Today marks the first day of my URSS summer project. I’m posting this to keep me sane. Also because I forgot to bring pens and pencils and I’m wondering what to do. So far I’ve found two excellent articles that should give me plenty to read for the next while. It’s good to be back on campus studying and researching again.

# Multiplication of two n-bit integers

Yo yo yo sup I’m back! – and ready to rock and roll. If you’re reading this, some general advice is to stop now and go do something useful, this post was not written with you in mind. Truth be told, you’ve probs arrived here by accident. If you’re not reading this, congrats! You’ve come to the right place.

To multiply A and B

To multiply integers

You want to divide,

Split into two or three parts,

Or four or more, you decide.

First put them in binary

Then make even splits:

A1 and B1 are easy,

Just write each as it is;

Now we must consider

What powers of 2

We must divide the other parts by

So they’re integers size n/(2^p)

Now multiply all out

A, B rewritten as above

Replace opposite multiplications

With pairs and minuses to spread da love.

Now all is done

We can find T(n) w.r.t. n/p

And solve the recursive relationship:

It’s quicker, you see!

# Basic Math: ∞

# Maths is awesome… EVERYWHERE!

To the elusive and almightily invisible crowd that is an Internet readership,

Tomorrow is the day Cambridge decision letters are due to arrive for 2016 undergraduate applicants, and I am seriously freaking out. Every five minutes I stop and Google (only realised the subtle mathsy pun on words after typing that – and yes, the magnitude of my freaking out is on the level of 10^{100}) Churchill College, where I applied, because I realise that I potentially only have a day left in which to daydream about going there before my dreams are crushed, and then I go on the websites of the other uni’s I’ve applied to to remind myself that it’s ok, they’re all awesome too, and by that time I’ve got nothing much done and so I realise that I need to do some more work if I’m ever going to get in ANYWHERE…

And so I decided to make a list of the reasons why maths (which is what I’ve applied to do because I like it – hence the name of this blog) is awesome EVERYWHERE:

- There are right answers and wrong answers: sometimes there are more than one right answer, so you can be creative, but there is a clean line between the correct and the incorrect, so you can aactually tell whether what you’re doing is any good.
- It stretches across centuries and the world in general, whether it’s the triangles of Pythagoras or the vectors of Stefan Banach
- It makes sense.
- The fundamental truths of mathematics stand alone, uninfluenced by public opinion and so on.
- It is abstract so even if the world blew up mathematics would remain intact.
- It stretches across cultures because it’s universal, like love, except it’s easier to understand.
- You can explore it yourself without any specialist equipment, just your mind.

There, that took my mind of Cambridge for 10 minutes or so. What shall we do for the 16 hours until the postlady comes?!

*Photo of Churchill from https://www.cambridgenetwork.co.uk/news/churchill-college-partners-with-onespacemedia-for-integrated3582/

**UPDATE** I’VE GOT AN OFFER FROM CAMBRIDGE!!!

# TheMathsBook reads maths books! (or at least, think about reading them)

I realised the other day just how many maths books are on my shelf waiting to be read. They all look so good! Having taken one more out of the library today, I thought I’d make a list of them here so much you can see what I’m going to be reading over Christmas and add your own suggestions in the comments section at the bottom if you so desire 🙂 Continue reading

# The Vector Equation of a Plane

# Painting by numbers, learning by sounds

Ok, so I cheated. Sure, I can do the Rubik’s cube, but only because I looked at the instructions. Except for for the second to third to last step – a total fluke, I managed to figure out that one for myself. I don’t even know if my method matches the instructions, but I refuse to look at that section lest my version turns out to be worse. Stubborn or what? I digress…

# Integrating x arctan x

I spent so long on this problem that when I ultimately had the answer, I made a video lest I ever forget!

# The Museum of Curiosity

This BBC Radio 4 special is too good to miss. This particular episode was recorded as part of the BBC “Make It Digital” season, and the “museum” has brought in three brilliant guests – Matt Parker (mathematician and comedian), Eben Upton (creator of the Raspberry Pi) and Sydney Padua (writer and illustrator of *The Thrilling Adventures of Lovelace and Babbage*) – along with “curators” John Lloyd and Sarah Millican to discuss how computers came to be whilst squeezing in as many laughs as possible.