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Advice for Maths Applicants (esp. Oxbridge)
Hi
Firstly, an introduction. I got an offer of AAA for Maths from Oxford nearly two weeks ago. When I was applying, I wanted all the information and help I could get so I thought I’d do everyone who is applying next year a favour and tell you (just about) everything I know. Actually, I’m really writing it because some people I talked to at interview had 100 people applying from their year at school and were getting all sorts of seminars and interview preparation, whilst others got nothing. At my school (independent) we get practically sod all, so I was tempted to be all “ I can find this stuff for myself, so anyone else can too” but hey, I need the rep. I’m writing it now because I can still actually remember it and because next year, I probably won’t care about applicants any more.
And there’s already a thread for 2007 applicants so some of you must be keen.
Secondly, a disclaimer. I have an offer. I have not made my offer and may well not get the grades. I may get the grades, go to Oxford, decide I hate Maths, fail all my exams and be back here warning you all against it. I could go, love it but be crap at Maths and get kicked out. Hopefully not, but what I mean is don’t give anything I’ve said too much respect.
Ok, so attached should be:
• Some advice someone gave me
• A report someone on TSR wrote about their Cambridge interview (I hope they don’t mind me posting it!)
• Other people’s personal statements
• My personal statement
• What I wrote on the OAF
• A document with 100 (
) interview questions from http://www.oxbridge-admissions.org.uk/
• Other, verbal interview questions (as opposed to mathematical problems)
• An article on the Philosophy of Maths (random)
• The Oxford, Cambridge and Imperial reading lists
• And various notes, some of which are posts from the TSR Maths forum
Some other stuff…
Books I read:
o A Very Short Introduction to Mathematics - Timothy Gowers
o The Man Who Loved Only Numbers – Paul Hoffman
o A Mathematician’s Apology – GH Hardy
o 1089 And All That – David Acheson
o (Some of) The Pleasures Of Counting – TW Körner
o (Some of) The Foundations of Mathematics – Stewart & Tall
o (Some of) The Music of the Primes – Marcus du Sautoy
o (Some of) The Emperor’s New Mind – Roger Penrose
Would I say that any of these were useful? My first thought would be no, most, if not all of my preparation was totally needless. However, at my interviews we did discuss Euclid’s proof of the infinitude of the primes (in 1089 And All That and A Very Short Introduction to Mathematics) and Cantor’s diagonal argument (in The Pleasures Of Counting). Also, they introduced me to concepts I couldn’t now imagine not knowing, like Euclid’s proof and proof by induction. So, these books specifically? Probably not that much (although most of them are on the reading lists) But being generally (mathematically) well-read? Definitely. A lot can be found on the internet
Useful Websites:
http://meikleriggs.org.uk
www.mathshelper.co.uk
http://www.mathsexams2.tk
http://www.nrich.maths.org
http://www.cut-the-knot.org
http://www.plus.maths.org
www.mathsexams.ukteachers.com
http://www.maths-exams.com
http://mathworld.wolfram.com/
http://en.wikipedia.org/wiki/Main_Page
http://www.maths-exams.com/
http://www.stepmaths.tk/
http://www.rugbyschool.net/sl/academic/departments/maths/oxbridge.htm
http://www.maths.ox.ac.uk/prospective-students/undergraduate/background/
http://www.maths.ox.ac.uk/prospective-students/undergraduate/sutton/lecture2.pdf
http://www.maths.ox.ac.uk/prospective-students/undergraduate/sutton/lecture1.pdf
http://www.mat.bham.ac.uk/maths_extension/
http://www.thepaperbank.co.uk/
http://integrals.wolfram.com/index.jsp
http://www.bmoc.maths.org/home/bmo.shtml
http://www.srcf.ucam.org/~apd35/STEP/
I know my preparation may seem extensive but it wasn’t really like that. More a case of “I’m bored, let’s see what’s on TSR. Hmm Maclaurin’s series. What are they. Let’s check Mathworld. Hmm, that looks like that question I was trying to do earlier about sketching
…etc.”
Interviews: so people said to me you can’t really prepare for them. Evidently, I didn’t believe them, but once you get down there and meet the tutors and everything, it just doesn’t seem like they would care about all of the minutiae that everyone thinks is so important (e.g. OAF).
In general, they were quite fun actually. My advice is as follows:
Sort out any problems, however small, with your Maths teacher.
Look at the proofs of things that are blindly asserted in class / in textbooks.
Have an area of interest to talk about.
Get the Siklos STEP booklet.
