Modular Arithmetic Courses and Certifications

Michael Penn

Quadratic Reciprocity Proof - Number Theory

A focused proof of quadratic reciprocity using Legendre symbols, an example, the Gauss Limit, and rewritten sets.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Michael Penn

Applications of Primitive Roots - Number Theory

Explores applications of primitive roots in number theory.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Michael Penn

More About Primitive Roots - Number Theory

A focused lesson exploring primitive roots in number theory.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Michael Penn

Some Important Facts About Congruence Modulo N

A concise proof-based introduction to congruence modulo n, covering examples, arithmetic properties, and computation on the integers.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Michael Penn

Primitive Roots Modulo N and the Structure of U-N

Explores primitive roots modulo n and uses them to determine the structure of the group of units modulo n.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Cryptography and Hashing Fundamentals in Python and Java

1683 ratings at Udemy

Private and Public Key Cryptosystems, DES, AES, Cryptoanalysis, RSA, Elliptic Curve Cryptography and Hashing

• Udemy
• 15 hours 18 minutes
• Self-Paced
• Paid Course

Introduction to Linear Algebra

46 ratings at Coursera

Master vector and matrix arithmetic: dot and cross products, lines and planes, Gaussian elimination, determinants, eigenvalues and diagonalisation, with applications to Markov processes.

• Coursera
• 4 weeks, 9 hours a week
• Self-Paced
• Paid Course

EDUCBA

Python Cryptography: Analyze & Break Ciphers

Break classical ciphers in Python: use GCD and modular inverses to crack multiplicative and affine ciphers, and digraph, trigraph and word-pattern analysis on substitution ciphers.

• Coursera
• 3 weeks, 3 hours a week
• Self-Paced
• Paid Course

Introduction to number theory

5 ratings at OpenLearn

This free course, Introduction to number theory, is a branch of mathematics concerned with the properties of integers. Section 1 introduces Euclid’s algorithm, which is used to find the HCF of two ...

• OpenLearn
• 18 hours
• Self-Paced
• Free Certificate

IIT Bombay;  NPTEL

A Basic Course in Number Theory

A foundational tour of classical number theory, from primes and congruences to quadratic forms, continued fractions, and Brahmagupta–Pell equations.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Kunal Kushwaha

Maths for Data Structures & Algorithms

Explore number theory techniques used in programming, from prime sieves and factorization to modular arithmetic, GCD, LCM, and Newton’s square root method.

• YouTube
• 1 hour 55 minutes
• Self-Paced
• Free Video

CodeHelp - by Babbar

Basic Maths for DSA - Sieve - Modular Arithmetics - Euclid’s Algorithm

Learn to use prime sieves, Euclid’s algorithm, modular arithmetic, and fast exponentiation for data-structure and algorithm problem solving.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Michael Penn

Primitive Roots Modulo n

Explore the mathematical foundations of primitive roots modulo n, covering order calculations, existence theorems, and applications to solving exponential congruences.

• YouTube
• 2 hours 42 minutes
• Self-Paced
• Free Video

Number Theory

A compact introduction to classical number theory through prime-related theorems, the Euclidean algorithm, and Diophantine equations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Factoring Large Numbers into Primes - Famous Math Problems

Explore the challenge of factoring an enormous number into primes, using modular arithmetic to test whether 7 divides it.

• YouTube
• 42 minutes
• Self-Paced
• Free Video