OOMC rewind

Previous Episodes

This page has past episodes of the Oxford Online Maths Club.

You can watch previous episodes and access all the further reading with the links below. There's no need to watch the episodes "in order"; choose one with a title that sounds interesting to you!

Season 6 (2023)

Summer Project Ideas

In this episode, lots of left-over ideas and bits and pieces that you might like to look into yourself over the summer.

Watch on YouTube

Further Reading

Probability for Counting

DPhil student Alex is a guest on the livestream in this episode to show us how to use probability to solve certain combinatorics (counting) problems.

Watch on YouTube

Further Reading

Quick Maths

On this episode, we look at some techniques for evaluating square roots quickly.

Watch on YouTube

Further Reading

Crate Labelling Problem

We've got three crates with three labels, but every label is on the wrong crate. In this episode we solve the problem and explore harder variants.

Watch on YouTube

Further Reading

Sums of Squares

On this episode, we're revisiting a classic livestream on the sums of two squares.

Watch on YouTube

Further Reading

Dicey Sums

Keep rolling a die and keep track of the running total. Are some numbers more likely to appear than others? We investigate in this episode of the maths club!

Watch on YouTube

Further Reading

Calkin-Wilf Tree

In this episode, James introduces the "tree of all fractions" and demonstrates what it's like to look up something in a mathematics research paper.

Watch on YouTube

Further Reading

Season 5 (2023)

Pascal (again!)

For our season finale, in this episode we're going all the way back to Pascal's triangle to complete some unfinished business...

Watch on YouTube

History with Zakkai

The history of maths is rich and complicated and on this episode, by popular demand, Zakkai is back on the livestream to tell some stories from across time.

Watch on YouTube

Counting Cubes

In this episode, James tries to count all the cubes with faces painted red or green or blue, using two different methods.

Watch on YouTube

Further Reading

Truchet Tiles with Mochan

Truchet tiles are small patterned tiles that create larger patterns when they're arranged together with random orientations. Mochan is on the livestream in this episode to explore how many patterns we can form.

Watch on YouTube

Further Reading

Quantum Zeno with Sijie

Zeno's paradox says that an arrow observed in flight has no motion. In classical physics, we can argue our way around this. But in the world of quantum mechanics, things are (even) weirder. Sijie joins us on this episode to explain.

Watch on YouTube

 

Graph Theory with Jonah

Jonah is back on the livestream to introduce graph theory, including a proof that the utilities problem can't be solved on a plane.

Watch on YouTube

Further Reading

Inversion with Rebekah

What does it mean to invert a point in a circle? What happens to lines and circles under inversion? Can we use this to solve geometry problems with lots of circles? Rebekah is here to answer all this and more.

Watch on YouTube

Further Reading

Surreal Numbers with Manna

In this episode; surreal numbers! They're made out of sets, they're recursive, they're really weird. Manna is on the livestream to show us how they work.

Watch on YouTube

Further Reading

Infinity with Zakkai

This week on the livestream, current student Zakkai is here to talk about infinity and history of mathematics.

Watch on YouTube

Pentagon Geometry

Pentagons are often overlooked because they don't tessellate nicely. In this episode we put that right by devoting a whole episode to the geometry of the pentagon.

Watch on YouTube

Further Reading

Powers & Patterns

What's the difference of two squares? What's the difference of the difference of two squares? Today we're looking for patterns in sequences, and patterns across different sequences.

Watch on YouTube

Further Reading

Symmetry & Asymmetry

An equilateral triangle with side length 1 fits inside a square box; what's the minimum possible side-length of the box? What's the best way to cover a disc with circles? We explore both problems in this episode!

Watch on YouTube

Further Reading

Pascal's Triangle

What's your favourite triangle? This episode introduces patterns in Pascal's triangles, with a detour to look at cellular automata.

Watch on YouTube

Season 4 (2022)

52 Problems

In this episode, we've got a pack of cards with maths facts or puzzles on every card. We talk about a few random cards before dropping the link where you can get all of them for free.

Watch on YouTube

Double Tangent

Can you find a line that's tangent to a given quartic in two different places? In this episode we give it a go. There's also a brief mention of a cool extension to the satellite-shadow problem from last week.

Watch on YouTube

Further Reading

Your Maths!

It's something different in this episode of the Oxford Online Maths Club; maths that you've shown us! We've recently met lots of people at open days and some of you showed us maths that you're interested in; here are some of the things people have told us about.

Watch on YouTube

Heads or Tails?

In this episode, the people in the live chat choose a sequence of three coin results; heads or tails, then James chooses a sequence. Which sequence will come up first? Let's find out!

