Teddy Rocks Maths Essay Competition

Entries for the first ‘Teddy Rocks Maths’ Essay Competition are now open! This is YOUR chance to write a short article about your favourite mathematical topic which could win you a prize of up to £100. ENTER HERE: https://seh.ac/teddyrocksmaths

All entries will be showcased on tomrocksmaths.com with the winners published on the St Edmund Hall website. St Edmund Hall (or Teddy Hall as it is affectionately known) is a college at the University of Oxford where Tom is based.

Entries should be between 1000-2000 words and must be submitted as Microsoft Word documents or PDF files using the form at https://seh.ac/teddyrocksmaths

The closing date is 12 March 2020 and the winners will be announced in April 2020.

Two prizes of £50 are available for the overall winner and for the best essay from a student under the age of 18. There are no eligibility requirements – all you need is a passion for Maths and a flair for writing to participate!

The winners will be selected by Dr Tom Crawford, Maths Tutor at St Edmund Hall and the creator of the ‘Tom Rocks Maths’ outreach programme. The mathematical topic of your entry can be anything you choose, but if you’re struggling to come up with ideas here are a few examples to get you started:

Where does river water go when it enters the ocean? – Numberphile

Would alien geometry break our brains? – Tom Rocks Maths intern and maths undergraduate Joe Double

How many ping-pong balls would it take to raise the Titanic from the ocean floor?

If you have any questions or would like more information please get in touch with Tom using the contact form here – Good luck!!

January 29, 2020 0

Visiting Students at St Edmund Hall

Calling all US-based students, if you have ever thought you would like to have me as your college professor, now is your chance. I am currently in charge of the visiting student mathematics programme at St Edmund Hall, which means anyone accepted onto the programme will have weekly tutorials with yours truly. Information on the course specifics and how to apply can be found on the St Edmund Hall website here.

Courses available include (but are not limited to):

Michaelmas Term (Autumn)

Linear Algebra
Geometry
Real Analysis: Sequences and Series
Probability
Introductory Calculus
Differential Equations
Metric Spaces and Complex Analysis
Quantum Theory

Hilary Term (Winter)

Linear Algebra
Groups and Group Actions (continues next term)
Real Analysis: Continuity and Differentiability
Dynamics
Fourier Series and PDEs
Multivariable Calculus
Differential Equations
Numerical Analysis
Statistics
Fluid and Waves
Integral Transforms

Trinity Term (Spring)

Constructive Mathematics
Groups and Group Actions (continued)
Real Analysis: Integration
Statistics and Data Analysis
Calculus of Variations
Special Relativity
Mathematical Biology

The detailed course synopses, as well as some course materials can be found here.

If you have any questions please get in touch with Tom via the contact form, or the admissions office at St Edmund Hall via admissions@seh.ox.ac.uk.

Photo: Flemming, Heidelberg Laureate Forum

January 28, 2020 0

12 Days of Christmas Puzzles

Looking for some festive fun over the holiday season? Why not try your hand at my 12 Christmas puzzles…

Answers to all puzzles at the bottom of the page.

Puzzle 1: If I set a puzzle every day of the advent period (1-25 December) and spend 1 minute on the first puzzle, 2 minutes on the second, 3 minutes on the third, and so on, with the final one being 25 minutes on the 25^thpuzzle, what is the total amount of time I will spend writing puzzles?

Puzzle 2: December 6th marked my birthday and to celebrate I travelled to Kiev with 4 friends. If I order a drink on the flight out and then each of my friends orders twice as many as the person before, how many drinks do we order in total?

Puzzle 3: This morning I built a snowman using three spheres of radius 0.5m, 0.4m and 0.2m. However, the sun has since come out and the snowman is starting to melt at a rate of 0.01 m³ per minute. How long will it take for him to disappear completely?

Puzzle 4: Suppose a newly-born pair of elves, one male, one female, are living together at the North pole. Elves are able to mate at the age of one month so that at the end of its second month a female elf can produce another pair of offspring. Suppose that the elves never die, and that the female always produces one new pair (one male, one female) every month from the start of the third month on. After one year, how many pairs of elves will there be?

Puzzle 5: On Christmas day I have 11 people coming to dinner and so I’m working on the seating plan ahead of time. For a round table with exactly 12 chairs, how many different seating plans are possible?

