Math Is Fun Forum

EDIT: Now on Facebook and Twitter!

I recently made a YouTube channel, Learn Maths Free, with the aim of creating video lectures (much in the style of KhanAcademy) on a variety of topics mainly at high-school level and undergraduate level.

At the moment, I've started a new playlist called Geometry and Groups, a course that loosely follows the syllabus of UCL's course*, that seeks to explore the fascinating links between group theory and geometry, starting with the Platonic solids and hopefully culminating in a discussion of the modular group, PSL(2,Z). More specifically, in this playlist I'd like to explore:

-Symmetry groups of Platonic solids
-Spherical and hyperbolic geometry
-A complete classification of Mobius transformations
-Isometries of hyperbolic space
-Euclidean space and quaternions

In the future (mostly dependent on popularity), I'd like to make videos on a number of other subjects, such as, GCSE Maths, AS and A-level Maths, SAT prep, Topology, Number Theory, Partial Differential Equations, Group Theory, Linear Algebra, Calculus, Real and Complex Analysis, Elliptic Curves, Fluid Mechanics.

*Taught in 2014-2015.

Videos so far:

Logarithm of a Complex Number
Integration by Parts: Basic Examples
Integrating log(x)
Calculating Partial Derivatives
Introduction to Summation Notation
Introducing Complex Numbers
Adding/Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers
Complex Conjugates
Calculating Powers of i
The Argand Diagram
Rationalising the Denominator
Simplifying Surds/Radicals
Proving Trig Identities Using Double-Angle Formulae
Proving a Complex Number Identity
Multiply 2-digit Numbers in 10 SECONDS!
Contour Integration #1 - Integrating 1/(x^2 + 1)
Contour Integration #2 - Integrating x^2 / (x^4 + 1)
Contour Integration #3 - Integrating cos(x) / (x^2 + 1)
Contour Integration #4 - Integrating Over Different Contours
How to Add ANY Pair of Fractions
How to Subtract ANY Pair of Fractions
How to Multiply Fractions
How to Divide Fractions in Three EASY Steps
Applying the AM-GM Inequality
Simplifying Expressions 1 - Basic Expressions
Simplifying Expressions 2 - Expressions with Powers
Expanding Brackets 1
Expanding Brackets 2
Continued Fractions #1 - Introduction and Finite Continued Fractions
Continued Fractions #2 - Infinite Continued Fractions
Metric Spaces #1 - Introduction
Geometry and Groups #1 - Platonic Solids Introduction
Geometry and Groups #2 - Platonic Solids and Duality
Geometry and Groups #3 - Duality
Geometry and Groups #4 - Group Actions
Geometry and Groups #5 - Orbits
Geometry and Groups #6 - Stabilisers
Geometry and Groups #7 - Orbit-Stabiliser Theorem
Is f(z) = z^2 + 2z* holomorphic?
Is f(z) = Im(z) holomorphic?
An Integration by Substitution Problem

EDIT 2: For the past couple of weeks, the above links were not functional. They are now fixed, as of the 1st of October, 2015.