applied-math

Just the other week, Baltimore Ravens offensive lineman John Urschel co-published a paper in the Journal of Computational Mathematics. The paper “A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians” can be found on arXiv.

In an article for the Player’s Tribune, Urschel says, “I am a mathematical researcher in my spare time, continuing to do research in the areas of numerical linear algebra, multigrid methods, spectral graph theory and machine learning. I’m also an avid chess player, and I have aspirations of eventually being a titled player one day.”

This reminded me of this tumblr post by classidiot I saw the other day that describes how it’s common to see mathematicians that are proficient in some non-mathematical hobby (playing an instrument, dancing, hiking, so on…), but often not the other way around. I think it’s really fantastic that John Urschel does mathematics just on the side as something he truly enjoys.

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The Heap Sort Algorithm

The Heap Sort Algorithm has a best and worst case time complexity of O(nlog(n)). This means that given a list of numbers n it will take Heap Sort only n*log(n) steps to sort the numbers. If the numbers are already in a heap, then Heap Sort is even more efficient. The sudocode for a Head Sort is as follows:

  • for the Wikipedia article with this sudocode [click here]
  • for an implementation of Heap Sort in C++ [click here]

Credit: Wolfram Alpha / Wikipedia

One thing I want to get across when I’m talking with people is that I view a mathematics library the same way an archaeologist views a prime digging site. There are all these wonderful treasures that are buried there and hidden from the rest of the world. If you pick up a typical book on sheaf theory, for example, it’s unreadable. But it’s full of stuff that is very, very important to solving really difficult problems. And I have this vision of digging through the obscure text and finding these gems and exporting them over to the engineering college and other domains where these tools can find utility.
—  Robert Ghrist, professor of mathematics and engineering at UPenn
Can we talk about this?

So there’s this physics journal that uses math and science to discuss the realities of fictional universes in a super legit, peer-reviewed manner?

And they did a thing on Frozen?

Combining research on the film?

With info on how water works and stuff?

Then applied math and chemistry (and other things in which I am not especially well versed) to reach this conclusion:

So.

Applying To Medical School Series- Part One: Are You Sure?

It starts early.

You’re 14 years old and your teacher tells you that you’re going to be starting the GCSE syllabus now. You still have to ask permission to go to the toilet but your future begins now. You have to start paying attention, even when everyone else is talking. You have to do your homework even if the rest of the class makes a pact not to do it and tell the teacher they forgot to assign any. You have to ask questions and study hard and do loads of practice questions to perfect your exam technique so that by the time exams roll around a year or two later, you can smash them.

August comes. You get your results.

Your results need to be great. Now this is relative, it really is. If the average GCSE grade across your year is a D and you got mostly Bs, a few As and maybe somehow scraped an A* or two, this can actually better than if everyone at your school averaged 11 A*s and you got 9 A*s and 2 As. Don’t worry whatever the case, all hope is not lost here.

Sixth Form begins. A lot of people will choose an “easy A” subject. Subjects they don’t really need to work very hard in and which aren’t particularly useful to them in the future.

You, on the other hand, need to have Chemistry. You also choose Biology and Maths. For your 4th subject, you decide on Spanish because you’d quite like to go to UCL and you’ve heard they prefer a non-scientific 4th subject. But crap. You were also thinking that with GCSEs like the ones you worked your butt off to get, maybe you’d consider Cambridge if your AS Results turn out well. And don’t Cambridge love you to have 4 sciences? Well whatever. What’s done is done. Biology, Chemistry, Maths and Spanish it’ll have to be.

Oh but this isn’t all. 

You’re volunteering in a care home, tutoring younger students, acting as a mentor, working with autistic children at a weekly club, captaining the basketball and hockey teams, raising money for the school in Senegal that your own school is affiliated with and of course, you’re going to South Korea over the summer to teach English to children.

You’re also reading New Scientist and books by Atul Gawande and other popular medical books. You don’t read The Man Who Mistook His Wife For A Hat because medicslacks on tumblr told you that everyone and their hat has read that book and seriously if you put it on your personal statement you are just wasting characters.

And of course. Work experience. You emailed every GP in the area and they all told you they can’t take you because it might compromise patient confidentiality. So you ask that girl in class who you kind of know but don’t really talk to if she could ask her dad, the GP, if you can shadow him for a day or two. She looks confused but says sure, she’ll ask.

Success.

You shadow the GP and realise this is only primary care. One of the patients really gets to you, a patient with Multiple Sclerosis and this intrigues you. You go home and read up about the condition. You then decide to email all the neurologists about your interest at your local hospital on the off-chance one of them will let you shadow them.

A miracle! A week later, one of them replies! Oh, but there’s a lengthy official process. That takes a month or so and then FINALLY you get some hospital work experience- just one afternoon, but you get to meet patients and ask the doctors more about MS and you decide it’s all worth it.

You grit your teeth as the kids with doctor parents talk about how they just follow their mum or dad around whenever they want.

And all this while you HAVE to keep working hard at school. You pay attention in class. You go home and do your homework, you flag things you don’t quite understand to ask at school. You start making notes early and you revise so hard in the run up to exams because secretly you’re still hoping to go to Cambridge and you’ve heard you need a minimum of 90% UMS in all your papers to have a chance. It’s okay if you don’t though- you know a family friend who got ABBC and still got an offer from Manchester.

But you’re hoping.

Results day rolls round aaaaand… YOU’VE DONE IT!

Congratulations.

Now the nightmare that is application season begins.

UKCAT booked. Okay. You’ll worry about that later.

Everyone else has until January but YOU need to get everything done by October. You panic and sit down to draft your personal statement aaaaannnndddddd…

You draw a blank.

What.

The hell.

Do you write?

It’s okay because I AM HERE TO HELP. Personal Statement Help Post Coming Soon!

But for now, let’s just assume you somehow get through it. You draft it and you take it to your careers advisor who looks at it and then asks where you’re thinking of applying. “Cambridge, Imperial, Leicester and Hull York.” you say. You like the variety.

Your careers advisor looks baffled. “You can’t apply to those 4.” She tells you. “Your personal statement will never tick all the boxes for them all, they’re far too different and are looking for completely different things. They all teach medicine in completely different ways. On the spectrum of Traditional to PBL, you’ve really run the whole gamut.”

So you go away and you look into the courses and you decide that you’re not particularly bothered about research and you want to see patients as early as possible. You don’t really care about the city you’re in or the prestige of the university.

“Ahh that’s better.” Your careers advisor smiles as she sees you’ve scrawled across the top of your page: “Leeds, Hull York, East Anglia and Sheffield. You know, with GCSEs like yours, you should really consider Birmingham.”

You decide to see how your UKCAT goes.

Your school also registers you for the BMAT since Leeds requires it. But you’ve got the whole summer to worry about that.

Over the summer you prep for next year by reading ahead in the text books a little and making some notes. You carry on with all of the extracurriculars and volunteering you were doing. On top of this, you start doing practice questions for the UKCAT and BMAT.

After your first day of these questions, you break down. This is impossible. How does ANYBODY do this?

The next day you take a deep breath and try again.

They’re a little easier.  

A week later and you’re finally starting to get the hang of it. You’re starting to know what to look for. You’re starting to notice patterns and learn the rules. You’re starting to think the right way.

You can do this!

You sit the UKCAT in the same seat where you did your driving theory exam. You get a 750. Excellent.

School starts again.

You refine your personal statement, you fill out the rest of your UCAS form. You see your reference.

You hold your breath as your Head Teacher clicks Send on your form.

Then you wait.

You don’t have time to stop. On top of school you’re now having to go over GCSE science again for the BMAT. And practicing writing as tiny as possible so you can fit an entire essay onto a page. As well as still struggling with all those logic questions. You’ve already applied to Leeds so now you HAVE to do it. You get a 2.5 in Section 2 of one of the past papers. You wonder if you might as well just give up on Leeds now.

You sit the BMAT and are fairly sure you failed every section. Whatever.

OMG.

OMG.OMG.OMG.

You’ve got an interview. AAARGGGHHHHH.

Mock interview. You NEED a mock interview. You beg your careers advisor who sorts out for a local doctor to come in and interview you. They ask you about your personal statement, your work experience, they ask you about a few ethical dilemmas and some odd questions that seem to have no purpose. They also discuss some topical issues in the NHS with you. You make a joke about Jeremy Hunt.

They laugh.

A few days later, you get your BMAT results. You did SO much better than you thought. Excellent.

OOOOOOMG.

Another interview.

You’re on cloud nine when… UCAS Track updates again.

Your first rejection.

It feels as though someone just snapped a rubber band around your heart. Why would they reject you? What was it they didn’t like? Were you not good enough? Did you not seem dedicated enough? Why?

You swallow down the disappointment. You already have TWO interviews. You’re so lucky. There are thousands of people who don’t even get that. And you have EARNED it. You’ve been working hard for years for this.

You prepare for the interview. You ask yourself questions and change the answer every time. “Why do you want to be a doctor?”

You know they’re going to ask you this but what do you say? You have an idea! You’ll talk about a patient. The patient with MS you saw at the GP who really touched your heart. You can say you liked how the science that the doctor knew would be nothing without the way he was able to console her more personal worries and concerns and this kind of application of science to help people really convinced you that you want to do this. At least by adding in a patient you saw, your answer will be more personal.

Interview day arrives and you’re sitting nervously with a few other students. A boy in an oversized suit and a girl wearing heels so high you’re worried she’ll break her ankle on her walk to the room. A student at the university smiles and calls your name. She walks you to the door. “Are you ready?” she asks. You nod but it’s not true, your stomach is full of butterflies and you feel a bit sick.

And for a second you pause.

Are you sure?

Are you ready for the path this could lead you down? The life of a doctor. Forget that. The life of a medical student! Antisocial hours, a lifetime of having to keep requalifying and doing exams, mountains of paperwork, not really saving lives so much as helping to reduce the effect of symptoms. Putting your heart and soul into delaying the inevitable.

Is making a difference to even just one life, is making life less painful or less miserable for just one person, is keeping just one person alive so their loved ones can see them for another day, or helping even one person to die in as little pain as possible… is that enough for you?

You take a deep breath and open the door.

Two weeks later. You get an offer.

A*AA.

You end up getting two more offers.

August rolls around again.

You cry when you get the email from UCAS confirming your place at your Firmed University.

A*A*A.

It was all worth it. You got into medical school.

Your parents buy you a copy of Gray’s Anatomy and this is when you realise… The work has only JUST begun. The first 18 years were nothing.

So I’ll ask you again.

Are You Sure?

Computing’s Search for Quantum Questions

Learn about the viability of quantum annealing to solve NP-hard problems.

Unlike a universal quantum computer, which is designed to tackle a range of problems, a quantum annealer is designed to tackle a specific type of problem called an NP-hard optimization problem. These can arise in many situations, but here’s an example: Say you went to a city and wanted to find the largest cluster of people who all know each other. (This is called the “maximum clique problem” in computer science.) You could try to tackle the problem with a brute-force approach, identifying every group of friends and comparing sizes until you settled on the largest. Such a strategy would work for a small village, but it becomes untenable if you want to identify and compare every group of friends in, say, Tokyo. […] To solve this kind of problem, the D-Wave 2X uses a process called annealing, which gets its name from a 7,000-year-old metallurgical practice. Early metalworkers figured out that if they made a material hot enough and then let it cool down slowly, it would make the final product stronger. The process works because the heat randomly jiggles around all the atoms in the metal, and then as it cools, the atoms slowly arrange themselves into their lowest-energy (and therefore most stable) configuration. Bartenders may also recognize the process: The secret to creating a flawless and clear ice cube is to let the water freeze very, very slowly.

Quanta Magazine - Image by Daan Botlek