Puzzle 6: My front yard is covered in snow and I need to clear a path connecting my front door to the pavement and then back to the garage. If each square in the diagram is 1m x 1m what is the shortest possible path?

Puzzle 7: The first night of Chanukah is December 22^nd when the first candle is lit. If it burns at a rate of 0.05cm per hour, how tall does the candle need to be to last the required 8 days?

Puzzle 8: If you have a square chimney which is 0.7m across, assuming Santa has a round belly what is the maximum waist size that can fit down the chimney?

Puzzle 9: On Christmas Eve Santa needs to visit each country around the world in 24 hours. Assuming time stands still whilst he is travelling, how long can he spend in each country?

Puzzle 10: I got carried away with buying presents this year and now have more than can fit into my stocking. If the stocking has a maximum capacity of 150, and my presents have the following sizes: 16, 27, 37, 65, 52, 42, 95, 59; what is the closest I can get to filling the stocking completely?

(NB: I am not looking for the highest number of presents that will fit, but the largest total that is less than or equal to 150).

Puzzle 11: Santa has 8 reindeer, and each one can pull a weight of 80kg. If Santa weights 90kg, his sleigh 180kg, and each present weighs at least 3kg, what is the maximum number of presents that can be carried in a single trip?

Puzzle 12: To mark the end of the 12 days of Christmas each student at the University of Oxford has kindly decided to donate some money to a charity of their choice. If the first person donates £12 and everyone after donates exactly half the amount of the person before them (rounding down to the nearest penny), how much will be donated in total?

Answers

Puzzle 1: 1 + 2 + 3 + … + 25 = 325. There is a faster way to do this which was first discovered by the mathematician Gauss when he was still at school. If you pair each of the numbers in your sum, eg. 0 + 25, 1 + 24, 2 + 23, etc. up to 12 + 13, then you have 13 pairs which each total 25 and so the overall total is 25*13 = 325. The same method works when adding up the first n numbers, with the total always being n(n+1)/2.

Puzzle 2: 1+2+4+8+16 = 31.

Puzzle 3: Volume of a sphere = (4/3)*pi*radius³ and so the total volume of snow = 0.52 + 0.27 + 0.03 = 0.82 m³. Melting at a rate of 0.01 m³per minute means the snowman will be gone after only 82 minutes!

Puzzle 4: This problem is actually a very famous sequence in disguise…

The first new pair is born at the start of the third month giving 2 pairs after three months. The question tells us that we have to wait one whole month before the new offspring can mate and so only the original pair can give birth during the fourth month which leaves a total of 3 pairs after four months. For the fifth month, both the original pair, and the first-born pair can now produce offspring and so we get two more pairs giving a total of 5 after five months. In month six, the second-born pair can now also produce offspring and so in total we have three offspring-producing pairs, giving 8 pairs after 6 months.

At this point, you may have spotted that the numbers follow the Fibonacci sequence, which is created by adding the previous two numbers together to get the next one along. The first twelve numbers in the sequence are below, which gives an answer of 144 – no wonder Santa is able to make so many toys!

Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

Puzzle 5: I have 12 choices of where to place the first person, 11 for the second, 10 for the third and so on, which gives 12*11*10*9*8*7*6*5*4*3*2*1 = 12! (read as 12 factorial) in total. BUT for any given seating plan we can rotate around the table one place to get the same order, which means we have in fact over counted by a factor of 12. Therefore, the total number is 11! = 39,916,800.

Puzzle 6: Reflect the yard in the pavement and draw a straight line connecting the front door to the edge of the garage closest to the front door (blue). Then add the same line from the ‘reflected’ front door at the top back down to the garage at the bottom (orange). The final shortest path is found by combining both paths for a valid one in the original diagram.

The length is found using Pythagoras’ Theorem. From the door to the pavement we have length

(1² + 2²)^1/2 = (5)^1/2

and from the pavement to the garage the length is

((1.5)²+ 3²)^1/2 = (11.25)^1/2

giving a total length of 2.23 + 3.35 = 5.58m.

Puzzle 7: 8 days = 8*24 hours = 192 hours. 192*0.05 = 9.6cm.

Puzzle 8: Chimney diameter = 0.7m so the maximum circumference (or waist size) that will fit is 0.7*pi = 2.2m or 88 inches!

