Modular Arithmetic Courses and Certifications

IIT Bombay;  NPTEL

A Basic Course in Number Theory

Develop foundational knowledge in number theory, covering prime numbers, quadratic reciprocity, binary quadratic forms, and Diophantine equations. Gain skills for advanced study in the field.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Number Theory

Explore the powers of divisibility, modular arithmetic, and infinity.

• Brilliant
• 4 hours
• Self-Paced
• Paid Course

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

Numberphile

100000001 Is Divisible by 17

Discover why 100000001 is divisible by 17 through fascinating mathematical patterns and divisibility rules with Matt Parker's engaging exploration of number theory.

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

Mathologer

Secret of Row 10 - A New Visual Key to Ancient Pascalian Puzzles

Explore hidden patterns in Pascal's triangle and snail shells through a visual key, featuring Sierpinski's triangle and modular arithmetic in this fascinating mathematical journey.

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

Wrath of Math

Man Finds Wallet, Leaves Math Problem, Then Goes Viral - Analyzing the Security of a Birthdate-Based Phone Number Code

Explore how a viral wallet return story reveals fascinating insights into mathematical probability, cryptography, and the security of birthday-based codes.

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

Michael Penn

Infinitely Many Primes of the Form an+b - Number Theory

Explore advanced number theory concepts proving infinitely many primes exist in specific arithmetic progressions like 3n+1, 4n+1, and 4n+3 forms.

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

Insights into Mathematics

Factoring Large Numbers into Primes - Famous Math Problems

Explore prime factorization of large numbers, modular arithmetic, and theorems by Fermat and Euler. Learn techniques to tackle complex mathematical problems and improve number theory skills.

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

Insights into Mathematics

Number Theory and Algebra in Asia - Math History - NJ Wildberger

Explores number theory, algebra, and astronomy in ancient Chinese, Indian, and Arab mathematics, highlighting key figures and their contributions to mathematical development.

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

Institute for Advanced Study

Primes and Knots - Akshay Venkatesh

Explore surprising parallels between number theory and 3D geometry, uncovering connections that continue to shape mathematical research.

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

Michael Penn

Primitive Roots - Number Theory

Explore primitive roots in number theory, delving into advanced mathematical concepts and their applications in this comprehensive video lecture.

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

Michael Penn

The Order of an Integer Modulo N - Number Theory

Explore the concept of order for integers modulo n in number theory, covering key propositions, primitive roots, and proofs to deepen understanding of modular arithmetic.

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

Michael Penn

Chinese Remainder Theorem - Number Theory

Explore the Chinese Remainder Theorem, a fundamental concept in number theory, and its applications in solving systems of linear congruences.

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

Wrath of Math

A 1000-Year-Old Trick for Testing Divisibility by 37 Using Casting Out Nines

Discover an ancient mathematical technique for testing divisibility by 37 through casting out nines, exploring modular congruence and number theory concepts in a practical way.

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

Discover AI

Understanding Grokking - A New Performance Phase in Large Language Models

Discover how extended training of LLMs leads to "grokking" - a breakthrough phase where models develop superior generalization abilities and form geometric patterns in embedding spaces.

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