Modular Arithmetic Courses and Certifications

Michael Penn

A Nice Ramanujan Sum

Explore the fascinating properties and applications of Ramanujan sums in this engaging mathematical exploration with Michael Penn.

• YouTube
• 18 minutes
• On-Demand
• 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
• On-Demand
• Free Video

Wrath of Math

They Lied to You About the 3 Divisibility Rule

Uncover the hidden truth behind divisibility rules and learn how digit addition can work for any number, not just 3, using modular arithmetic principles.

• YouTube
• 19 minutes
• On-Demand
• 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
• On-Demand
• Free Video

Sending Secrets: Security and Cryptography in a Quantum World

Explore cryptography's evolution, from Caesar's cipher to quantum computing challenges. Learn about modern encryption, prime numbers, and the potential impact of quantum computers on cybersecurity.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Basic Group Theory - Lecture 11

Explore fundamental group theory concepts including group definitions, subgroups, cosets, and Lagrange's theorem, culminating in a proof of Fermat's little theorem.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Insights into Mathematics

Irreducibility and the Schoenemann-Eisenstein Criterion - Famous Math Problems 20

Explores irreducibility in cyclotomic polynomials, Gauss's lemma, and Schoenemann's criterion. Applies concepts to prime-indexed cyclotomic polynomials and establishes Eisenstein's criterion.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Insights into Mathematics

Reciprocals, Powers of 10, and Euler's Totient Function - Math Foundations 202

Explore decimal expansions of fractions, their connection to modular arithmetic, and Euler's totient function. Gain insights into repeated decimal cycles and their relationship with powers of 10 mod n.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Insights into Mathematics

Clock Mathematics and the 12-Tone Chromatic Scale - Connecting Music Theory and Mod 12 Arithmetic

Explores the connection between mathematics and music through the 12-tone chromatic scale, clock geometry, and mod 12 arithmetic, offering a fresh perspective on music theory and mathematical notation.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Michael Penn

Ramanujan's Famous Mod 5 Congruence - Number Theory

Explore Ramanujan's famous (mod 5) congruence in number theory, delving into its mathematical significance and applications. Gain insights into this intriguing concept through clear explanations and examples.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Michael Penn

A Completely Average Number Theory Contest Problem

Dive into solving a typical number theory competition problem with step-by-step mathematical reasoning and problem-solving techniques.

• YouTube
• 19 minutes
• On-Demand
• Free Video

Wrath of Math

The Quirky Divisibility Rules of Binary Numbers

Explore divisibility rules for binary numbers 0-10, understanding modular congruence and base-2 number system principles through clear mathematical explanations and examples.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Michael Penn

A Simple Trick to Prove an Equation Has No Integer Solutions - Live Example

Discover a clever mathematical technique to prove equations lack integer solutions through a practical demonstration in number theory.

• YouTube
• 11 minutes
• On-Demand
• Free Video

Michael Penn

A Nice Simple Number Theory Exercise

Explore a straightforward number theory problem through step-by-step mathematical reasoning and proof techniques in this focused exercise.

• YouTube
• 16 minutes
• On-Demand
• Free Video

Sending Secrets - Cryptography & Privacy in a Quantum World

Explore cryptography's evolution, from ancient methods to quantum challenges, and discover potential future-proof encryption techniques. No advanced math required.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video