Puzzle 9: Using the UN list of 193 countries, Santa has 24 * 60 = 1440 minutes total, which means spending only 7.5 minutes in each country!

Puzzle 10: 150 exactly with 16 + 27 + 42 + 65 = 150.

Puzzle 11: We have 8 reindeer each with a capacity of 80kg giving a total of 640kg that can be carried. Subtracting the 90kg for Santa and 180kg for the sleigh leaves 370kg available. Dividing this by 3 gives 123.33 so a maximum of 123 presents can be carried at once.

Puzzle 12: 12 + 6 + 3 + 1.5 + 0.75 + 0.37 + 0.18 + 0.09 + 0.04 + 0.02 + 0.01 + 0 + 0 + 0 + …

The donations stop after the 11^th person giving a total of £23.87. Even if we had allowed donations of part of a penny the total would never quite reach £24.00. This is an example of an infinite sum (or Geometric Series) where the total is always two times the first number.

December 23, 2019 2

Maths, but not as you know it… (St Edmund Hall Oxford Magazine)

Dr Tom Crawford joined the Hall in October 2018 as a Stipendiary Lecturer in Mathematics, but he is far from your usual mathematician…

Tom’s research investigates where river water goes when it enters the ocean. A simple question, you might first think, but the complexity of the interaction between the lighter freshwater and the heavier saltwater, mixed together by the tides and wind, and pushed ‘right’ along the coast due to the Earth’s rotation, is anything but. The motivation for understanding this process comes from recent attempts to clean-up our oceans. Rivers are the main source of pollution in the ocean, and therefore by understanding where freshwater ends up in the ocean, we can identify the area’s most susceptible to pollution and mitigate for its effects accordingly.

To better understand this process, Tom conducts experiments in the lab and has conducted fieldwork expeditions to places as far-flung as Antarctica. What the southern-most continent lacks in rivers, it makes up for in meltwater from its plethora of ice sheets. The ultimate process is the same – lighter freshwater being discharged into a heavier saltwater ocean – and as the most remote location on Earth the influence of humans is at its least.

If you thought that a mathematician performing experiments and taking part in fieldwork expeditions was unusual, then you haven’t seen anything yet. Tom is also very active in outreach and public engagement as the author of the award-winning website tomrocksmaths.com which looks to entertain, excite and educate about all thing’s maths. The key approach to Tom’s work is to make entertaining content that people want to engage with, without necessarily having an active interest in maths. Questions such as ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’ and ‘what is the blast radius of an atomic bomb?’ peak your attention and curiosity meaning you have no choice but to click to find out the answer!

Tom is also the creator of the ‘Funbers’ series which was broadcast on BBC Radio throughout 2018 telling you the ‘fun facts you didn’t realise you’ve secretly always wanted to know’ about a different number every week. From the beauty of the ‘Golden Ratio’ to the world’s unluckiest number (is it really 13?) via the murderous tale of ‘Pythagoras’ Constant’, Funbers is a source of endless entertainment for all ages and mathematical abilities alike.

And now for the big finale. If you are familiar with Tom’s work, you may know where we are heading with this, but if not, strap yourself in for the big reveal. Dr Tom Crawford is the man behind the ‘Naked Mathematician’ (yes you did read that correctly). To try to show that maths isn’t as serious as many people believe, to try to engage a new audience with the subject, and just to have fun, Tom regularly gives maths talks in his underwear! His ‘Equations Stripped’ series on YouTube has reached 250,000 views – that’s a quarter of a million people that have engaged with maths that may otherwise have never done so. His recent tour of UK universities saw several thousand students come to a maths lecture of their own accord to learn about fluid dynamics. It may not be to everyone’s tastes, but our current methods of trying to engage people with maths are failing, so why not try something new? This is maths, but not as you know it.

You can find all of Tom’s work on his award-winning website and you can follow him on Facebook, Twitter, YouTube and Instagram @tomrocksmaths for the latest updates.

The original article published in the Aularian magazine can be found here.

