Mathematics Mock Interview, University of Cambridge 

who are the mathematics and why are they mocking the interview

nightmare blunt rotation

I love this channel reminds me of Olympiads and those beautiful challenging math problems

Loved the interview!

Good interview! I think she has a good chance. As for the whiteboard, zoom offers a much better one with lower latency.

The prospective student is really strong, in my opinion. She will have a fun time studying maths :)

Surprisingly All questions asked, were from computer science engineering, design and analysis of algorithms, asymptotic functions analysis chapter.

Many commenters well versed in mathematics seem unable to grasp the difference between a maths exam and a maths interview.

I haven’t got a clue what they’re talking about. Haven’t done maths for 21 years! 😂

Number of times y = ax intersects y = ln(x) depends on a as follows: Case 1: 'a' is negative. In such a case, y = ax will intersect ln(x) exactly once between x = 0 and x = 1, where the value ln(x) is equal to ax. Case 2: 'a' is zero. In such a case, y = ax is constant function y = 0 and intersects y = ln(x) at x = 1. Hence, it intersects y = ln(x) only once. Case 3: 'a' is positive. In such a case, the curve y = ax may never intersect y = ln(x) given 'a' is larger than a specific value, and may intersect y = ln(x) twice if 'a' is smaller than that specific value. That specific value of 'a' occurs when y = ax touches y = ln(x) at exactly one point. For the touching case, d/dx(ln(x)) = d/dx(ax) at x = x0 => 1/x0 = a; Since (x0,y0) lies on both y = ax and y = ln(x) y0 = ln(x0) = ax0 = 1 => x0 = e and a = 1/e Hence, if a is greater than 1/e the two curves never intersect; and if a less than 1/e the two curves intersect twice. And if a = 1/e, the two curves intersect only once. Hence, the number of point of intersection is as follows: a 1 0 < a < 1/e => 2 a = 1/e => 1 a > 1/e => 0

This was a really helpful video, thank you. Please could you do an example interview with a stats and mechanics question?

Indeed a positive gradient here is necessary but not sufficient for a function to tend to positive infinity. Proving that ln(x) tends to infinity as x tends to infinity might take a while, and in this short example of interview questions the aim was to explore the question “For what values of m there are zero, one or two intersections between ln(x) and mx?”. It is often the case that an interviewer might choose not to pursue a line of inquiry and move on with the question. In this video it has happened - in different ways - with both questions.

I think Amy's argument for why log(x) -> inf was better than the interviewers' gradient argument, which doesn't hold in general

I'm so thankful I never have to do thia kind of maths ever in daily life after being gaslit in secondary school being told 'you won't always be able to use a calculator and you'll need to use proper maths'

Taking two times logarithm of base 2, we are comparing the quantities: 2^n and n*log_2(100) + log_2(log_2(100)). It is obvious that the first grows much faster.

How can you argue that just because the derivative is > 0 the function tends to infinity? Isn't the derivative of the sigmoid always positive as well and it just tends to 1?

If I were marking a student who said that a function tends to infinity because its derivative is always positive, as Dr Spivack suggested, that would be worth 0 marks (in light of all such functions that don't tend to infinity).

Why am i Here?

I was watching people falling down stairs. What am I doing here

Was she a student coming out of hs and applying to an undergraduate program or a higher level like graduate?

Amy is the person I would like to sit next to during a math exam 🧐

well... at the last few questions, I paused for way too long, just because I hadn't done this question before, I wanted to find out the solutions to the equation and even though I knew pretty early on I wouldn't be successful because (e^(ax))=x is not made to be solved on simple ways, I kept sticking with it for too long, until eventually doing the ye^(y)=ax. I'm way too stubborn. I found the first question much easier than the other ones, as just using the properties of e and ln-functions will carry you to the solution with barely any effort.

This logs not leaving me alone even now😅😅

14:10 why does having a gradient that's always positive mean it tends to infinity? e.g. y=-1/x has a positive gradient whenever x>0 but it tends to 0

How is possible to evaluate if a person is capable of Cambridge studies from just one question of this kind? In my opinion if a student replies correctly to this question then I could not be sure to accept him/her. Even if a student fails to answer this question it would be a bad indication but I would not reject at one, I would need to ask more questions.

could i ask; would this be considered a "successful interview" would this applicant be offered a place just off this interview performance? not including anything else?

