MAT Prep Thread 2018

In the above question, is the recursion depth of $f(x)$ equal to

Ignore the attachment thing. Nothing has been attached to the answer. The answer is the one in the bottom image.

Thamks for the offer @Integer123 . How were your interviews? To which college did you apply to?

No worries

I applied to Worcester College and had 5 interviews in total, 2 for maths and 3 for CS. Every applicant is allocated a second college, and I was allocated Balliol College. At Balliol College and Worcester, I had an interview for CS and an interview for maths. On the Tuesday, I saw that I had another interview at Lady Margaret Hall on the Wednesday; and when I arrived at Lady Margaret Hall, I found out it was a computer science interview.

Overall, I felt my maths interviews had gone better than my computer science interviews

If you want me to discuss what happened in my interviews, I can

Is it alright to use such a time consuming method in the MAT?

Does anyone know if you apply for a joint course say Computer Science and Mathematics and interview goes exceptionally well for one subject and not so well on the other, would you be considered for Mathematics or Computer Science only? I am asking this because people applying for Physics and Philosophy get considered for Physics if they are not selected by Philosophy department.

Thank You!

Does anyone know if you apply for a joint course say Computer Science and Mathematics and interview goes exceptionally well for one subject and not so well on the other, would you be considered for Mathematics or Computer Science only? I am asking this because people applying for Physics and Philosophy get considered for Physics if they are not selected by Philosophy department.

Thank You!

Please discuss your interviews. How were the maths interviews different from your CS interviews? Did they keep in mind that you were a Maths and CS applicant?

Did it have any specific material/algorithms which are not in the A-Level syllabus like the master theorem(just an example)?

How would you rate the questions' difficulty on a scale from 0-5?

Please mention all the questions which the tutors/professors asked you.

Are they actually considered for the physics-only course?

Mostly, the difference between the maths interviews and the computer science interviews was that there was less maths in the computer science interviews - my interview at Lady Margaret Hall had very little maths, as did my interview at Balliol College, whilst my interview at Worcester had a bit more maths, including a maths question itself. I think the main idea of the interviews was that they expected me to be able to apply my mathematical knowledge to more algorithmic situations.

I'd say the interviewers may take into account you being a Maths and CS applicant, for me, the maths interviews at Balliol College and Worcester seemed very much like interviews that were standard maths interviews, although I have a friend who was given more discrete maths like questions in their maths interview at St Hugh's College. Also, one of my friends interviewed at Keble College where their interview was a combined Maths and CS interview. So I'd say that it may depend on college, but I think the interviewers are aware that you are a Maths and CS applicant.

There was nothing in the interviews that was designed to catch you out - even though all the questions were very unknown, they tested applying your knowledge in unfamiliar circumstances. For example, in my Worcester maths interview, I knew Vieta's formulae, although I was asked whether I recognised a pattern in the numbers. In my Balliol College computer science interview, the question probably required very little knowledge but I still found very challenging. At Lady Margaret Hall, for my CS interview, one of my questions required knowledge of graph theory, which I knew from having done D1 (Decision Maths module) in year 12, although the focus was less on knowing the graph theory itself and more applying algorithmic techniques. All the knowledge about graph theory I think was needed was the idea of a graph and edges/vertices, and what a conected graph is.

In terms of rating the difficulty, I think it does depend on your strengths and how you find the interviews themselves.

Balliol College:
Maths: This was my third interview (around midday on Tuesday). The first question was a graph sketch of $y=\ln(\sin^2 x)$, and graph sketching is one of my stronger topics so I found that relatively straightforward; and the second question was on probability, which normally is also one of my stronger topics, but for some reason I just said some stuff that wasn't making very much sense at all, although the interviewers managed to get me back onto the right track and answer the question correctly. I was happy with this interview; I was a bit worried I hadn't done as well as I could have on the probability, but still felt it was a good interview, but not as good as my Maths interview at Worcester. I'd rate that 3/5 difficulty.

CS: This was my fourth interview (Tuesday afternoon). In this interview, I felt quite out of my depth, perhaps because I'm less confident in CS than maths, but nevertheless I felt quite happy with my performance when I left the interview. One of the tutors was writing on a whiteboard, whilst I sat on a chair facing the whiteboard, basically trying to explain how to solve the problem. I think I grasped how to do the problem quite quickly but perhaps I didn't explain everything as clearly as I should have, and when asked the question at the end of "is this the most efficient algorithm?", I wasn't really sure and said if I followed another algorithm, it would be much slower - although the tutor did tell me that trying to explain whether this was the most efficient algorithm was too difficult to be done in an interview. Also, there was another short question at the end from the other tutor about my interest to study the subject, which did throw me a bit, although the main focus of the interview was on the algorithm. I felt happier with this than my CS interview at Worcester College. I'd rate this 4/5 difficulty.

