Continued Fractions Courses and Certifications

Fibonacci Numbers and the Golden Ratio

251 reviews

In this course, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio.

• Coursera
• 9 hours 26 minutes
• On-Demand
• Free Online Course (Audit)

• Best of All Time

Hausdorff Center for Mathematics

Manfred Denker: Toral Automorphisms Driven by Continued Fractions

Explore toral automorphisms driven by continued fractions, discussing Poisson limits, homoclinic groups, and Steiner's theorem in dynamical systems and number theory.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Turn Angles, Continued Fractions and Approximate Geometry - WildTrig: Intro to Rational Trigonometry

Explore turn angles and continued fractions to approximate geometry, using the Euclidean algorithm for angles and circular arcs. Learn about the natural unit of angle and its applications.

• YouTube
• 32 minutes
• On-Demand
• Free Online Course

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
• On-Demand
• Free Online Course

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3

Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2

Explore connections between Rogers-Ramanujan identities and icosahedron, linking number theory, modular forms, combinatorics, and conformal field theory in an accessible survey for mathematicians.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Online Course

Mathologer

How Did Ramanujan Solve the Strand Puzzle?

Explore Ramanujan's genius through an infinite fraction puzzle, delving into continued fractions, Pell equations, and the Euclidean algorithm. Gain unique insights into mathematical concepts and problem-solving techniques.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

Mathologer

The Golden Ratio Spiral - Visual Infinite Descent

Explore number-associated spirals, infinite descent proofs, and continued fractions. Debunk golden ratio myths while gaining insights into number properties through visual representations.

• YouTube
• 22 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Teaching Connections Between Algebra and Geometry I - A MANSW Presentation

Exploring connections between algebra and geometry, covering topics like Euclidean algorithm, continued fractions, and projective geometry. Aims to revitalize interest in geometry as a core subject for students.

• YouTube
• 32 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including primes, perfect numbers, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Pell's equation.

• YouTube
• 25 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including squares, primes, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Archimedes' Cattle Problem.

• YouTube
• 42 minutes
• On-Demand
• Free Online Course

Introduction to Number Theory

Explore divisibility, primes, and algorithms in number theory. Learn modular arithmetic, continued fractions, and Diophantine equations. Develop problem-solving skills and gain insights into fundamental mathematical concepts.

• Coursera
• 12 weeks
• Finished
• Free Online Course (Audit)