Why did this video summon some of the most annoying people on the planet in the comments 😭

Does anyone here know what the mean radio of the earth is? I’m lead to believe it’s 3959 miles. Can anyone here confirm and agree this axiom so we can discuss further this. Thanks

wrotoeshaw has come a long way

What is this? Do i have to do this when i apply for cambridge chemical Engineering and biotechnology?

would love to see one for economics!

why would they interview students for mathematics? is is for prefential admission to a specific program?

Take base 2 logarithm once, we get 2^2^n vs C1*100^n Take logarithm one more time: 2^n vs C2 + C3*n Can stop right here - the exponent on the left always beats the linear function on the right for large enough n. How could this solution can take more than two minutes at the most? “Logarithms with base > 1 are monotonously increasing functions” - that’s all she should’ve answered to justify how proof for logarithms proves the original statement. Which she did not. As to the generalized second question, the “strategy” should’ve been stated as follows: for arbitrary functions f(x) and g(x) finding the point x0 where they both touch each other is a matter of solving two equations: f(x0) = g(x0) f’(x0) = g’(x0) In high school in Russia I finished that would be considered an extremely weak performance. Not Cambridge quality … or perhaps Cambridge quality is not what I imagined?

Is the mathematics in the room with us right now

why is she saying only 2 to the 2 to the n while its 2 to the 2 to the 2 to the n?

If this is the entrance interview, what's the exit interview? What is 2+2 and why should you switch to a state public school?

Is this done for teaching positions?

is this for undergraduate or graduate courses

That was quite less challenging than one would think for Cambridge, It was fun regardless

Apart from the croaky voice she nailed the Qs.

At 15:00 I do not agree that lnx goes to infinity when x goes to infinity just because the derivative is positive.

Impressive young lady

w2s moving nuts

The trouble with this selection process is that it eliminates all potentially exceptional students who have not yet learned the skills of problem solving. Surely that's your job, Cambridge, to teach such skills! Or are you just upping your university rankings by taking in the already-skilled problem solvers?

Why does the guy on the left kinda look like Harry from Sidmen 😭😭😭

w2s?

16^n > 100^100^n obviously...am i missing something?

Ah, this reminds me of my mathematics interview at imperial college London 22 years ago, which I aced, might I say. 😁

that was easy bro ong i couldve made it to cambridge

I thought It was a coding Interview hehe DSA

it's hard to picture "a hundred of those, a hundred of those, a hundred of those..." growing slower than "2 of those, 2 of those, 2 of those..." at least that's how a 14 year old feels about it...

Obviously f(n)=2^2^2^n grows faster than g(n)=100^100^n ... log(log(log(f(n)))) / log(log(log(g(n)))) ~ n / log n -> infinity.

why does the top left look like harry from the sidemen

That first question was a horrible question to start with.

damn jee aspirants could do this in 5 mins and leave

I think im lost, I was looking for the cute cats channel

W

They lost me when they asked the question.

Im living turkey and ı admit turkey math lessons are more dificult then cambridge lessons

This is elementary school maths

arent these questions too easy???

the magic number is e^(1/e)

God, I hate maths.

Not diverse enough to get a place.

Mocking mathematics???? Are you insane??

Wtf is this I'm preparing for IIT (India).we do solve this type of problems in basic maths level 1😮

Oh this is intermediate-level maths in college In India these are taught in 11th standard

Future woke interviews

she was noobie

I hope this doesn't come across as too critical or offensive, but is attitude/composure/professionalism considered in these interviews? I found Amy's frustrated "eugh" early in the interview came across as very unprofessional, and seemed like a disregard for the importance of the interview (and I'm sure she does understand the importance of it). This also obviously has no bearing on her mathematical ability.

As an indian, i already know the bigger number is 2^2^2^n... Just math intuition

In the first question here, they are actually wrong. This is a trick question as N goes to infinity which is a concept that we cannot conceptually grasp, meaning they are equally big (or sized, as their size is actually undefinable)

Maths is nonsense and unnatural but she seems nice so i hope she gets a place

w2s if he didnt do hardcore drugs: