter whether you are beginner or expert.To start this course, you don't require any prerequisites because all prerequisites are covered in course only.Here all course contents are organized in very systematic manner with clear crystal explanation.In this Course all types of problems are included which start from very basics to advanced.This Couse will be not only helpful to crack your university exam but also competitive exam like. GATE, NET, SET etc.To design this course inputs has been taken from experts who belong to reputed university professor, industrial expert, and university students.In this course we will cover, Euclidean Algorithm, Diophantine Equation, Inverse Modulus Calculation, Chinese Remainder Theorem, Modular Exponentiation, Little Fermat’s Theorem, Euler Theorem, Euler Totient Function, Prime Factor, Quadratic Residue, Legendre Symbol, and Jacobi Symbol.This Course is designed for those who belongs to Engineering Students, Mathematics Scholar, Research scholar from Information and Network security background.Engineering Vidya team ensure that you will like this course and after purchasing the course if you realize it doesn't full fill your requirements, so you can claim for refund as per policy of Udemy.

Overview

Section 1: Introduction

Lecture 1 Introduction to Modular arithmetic or Number Theory.

Lecture 2 Road Map of Modular Arithmetic or Number Theory

Section 2: Calculation of Modulus Value

Lecture 3 Modulus value Calculation from given Number part-1

Lecture 4 Modulus value Calculation from given Number Part-2

Section 3: Simplification of a ≡ b (mod m)

Lecture 5 Prerequisite Lecture ( How to Calculate divisor of any number).

Lecture 6 Simplification Procedure of a ≡ b (mod m)

Lecture 7 Examples on a ≡ b (mod m)

Section 4: Commutative Law and Associative Law of Modular Arithmetic

Lecture 8 Mathematical Description of Commutative law and Associative law.

Lecture 9 Examples on Commutative and Associative law

Section 5: Euclidean Algorithm

Lecture 10 Examples to Calculate GCD Using Euclidean Algorithm Part-1.

Lecture 11 Examples to Calculate GCD Using Euclidean Algorithm Part-2.

Section 6: Diophantine Equation

Lecture 12 Procedure to solve Diophantine Equation

Lecture 13 Examples on Diophantine Equation Part-1

Lecture 14 Examples on Diophantine Equation Part-2

Lecture 15 Examples on Diophantine Equation Part-3

Lecture 16 Examples on Diophantine Equation Part-4

Lecture 17 Examples on Diophantine Equation Part-5

Lecture 18 Examples on Diophantine Equation Part-6

Section 7: Inverse Modulus Calculation

Lecture 19 Procedure to Calculate Inverse Modulus

Lecture 20 Examples on Inverse Modulus Calculation Part-1.

Lecture 21 Examples on Inverse Modulus Calculation Part-2.

Lecture 22 Examples on Inverse Modulus Calculation Part-3.

Lecture 23 Examples on Inverse Modulus Calculation Part-4.

Lecture 24 Examples on Inverse Modulus Calculation Part-5.

Section 8: Linear Congruence ax ≡ b (mod m)

Lecture 25 Theorem and Classification of Linear Congruence ax ≡ b (mod m)

Lecture 26 Examples on Linear Congruence ax ≡ b (mod m) part-1.

Lecture 27 Examples on Linear Congruence ax ≡ b (mod m) part-2.

Lecture 28 Examples on Linear Congruence ax ≡ b (mod m) part-3.

Lecture 29 Examples on Linear Congruence ax ≡ b (mod m) part-4.

Lecture 30 Examples on Linear Congruence ax ≡ b (mod m) part-5.

Lecture 31 Examples on Linear Congruence ax ≡ b (mod m) part-6.

Lecture 32 Examples on Linear Congruence ax ≡ b (mod m) part-7.

Section 9: Chinese Remainder Theorem

Lecture 33 Introduction and Formula To Solve Chinese Remainder Theorem

Lecture 34 Procedure To Solve Chinese Remainder Theorem

Lecture 35 Examples on CRT part-1.

Lecture 36 Examples on CRT part-2.

Lecture 37 Examples on CRT part-3.

Lecture 38 Examples on CRT part-4.

Lecture 39 Examples on CRT part-5.

Lecture 40 Examples on CRT part-6.

Section 10: Modular Exponentiation using Distributive Law

Lecture 41 Mathematical Description of Distributive Law

Lecture 42 Examples of Modular Exponentiation using Distributive law part-1.

Lecture 43 Examples of Modular Exponentiation using Distributive law part-2.

Lecture 44 Examples of Modular Exponentiation using Distributive law part-3.

Lecture 45 Examples of Modular Exponentiation using Distributive law part-4.

Lecture 46 Examples of Modular Exponentiation using Distributive law part-5.

Section 11: Fermat's Little Theorem

Lecture 47 Fermat's Little Theorem Mathematical description.

Lecture 48 Examples on Fermat's Little Theorem Part-1.

Lecture 49 Examples on Fermat's Little Theorem Part-2.

Lecture 50 Examples on Fermat's Little Theorem Part-3.

Lecture 51 Examples on Fermat's Little Theorem Part-4.

Lecture 52 Examples on Fermat's Little Theorem Part-5.

Lecture 53 Examples on Fermat's Little Theorem Part-6.

Lecture 54 Examples on Fermat's Little Theorem Part-7.

Section 12: Euler Totient Function

Lecture 55 Relative Prime Number and Co-Prime Number

Lecture 56 Definition and Procedure To find Euler Totient Function

Lecture 57 Properties of Euler's Totient Function

Lecture 58 Examples on Euler's Totient Function

Section 13: Euler's Theorem

Lecture 59 Euler's Theorem Mathematical Description and Application.

Lecture 60 Examples on Euler's Theorem Part-1.

Lecture 61 Examples on Euler's Theorem Part-2.

Lecture 62 Examples on Euler's Theorem Part-3.

Lecture 63 Examples on Euler's Theorem Part-4.

Lecture 64 Linear Congruence ax ≡ b (mod m) Simplification Using Euler's Theorem.

Lecture 65 Examples on Linear Congruence Simplification Using Euler's Theorem Part-1.

Lecture 66 Examples on Linear Congruence Simplification Using Euler's Theorem Part-2.

Section 14: Prime Number

Lecture 67 Prime Number Generation and Eratosthenes Algorithm.

Lecture 68 Examples on Prime Number Generation.

Section 15: Prime Factor Calculation

Lecture 69 Prime Number and Composite Number

Lecture 70 Examples on Prime Factor Calculation Part-1.

Lecture 71 Examples on Prime Factor Calculation Part-2.

Section 16: Quadratic Residue

Lecture 72 Quadratic Residue Mathematical explanation

Lecture 73 Examples on Quadratic Residue

Section 17: Legendre Symbol and Jacobi Symbol

Lecture 74 Legendre Symbol Definition,Formula and Properties.

Lecture 75 Examples on Legendre symbol Part-1.

Lecture 76 Examples on Legendre symbol Part-2.

Lecture 77 Examples on Legendre symbol Part-3.

Lecture 78 Examples on Legendre symbol Part-4.

Lecture 79 Jacobi Symbol Definition and Algorithm.

Lecture 80 Jacobi Symbol Examples part-1.

Lecture 81 Jacobi Symbol Examples part-2.

Lecture 82 Jacobi Symbol Examples part-3.

Lecture 83 Jacobi Symbol Examples part-4.

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