September 10, 2019 0

Tom Rocks Maths S02 E08

Another fantastic guest joins me in the latest episode of Tom Rocks Maths on Oxide Radio as my student Bonnor explains the Bridges of Koenigsberg and their link to Topology and Graph Theory. Plus, news from the Royal Society, a prime puzzle, and a numbers quiz featuring everything from the Simpsons and owls, to counting to one billion using only 10% of our brains. All interspersed with amazing music from Paramore, Linkin Park and Bring me the Horizon. This is maths, but not as you know it…

August 27, 2019 0

Tom Rocks Maths: S02 E06

Another fun-filled hour of your favourite two things – maths and rock music – courtesy of Tom Rocks Maths on Oxide Radio. This week I’m joined by two of my students from Teddy Hall, Fran and Tom, who will be explaining their favourite mathematical topics, taking part in a bumper numbers quiz, and sharing some of their music tastes. Plus, the usual dose of Funbers, and excellent music from Panic at the Disco, Sum 41 and Muse.

With thanks to Alice Taylor for production assistance.

July 31, 2019 0

Koch Snowflake

A short sneak preview of the full-length ‘Mandelbulbs’ video currently in production. A Koch Snowflake is an example of a 2D fractal with infinite perimeter but finite area. Full details of the calculation in the final video… COMING SOON!

June 19, 2019 0

Using maths to clean-up our oceans

Video of my ‘Teddy Talk’ at the 2019 St Edmund Hall open day.

Rivers are the major source of pollution in the oceans and if we are to clean them up, we first need to know where the majority of the pollution is concentrated. By creating a mathematical model for river outflows – verified by laboratory experiments and fieldwork – the goal is to be able to predict which areas are most susceptible to pollution from rivers and thus coordinate clean-up operations as effectively as possible.

June 11, 2019 0

Maths and the Media

Arriving at St John’s in 2008 to begin my study of mathematics, I was certain that within 4 years I would be working in the city as an actuary or an investment banker. Whilst I loved my subject, I saw it as means to obtain a good degree that would set me up for a career in finance. I’m not sure I could have been more wrong…

My current journey began towards the end of my second year, where I found myself enjoying the course so much that I wanted to continue to do so for as long as possible. This led me to research PhD programmes in the UK and the US, and I was fortunate enough to be offered a place to study Applied Maths at the University of Cambridge in 2012. During my time at Oxford, I found myself straying further and further into the territory of applied maths, culminating in a fourth-year course in fluid mechanics – the study of how fluids such as water, air and ice move around. This ultimately led to my PhD topic at Cambridge: where does river water go when it enters the ocean? (If you’re interested to find out more I’ve written a series of articles here explaining my thesis in simple terms.)

As part of my PhD I conducted experiments, worked on equations and even took part in a research cruise to the Southern Ocean. It was on my return from 6 weeks at sea that I had my first taste of the media industry via a 2-month internship with the Naked Scientists. I would spend each day searching out the most interesting breaking science research, before arranging an interview with the author for BBC radio. It was great fun and I learnt so much in so many different fields that I was instantly hooked. Upon completion of my PhD I went to work with the Naked Scientists full time creating a series of maths videos looking at everything from beehives and surfing, to artwork and criminals. You can watch a short trailer for the Naked Maths series below.

My work with the BBC and the media in general ultimately led me to my current position as a Mathematics Tutor at three Oxford colleges: St John’s, St Hugh’s and St Edmund Hall. This may not sound like the media industry, but the flexibility of the position has allowed me to work on several projects, including launching my website and my YouTube channel @tomrocksmaths where I am currently running two ongoing series. In the first, Equations Stripped, I strip back the most important equations in maths layer-by-layer; and for the second series in partnership with the website I Love Mathematics, I answer the questions sent in and voted for by students and maths-enthusiasts across the world.

Alongside my online videos, I am also writing a book discussing the maths of Pokémon – Pokémaths – and have a weekly show with BBC radio called ‘Funbers’ where I tell you the fun facts about numbers that you didn’t realise you’ve secretly always wanted to know. I have also recently presented at conferences in the US and India and hold regular talks at schools and universities, including for the Oxford Invariants and the Maths in Action series at Warwick University where I faced my biggest audience yet of 1200.

Looking back at my time at St John’s, I never would have imagined a career in the media industry lay before me, but the skills, experience and relationships that I formed there have undoubtedly helped to guide me along this path. I think it just goes to show that Maths is possibly the most universal of all subjects and really can lead to a career in any industry.

You can follow Tom on Twitter, Facebook and Instagram @tomrocksmaths for the latest updates.

April 3, 2019 0