Geometry & Topology Courses and Certifications

An introduction to Point-Set-Topology Part - II

Advanced point-set topology through compactness, metrization, compactifications, function-space topologies, and ordinal-topology counterexamples.

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

The Geometry of Möbius Transformations

Explore the geometry of Möbius transformations, fundamental symmetries of the Riemann sphere, at the intersection of complex analysis and geometry.

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

Insights into Mathematics

Introduction to Topology in Mathematics History

1 rating

Trace how rational turn angles connect polyhedral curvature to the Euler characteristic, then explore surfaces and their classification.

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

The Royal Institution

How Geometry Created Modern Physics

A historical journey from Euclid’s axioms to non-Euclidean geometry shows how changing geometry reshaped our understanding of spacetime.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

3Blue1Brown

The Wallis Product for Pi - A Geometric Proof

A geometric proof of the Wallis product for π, with pointers to dominated convergence for a more rigorous treatment.

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

JL Mussi

5 Common Topology Traps to Avoid in 3D Modeling

Master essential topology principles and avoid 5 critical mistakes in 3D modeling to create professional-grade models across major software platforms like Maya, Blender, and Cinema 4D.

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

3Blue1Brown

The Cosmic Distance Ladder: How We Measure the Universe - Part 1

Explore the fascinating methods astronomers use to measure cosmic distances, from Earth to the solar system, featuring insights from mathematician Terence Tao and historical breakthroughs.

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

3Blue1Brown

The AI That Solved IMO Geometry Problems - How AlphaGeometry Combines Logic and Intuition

Discover how AlphaGeometry revolutionizes mathematical problem-solving by combining logical reasoning with AI intuition to tackle Olympic-level geometry challenges.

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

Wrath of Math

Exploring Finite Geometry: Are the Red Lines Parallel?

Explore the mathematics behind parallel red lines in finite geometries, examining a viral math meme and introducing projective and affine geometry concepts with proofs and visual explanations.

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

3Blue1Brown

Understanding Topology Through the Inscribed Rectangle Problem

Explore the fascinating world of topology through an elegant solution to the inscribed rectangle problem, featuring innovative animations and mathematical insights into geometric principles.

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

Insights into Mathematics

Universal Hyperbolic Geometry - A Projective and Algebraic Approach

A projective, algebraic approach to hyperbolic geometry builds distance and angle laws from quadrance and spread, without transcendental functions.

• YouTube
• 1 day 7 hours 7 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Differential Geometry - Complete Course with Classical Curves, Surfaces, and Curvature Theory

Explore how curvature connects algebraic and geometric views of curves and surfaces, from Frenet–Serret equations to Gauss’s Theorema Egregium.

• YouTube
• 1 day 1 hour 10 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symplectic Geometry and Classical Mechanics

Explores the connection between symplectic geometry and classical mechanics in a 21-lecture series.

• YouTube
• 1 day 4 hours 53 minutes
• Self-Paced
• Free Video

Eddie Woo

Introduction to Vectors

Discover vector fundamentals through ratio division, arithmetic operations, and geometric thinking with practical exam questions and worked examples.

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

3Blue1Brown

The Hairy Ball Theorem

An animated explanation of why a hairy sphere must have a point where its tangent field vanishes, with an intuitive proof built around orientation.

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