PBS
A Breakthrough in Higher Dimensional Spheres
Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed...
PBS
What are Numbers Made of?
In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of?
PBS
Topology Riddles | Infinite Series
Can you turn your pants inside out without taking your feet off the ground?
3Blue1Brown
Why is pi here? And why is it squared? A geometric answer to the Basel problem
A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.
TED Talks
John Green: The nerd's guide to learning everything online
Some of us learn best in the classroom, and some of us ... well, we don't. But we still love to learn -- we just need to find the way that works for us. In this charming, personal talk, author John Green shares the community of learning...
PBS
Singularities Explained
Mathematician Kelsey Houston-Edwards explains exactly what singularities are and how they exist right under our noses.
PBS
Building an Infinite Bridge
Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009.
PBS
Splitting Rent with Triangles
You can find out how to fairly divide rent between three different people even when you don't know the third person's preferences! Find out how with Sperner's Lemma.
PBS
How Infinity Explains the Finite
Peano arithmetic proves many theories in mathematics but does have its limits. In order to prove certain things you have to step beyond these axioms. Sometimes you need infinity.
TED-Ed
TED-Ed: What is Zeno's Dichotomy Paradox? - Colm Kelleher
Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy...
Catalyst University
Series | Introduction, Notation, Convergence & Divergence
Series | Introduction, Notation, Convergence & Divergence
Brian McLogan
What is a factorial
👉 Learn all about factorials. Factorials are the multiplication of a number in descending integer values back to one. Factorials are used often in sequences, series, permutations, and combinations. Factorial quotient expressions are...
Brian McLogan
Finding the formula of alternating signs of a sequence
👉 Learn how to write the rule of a sequence given a sequence of numbers. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. To write the explicit formula of...
Brian McLogan
How to determine the sum of a infinite geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by...
Brian McLogan
Simplifying a factorial divided by another factorial
👉 Learn all about factorials. Factorials are the multiplication of a number in descending integer values back to one. Factorials are used often in sequences, series, permutations, and combinations. Factorial quotient expressions are...
Brian McLogan
Evaluating a rational expression with factorials
👉 Learn all about factorials. Factorials are the multiplication of a number in descending integer values back to one. Factorials are used often in sequences, series, permutations, and combinations. Factorial quotient expressions are...
Brian McLogan
Learn to find the partial sum of a geometric sequence
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by...
Brian McLogan
Find the partial sum of the geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by...
Brian McLogan
Learn how to find the sum of an arithmetic series
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic...
Brian McLogan
Evaluating the partial sum of a arithmetic series
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic...
Brian McLogan
Finding the sum or an arithmetic series using summation notation
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic...