Oxford University Mathematician takes Cambridge Entrance Exam (STEP Paper) PART 1

lol, the exams cypriot and especialy greek student give in order to enter the local unies are faaaaaaaaaaaaar harder than this.

just tell them how woke you are. m@th is rascist anyway

Nice. He did exactly what i would have done. Nice work

I'll pretend i understand this

not smart enough not to butcher his face lol

I am a retied auditor (79 years old) with a lifelong passion for maths (A levels early 1960s, A grades in pure maths and applied maths). I have listened to your video up to question 1 (will view the rest later on). Think I have an easy solution for the final part of Qu. 1: We have 1 + tanxcot3x = 1+ tan2xtan4x, (cosxsin3x + sinxcos3x)/(cosxsin3x) = (cos2xcos4x + sin2xsin4x)/(cos2xcos4x), sin4x/(sin3xcosx) = cos2x/(cos2xcos4x) = 1/cos4x, 2sin4xcos4x = 2sin3xcosx = sin4x + sin2x = sin8x, sin2x = sin8x - sin4x = 2sin2xcos6x, sin2x(1 - 2cos6x) = 0 & sin2x = 0 or cos6x = 1/2.

I wonder how he will fare with the toughest university entrance in the world, the Gaokao

don't forget the '0'. 'x=0' should be the 8th solution.

In Eastern Europe this is 10th grade stuff.

What are you guys doing in the West?

I have no idea what's going on but still watched 1 hour 36 minutes and 54 seconds of this video.

Great! But doubt the value of such questions. Give them a real world ( simple ) challenge/ situation and see these top students crumble.

Wtf did I just watch? I work at mcdonalds

This chap reminds me of all those girls that say “ all my friends say I am mad, me”. Of course the friends think nothing of the sort. It’s much less positive in truth…….

Are these questions in increasing difficulty?

Lol I am a electrical engineering grad student and cant solve that with hand.

I’m a final year high school maths student, and the absolute joy I felt when I paused the video, worked out 2 i, and got it right, cannot be put into words.

Definitely worth the wait, looking forward to part two <3. Definitely worth the wait, looking forward to part two <3.

Tom probably has a chance of getting an interview. But will he have enough outside interests on his CV that demonstrate his interest in maths ?

Ah the tattoo equation !!! That will do nicely.

Yeah... lost me at cos(a±b)=


Who am i kidding, lost me at cos 😅

Amazing!

Don't worry, if you practice like this in due time you will be accepted into a bachelor's program.

30 minutes for just question 1
BRUTAL!!

hello there, german here, so sorry for my bad english.... stumbled over your channel yesterday. i passed my maths examen over 20 years ago, one of my favourite topics was spherical geometry, but algebra was nice, too.... never needed any of that afterwards, BUT: i had a very bad night last night, and watching you solving mathematical problems helped me over some hard hours. thanks for being so passionate and sharing it with us! 🙂

Think I’m trying to say thank you for making maths cool..the kids nowadays need to realise maths is GREAT!

I adored pure maths as an A level student. However I became a dentist.. and 30 years later can’t remember any of my beloved maths. But still love watching the mathamagicians. Lol.. my daughter is doing a msc in maths!!

I dont know if I could take a math professor with pokeball tattoes seriously xD

A different approach for the problem 7 (iii)
We know from (ii) that S^2=S*S=-(I+S).
We also know that det(S)=1, which means that S is invertible.
Hence S*S*S(-1)=-(I+S)*S(-1), hence S= -[S^(-1)+I]
We notice that [S^(-1)+I]*[S+I]=2I+S+S^(-1)=2I-[S^(-1)+I]+S^(-1)=I
Hence -S is the inverse of (S+I), which is also a rotation: that implies that S is a rotation.
Since [S+I]^(-1)=[S+I]^(T)=S^T+I (because the diagonal doesn't chenge), we get that S=-S^T-I
So we have that S+S^T=-I
Hence b+c=0 and 2a=-1 and 2d=-1, it follows that a=d=-1/2 and c=-b
Since det(S)=1=1/4+b^2, we conclude that b=+-sqrt(3)/2

I will recommend you to attempt maths paper from the IIT JEE Advanced exam from india

Not sure why they don't just let you prove the sum product formulae in general for Q1. Maybe this would be acceptable.

Lovely guy with a great approach to getting the subject online. But please try to avoid the hands on head captions as you clearly dont find these tests too demanding.

16.20 instead of factorizing and loosing 10 hours couldn't you group 2u^2(2u+1) - (2u+1)=0 ???

Interesting video, but I must confess I resolved Q1 in less than 10 mins. Wating now impatiently for Q2 to come up.

Is Tom a 'professor' as claimed in the title for this video?

The hardest test for Dr Tom would be no mirror, hair dryer, or teeth whitener for a week.

For me i prefer old fashion Professor, These fake Pr they can’t gave more than they have.

I am a American Registered Nurse. I have always struggled with Math. I find this so amazing someone can grasp all of this so easily Algebra was so hard for me. I passed and was a Nurse until I just retired.. l have a Grandson who loves math . Hopefully he will succeed at least half of what you have and he will be way smarter than his Granny . A great Uncle was an Engineer so that is where he gets it. UR coolest Professor I have ever seen.

Hello Dr Crawford. Thank you for the video. I was wondering if you are planning to do any more step papers. I thought your explanation of these questions were very insightful

Trump called and wants his hair back mate

In the first problem, didn't you miss x=0 as a solution, since sin(0) is also an x intercept, and 0 is within the valid range of x?

STEP is devised to ensure that only wealthy students whose parents can afford a private school and a tutor will ever attend Cambridge. I guess that Tom would support the no peasants rule.

math is too easy and boring

I found the biggest stumbling block for me in mathematics was understanding the complexities of the 'Gusintu's theorem - as in I Gusintu 2 and 2 Gustintu 4!!!

I've stumbled upon this. How do I select the English translation? Mine seems to be stuck in a foreign language. ;-)

Have you ever had a look at the Indian test: Joint Entrance Examination (Advanced)?
On the website there is an archive with the tests from the past years.

What's the math chair at Oxford called? And what's the origin of the word "Lucasian"?

I was going to go for something similar , But I had to quit and run quickly because my grandad had a squerrel stuck on his head and I had to run and save him, I guess I will try again.

for a non-mathematician like me, this is like trying to read & decipher the cuneiform text from Sumerian tablets. but love your mind that can solve these equations. wonderful stuff. awesome vid!!