Watch on YouTube

Curve Slideshow

This episode had serious tech issues - the audio is OK but the video is very laggy, and everything breaks after half an hour. Don't worry, it's back to normal next week! James tries to draw a curve using only straight lines.

Watch on YouTube

Spirals with Vectors

What happens if four dogs start at the corners of a square and each run towards the next dog around? In this episode, we try to find out with pencil and paper, and then with computer code, and then with vector calculus.

Watch on YouTube

Sums and Integrals

In this episode, we use integrals to approximate sums and deduce some facts about the harmonic sum (one plus one-half plus one-third plus...).

Watch on YouTube

River Crossings

In this episode, the cabbage problem. A farmer needs to get across a river with a sheep, a fox, and a cabbage; we solve the classic problem and chat about some variants.

Watch on YouTube

Hat Puzzles

Three people are wearing red or blue hats; they can see each others' hats and they have to work out the colour of their own hat. We find out how in this episode.

Watch on YouTube

Liars & Tigers

Two guards stand before two doors. One always tells the truth and the other always lies. In this episode, we work out how to get the guards to tell us which door has a tiger behind it.

Watch on YouTube

Further Reading

Birthday Paradox

What's the probability that two people from a group of $n$ people have the same birthday? In this episode, we find out!

Watch on YouTube

Further Reading

Lightbulb Switching

Another classic problem in this episode; we start with a thousand lightbulbs, all of which are off, and then people start switching them on and off. We'll solve the problem and discuss some variants.

Watch on YouTube

Further Reading

Domino Tilings

Can we cover an 8 by 8 square with 32 dominoes (2 by 1 rectangles)? Yes we can! What if we remove two corners? In this episode we solve this problem and some variants.

Watch on YouTube

Further Reading

Season 3 (2022)

Fluid Dynamics

What's the shape of water falling from a tap? We investigate in this episode. There's also time to revisit a problem with squares from a couple of weeks ago.

Watch on YouTube

Hanging Chains

Ioana shows us how to find a differential equation for a hanging chain, and solve it too!

Watch on YouTube

Bridges & Tea Cups

In this episode, James works on two problems from the NRICH website.

Watch on YouTube

Changing Parameters

What's a good way to describe the points inside a circle? What about ellipses? In this slightly unusual livestream, James investigates.

Watch on YouTube

Fourier Series

Max is on the livestream to explain what a Fourier series is, how to find one, and what to do with it once you've found it.

Watch on YouTube

Snakes & Ladders with Jacques

Jacques has been simulating Snakes and Ladders with Python, and comparing the results with theoretical Snakes and Ladders speedrunning strategies.

Watch on YouTube

Measure Theory with Flora

What does it mean to measure something? Which things can we measure? And which branch of mathematics is this? Flora is on the livestream to explain!

Watch on YouTube

Further Reading

Inequalities with Ittihad

Ittihad introduces inequalities, from AM-GM to the Power Mean Inequality.

Watch on YouTube

Further Reading

Tricks with Metrics with Immy

Immy defines distance and shows us some other weird metrics that satisfy that definition.

Watch on YouTube

Further Reading

Double Integration with Lucy

Lucy joins the livestream to demonstrate something she's learning at university; Double Integration.

Watch on YouTube

Further Reading

Groups, bosons, and monsters with Jonah

Jonah introduces group theory with symmetries of a square, and talks about the Higg's Boson and the Monster Group.

Watch on YouTube

Further Reading

Sums of squares

Dr Vicky Neale joins the stream for epsiode 1 with a problem for us; which numbers can be written as the sum of two squares?

Watch on YouTube

Further Reading

Platonic Solids

We're back for Season 3! In episode 0, we had a look at the Platonic solids, and tried to prove that there are exactly five, assuming something mysterious called Euler's formula.

Watch on YouTube

Further Reading

Season 2 (2021)

A few more things

In the last episode of Season 2, there are just a few more things to cover...

Watch on YouTube

Further Reading
 

Everything Wrong

In this episode, James gets everything wrong. On purpose maybe? We look at the number of ways to rearrange things without getting any in their original place, and there's an extension to sets of two with an incredible answer.

Watch on YouTube

Further Reading
 

Countability with James

In this episode, James defines what it means for a set to be countable, and proves that we can't describe most of the numbers.

Watch on YouTube

Further Reading

Interview Question with Tom

Dr Tom Crawford, the Oxford tutor behind the YouTube channel Tom Rocks Maths, presents an interview question that he used last year. Can the people watching live solve it?

Watch on YouTube

Further Reading
 

Dotty Maths

The dot product, dots for time derivatives, dots of dotted dotty vectors, dots on dominoes, and dots on dice. Has James finally gone completely dotty? Find out in this episode.

Watch on YouTube

Further Reading

Chaotic Viruses with Francesca

In this episode, Francesca describes the mathematics of competing virus strains, with chaotic consequences.

Watch on YouTube

Further Reading

Complex Integration

Have you ever thought about what might happen if we tried to combine complex numbers and integration? In this episode, we explore what that might involve! There's a surprising link between integration, complex numbers, and logarithms

Watch on YouTube

Further Reading
 

Geometry

In this episode, James explores a geometry problem with a complicated answer, and discovers an ancient formula along the way. There's also an arithmetic problem, and a geometry puzzle based on a band logo.

Watch on YouTube

Further Reading

Functions with Aditi

In this episode, Aditi introduces the fundamentals of differentiation and integration, as they're taught on a university Maths degree. We take a look at continuous and differentiable functions, and prove the fundamental theorem of calculus.

Watch on YouTube

Further Reading

Prime Time with Ittihad

Do you like prime numbers? Do you like complex numbers? We've got both! In this episode, Ittihad explains the theory behind Gaussian Primes, which is a theory of prime numbers which are also the complex numbers. We also prove a theorem about writing real primes as the sum of two squares.

Watch on YouTube

Further Reading

PDEs with Jonah

This week, first-year student Jonah joins us on the livestream to talk about some first-year maths; partial differential equations (PDEs). They're like normal differential equations, but with more variables, and with more directions we can take them.

Watch on YouTube

Further Reading

Penrose Tiles with Flora

Flora's back on the livestream with Penrose tiles! We'll show you why the Penrose tiling is special, how it's constructed, and why it works. There's also a bit where James and Flora try to remember the digits of pi, with mixed results.

Watch on YouTube

Further Reading

Number Theory with Vicky

We're back for season 2, kicking things off with some Number Theory with Dr Vicky Neale. Vicky has some numbers and some pictures of squares. Can you work out the relationship between the numbers and the squares?

Watch on YouTube

Further Reading

Season 1 (2021)

More Curve Sketching with Deepak

After Season 1, James and Deepak met up to do some more curve sketching!

Watch on YouTube

Season 1 wrap-up

James, Deepak, Flora, Francesca, and Ittihad met up again to discuss Season 1 of the Oxford Online Maths Club.

Watch on YouTube

Integration with David

In episode 12, David introduces integration by substitution, and James sets him a challenging unseen problem.

Watch on YouTube

Further Reading

Olympiad Problems with Ittihad

In episode 11, Ittihad shows us a variety of cute olympiad-style problems!

Watch on YouTube

Further Reading

Topology with Flora

In episode 10, Flora shows us a trick with a Möbius strip that you can try at home.

Watch on YouTube

Further Reading

Primes and Triangles

In episode 9, James proves Wilson's Theorem and does some tricks with a triangle.

Watch on YouTube

Further Reading

Epidemic Maths with Francesca

In episode 8, Francesca tells us about her research on mathematical modelling of epidemics. There's also time for James to do something cryptic with knots.

Watch on YouTube

Further Reading

The Chain Rule

In episode 7, James describes the chain rule for differentiation, including a higher-dimensional version.

Watch on YouTube

Further Reading

Testing times with Zheneng

In episode 6, Oxford DPhil student Zheneng joins us to explain hypothesis testing, and we finish some curve sketching from the previous episode.

Watch on YouTube

Further Reading

Fantastic Graphs with Deepak

In episode 5, Deepak presents Fantastic Graphs and Where to Find Them. We also revisit a pigeonhole principle question from episode 4.

Watch on YouTube

Further Reading

Pigeons with Christian

In episode 4, all the problems involve pigeons. James is joined by current student Christian to explain.

Watch on YouTube

Further Reading

Probability with Lauren

In episode 3, we look at as some probability with Lauren (3rd year, Maths & Stats), and we approximate some functions with James.

Watch on YouTube

Further Reading

Unseen MAT with David

In episode 2, we look at some unseen MAT questions with help from David (first-year student), before returning to the square problem from episode 0 and the cube problem from episode 1.

Watch on YouTube

Further Reading

Cubes and other shapes

In episode 1, we talk about shapes and about watching YouTube videos quickly, and answer some of your questions.

Watch on YouTube

Further Reading

Welcome to the club

In episode 0, we solve a problem with square numbers, learn about quadratic residues, and talk about an Oxford maths interview question about cubics.

Watch on YouTube

Further Reading

Please contact us with feedback and comments about this page. Last updated on 03 Jan 2024 16:32.