Oxford Online Maths Club
Oxford Online Maths Club
Welcome to the club! The Oxford Online Maths Club is a weekly livestream from the University of Oxford with maths problems, puzzles, mini-lectures, and Q&A. It’s free, interactive, casual, and relaxed, and the livestreams are recorded so that you can watch back afterwards if you can't make it to the live broadcast on Thursday afternoons. The club is mostly aimed at people about to apply to university or about to start a Maths course, but everyone's welcome and there's no registration needed. Whether you’re the only person you know who’s interested in mathematics, or if you’re an entire sixth-form maths club looking for more maths content, we’re here for you.
Our regular host is Dr James Munro (admissions and outreach coordinator for Maths at Oxford), and we often have current Oxford students answering questions in chat and appearing on the livestream to talk about maths. In some of the episodes we tackle tricky maths problems, in some of them we explore one maths topic in more detail, and in some of them we have a current Oxford student or member of staff on the livestream to talk about a bit of maths they love.
(Almost) every episode comes with some further reading notes for you to explore the topics we cover in the livestream in more depth. If you're looking for super-curricular mathematics (perhaps you're looking for an EPQ topic, or you're trying to explore maths beyond the classroom before applying to university), then this should be a good place to start. Click on "Further Reading" under any episode on this page to see these notes.
Next Livestream
The Oxford Online Maths Club is expected to return for new episodes in January 2024. Until then, there are more than 70 recordings below, and you're welcome to join us for the MAT Livestream.
Contact us
If you’d like to ask us anything about anything we've covered on OOMC, send an email to oomc [at] maths.ox.ac.uk.
We'd love your suggestions for Maths topics, or feedback or comments on the livestream, which you can also send to the email address above.
Here's what some anonymous participants have said about the club;
"Thank you for being a constant and giving me a way to enjoy maths without having to leave the house or having to feel bad if I miss it. I honestly love this" - Anonymous participant
"Thank you! I'm both confused and more interested." - Anonymous participant
"How does that make any sense :D" - Anonymous participant
Previous Episodes
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
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.
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.
Quick Maths
On this episode, we look at some techniques for evaluating square roots quickly.
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.
Sums of Squares
On this episode, we're revisiting a classic livestream on the sums of two squares.
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!
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.
Season 5
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...
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.
Counting Cubes
In this episode, James tries to count all the cubes with faces painted red or green or blue, using two different methods.
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.
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.
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.
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.
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.
Infinity with Zakkai
This week on the livestream, current student Zakkai is here to talk about infinity and history of mathematics.
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.
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.
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!
Pascal's Triangle
What's your favourite triangle? This episode introduces patterns in Pascal's triangles, with a detour to look at cellular automata.
Season 4
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.
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.
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.
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!
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.
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.
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...).
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.
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.
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.
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!
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.
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.
Season 3
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.
Hanging Chains
Ioana shows us how to find a differential equation for a hanging chain, and solve it too!
Bridges & Tea Cups
Changing Parameters
What's a good way to describe the points inside a circle? What about ellipses? In this slightly unusual livestream, James investigates.
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.
Snakes & Ladders with Jacques
Jacques has been simulating Snakes and Ladders with Python, and comparing the results with theoretical Snakes and Ladders speedrunning strategies.
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!
Inequalities with Ittihad
Ittihad introduces inequalities, from AM-GM to the Power Mean Inequality.
Tricks with Metrics with Immy
Immy defines distance and shows us some other weird metrics that satisfy that definition.
Double Integration with Lucy
Lucy joins the livestream to demonstrate something she's learning at university; Double Integration.
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.
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?
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.
Season 2
A few more things
In the last episode of Season 2, there are just a few more things to cover...
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.
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.
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?
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.
Chaotic Viruses with Francesca
In this episode, Francesca describes the mathematics of competing virus strains, with chaotic consequences.
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
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.
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.
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.
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.
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.
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?
Season 1
More Curve Sketching with Deepak
Season 1 wrap-up
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James, Deepak, Flora, Francesca, and Ittihad met up again to discuss Season 1 of the Oxford Online Maths Club. |
Integration with David
In episode 12, David introduces integration by substitution, and James sets him a challenging unseen problem.
Olympiad Problems with Ittihad
In episode 11, Ittihad shows us a variety of cute olympiad-style problems!
Topology with Flora
In episode 10, Flora shows us a trick with a Möbius strip that you can try at home.
Primes and Triangles
In episode 9, James proves Wilson's Theorem and does some tricks with a triangle.
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.
The Chain Rule
In episode 7, James describes the chain rule for differentiation, including a higher-dimensional version.
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.
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.
Pigeons with Christian
In episode 4, all the problems involve pigeons. James is joined by current student Christian to explain.
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.
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.
Cubes and other shapes
In episode 1, we talk about shapes and about watching YouTube videos quickly, and answer some of your questions.
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.
More links
The STEP support programme is a great set of maths resources, even if you're not going to take the STEP exams. Start here and then work through these; if they're too easy for you, then try these or eventually these. Dr Stephen Siklos's book Advanced Problems in Mathematics: Preparing for University is great, and free.
NRICH has lots of maths problems, investigations, games, and activities.
The Maths department at Oxford has written practice problems and material to help with bridging the gap, which some colleges send out to students to look at over the summer before starting the Oxford maths degree. The Bridging the Gap material has been expanded into the book "Towards Higher Mathematics: A Companion" by Dr Richard Earl.
The maths departmental prospectus has more information about the Oxford maths and joint honours degrees.
Full details of the courses currently offered as part of the Maths degree are available here. Please note that the courses offered may change year-on-year, and course details may change. Links to courses in specific years of the Maths degree;
Note that the courses are sorted by term (Michaelmas, Hilary, and Trinity are Oxford's names for the three terms).
University College at Oxford has compiled a list of other resources, Staircase 12.
Parallel Circles
You might be interested in another Maths livestream hosted by Kyle D Evans with bestselling science author Simon Singh and Countdown champion Junaid Mubeen.
They stream on Mondays at Parallel Circles.