Worcester College:
Maths: This was the interview I felt went best out of all of my interviews. This was my second interview (Tuesday morning), and was after my CS interview at Worcester which I definitely felt could have gone better, so I think I was feeling some pressure on this interview to go well. I was interviewed by a maths tutor and a PhD student, with the maths tutor asking most of the questions, and the PhD student taking notes, but also asking me some questions too, especially to test whether I knew what I was talking about. Incidentally, I don't think I would have chosen these questions had I been offered a list of questions, although I think this does go to show how the interviewers try and lead you to the solution, whether you are best suited to the problem or not. The first question was on number theory, and was very enjoyable, and it involved me effectively investigating the properties of this function, trying to generalise what F(n) was for all n, with the interviewers often saying "what about this number", with me referring back to the function. The second question was on simultaneous equations, although it was actually using Vieta's formulae, and I found this question very fun too. Although the skills it tested weren't too difficult in themselves, it definitely tested a lot of them and I had to reason clearly. At one point, the PhD student asked me what a<b<c meant about the numbers, to which I only answered "they are ascending", however, when asked "can you compare complex numbers?", I then was able to explain that it meant that they must be real numbers. At some points, I should have done more drawings instead of mentally trying to visualise things, but when I finished the interview, I felt satisfied with how I had done. I'd rate this difficulty 3/5.

CS: This was my first interview (Monday morning). On the Sunday when I arrived, we were given a problem sheet in my arrival pack, from which I had to complete some compulsory questions and some optional questions before my interview. I found this problem sheet pretty tricky, and some of the questions were harder for me than others, and I was unable to do much on one of the optional questions on matrices, so I left that. In the interview, I had to explain my reasoning for my solutions; and if I had solved the problem wrong, or less efficiently, I would be led to a solution. I first explained one of the compulsory problems, and then moved onto the second. When I had to explain why a list with n items could not be sorted in any less than n operations, I for some reason failed to see that each item has to be checked, and so was going on about the list being sorted, perhaps I didn't underatand what I was being asked. However, the interviewers moved on and we eventually extended the second compulsory problem from the initial problem given, and got a general case where I had to find an upper bound for the number of comparisons made, and I was happy with how I did here. After doing the compulsory number theory question from the problem sheet, which I had solved mostly correctly, but overcomplicated one part of, which I was told and realised how I'd overcomplicated, I was asked which of the optional questions I would like to explain, and so I chose the one I thought I had completed correctly. In fact, I hadn't solved it correctly (I'd found a much less efficient solution) and so the tutors tried to lead me to the solution. Initially, I made some progress from how the tutors asked me the question, and then as we progressed, I got very confused with things seeming to be the "smallest of the smallest" or something like that, and the tutor drew some less than signs on a diagram, and I feel very much guided me with not enough input from me, to the solution. I feel in this problem, I didn't respond as well as I could have to the hints I was given. After the interview, I felt it hadn't gone as well as I wanted, and definitely felt I had to do better in my other interviews. I'd rate this difficulty 4.5/5

Lady Margaret Hall:
CS: This was my fifth interview (Wednesday late morning). When I got to the interview, I was first asked a brief question about why I wanted to study Computer Science, which I answered in a couple of minutes, and then we moved on. I was interviewed by a tutor and a PhD student. I was given, in the interview room itself, a sheet to read over, and then we would start discussing it. This was on graph theory, which is a topic I really like, so I was happy about that. Throughout the problem, I tried to apply logic to the situation as well to eliminate certain possibilities. Most of this problem I felt went quite well, although at one point, I had to explain why something was true on any general graph, and I think, because I had some idea of a proof, but this was different to their idea, I was perhaps being a bit inflexible, and struggled to explain why it was true. I was then given a second problem to read, which I felt went quite well too, although towards the end, I forgot the premise of the problem, and got very confused, although the tutors helped explain it again. I felt this went about as well as my Balliol College CS, but better than my Worcester CS interview, and was overall happy with it. I'd rate this difficulty 4/5.

If I had to rank my interviews, from which I felt went best to which I felt went worst, I would say:
1) Worcester College Maths
2) Balliol College Maths
3) Balliol College CS (tie with Lady Margaret Hall CS)
3) Lady Margaret Hall CS (tie with Balliol College CS)
5) Worcester College CS

I'm currently working on writing up a pdf document of my interview questions, but I'll try and post that here soon Also if any people I know have got questions they can remember, I'll try and add those to a separate document

Integer 123 thanks a lot for you extremely heplful post .
Do you require prior knowedge on graph theory to solve questions ,like an idea about dense/sparse graphs, breadth/depth first search or composing a path with strongly connnected components?

And please try to post the pdf at the earliest. I would love to see it.

Has anyone else found that the 2018 MAT date lies during October half term? What does this mean