Do some of the old Oxford Maths Tests from the 80's on www.mathsexams2.tk as well as obviously the ones on the Oxford website.
Be comfortable doing questions which look hard but are on things you know eg. differentiating e^e^cosx^e^x. It's just using the chain rule 3 times rather than one.
Also, knowing how to prove basic number theory is invaluable. There are tricks which you must learn like, proof by induction, contradiction, considering the cases of odd and even, modular arithmetic, writing odds as 2k+1 and evens as 2k etc. etc.
My advice would be to prepare as much as is going to make you feel most confident. Also, be calm. Most of the questions aren’t that hard.
EDIT: If you're applying to Oxford, the written test is really important to some tutors, they may place A LOT of emphasis on it.
Lastly, don’t just copy any of the personal statements or do any of the stuff I’ve done just for the sake of it. For a start, I only did this stuff because I enjoyed it (oh, how revision for C2 in January is making me realise that!!!). Secondly, I’m not even that good at Maths, there are some far better people on here than me (e.g. KaiserMole, Chewwy, even though he’s a year below me and loads more) and people much better placed to give you advice (e.g. Wrangler, RichE, Alphanumeric, ElChueco, Neapolitan and others) Everyone will tell you that you’ll only read stuff because it interests you. That’s not true, you’ll only remember stuff if it interests you. So do what you enjoy doing. Hopefully that should be loads of (but not too much!) Maths.
And that's it.
Good Luck next year!
PS – someone else can bump this later, when it becomes more relevant time-wise.
EDIT: Popa Dom's Personal Statement. I hope he doesn't mind me stealing it.
[INDENT]The idea of proof has always held a real fascination for me. The process of starting from a simple set of axioms and deriving almost any mathematical truth (putting Godel to one side) is what truly separates Mathematics from any other subject. It is the closest we can ever get to absolute truth, and therein lies its sheer beauty and the reason it is the only subject for me. Of course, it's also a good deal of fun.
I have tried to extend my Maths as much as possible beyond the classroom, and whenever I do so I uncover either some completely new and intriguing area of Mathematics or a very neat trick I hadn't thought of in more familiar territory. One example of this is my attendance at weekly lectures given by the department of Mathematics at Bristol University, covering topics from the Mathematics of juggling to quantum mechanics, although some of my favourites have been those on the less exotic "inequalities", which taught me a lot about thinking about problems creatively. I also attended a summer school run by the National Academy of Gifted and Talented Youth at the University of Durham, where I spent two weeks being introduced to various approachable first year undergraduate topics such as proof by induction, Markov chains and using Maple. This experience not only allowed me to discover areas of Mathematics I would not otherwise have encountered, but also gave me a small taste of university life, as there was a large number of us living in one of the colleges. I am also involved in the UKMT mentoring scheme, whereby each month I am given a sheet of questions in areas not touched on at A level, such as geometry and number theory, giving me a good opportunity to explore new mathematical ideas myself, and gain a much deeper appreciation of the interconnections within Mathematics and the creation of proofs. I am a member of the school's Maths team and we are regularly successful in competing against teams from other schools in the area. I also attend STEP sessions at local schools when available, as I find the questions much more interesting than the standard A level ones, and thinking about how to solve them has greatly improved my rigour in approaching problems.
Among the mathematical books I have read, I enjoyed "Godel, Escher, Bach", which gives a good grounding in axiomatic reasoning and formal systems, whilst at the same time pointing out their major flaw. I also liked "To infinity and beyond" by Eli Maor, which deals with the concept of infinity, its implications and its paradoxes, both in Maths and elsewhere.
I particularly enjoy the pure side of the A level syllabus, especially trigonometry and calculus, as they involve a certain degree of proof and introduce new concepts. I believe my other academic subjects all complement Mathematics as they are about finding ways of describing reality, be it through language in French or through equations and models in Physics and Chemistry. I find Critical Thinking especially relevant as it is about the construction of sound logical arguments, an art lying at the heart of Mathematics in proof. I have acheived an A grade in all modules across all my subjects.
In my spare time, I practise kickboxing, and have competed in various local competitions. As a volunteer, I am involved in a year seven Maths mentoring scheme and help at a homeless shelter. I enjoy travelling, and will be going to Nicaragua for a month after my A levels to help in a small village, explore the local jungles and volcanoes and practise my Spanish. I lived in France from the ages of 9 to 12, and learnt to adapt to a new language and culture.
I very much look forward to exploring the new ideas of University level Mathematics, and playing a full part in University life.
[/INDENT]
e-unit
Firstly, an introduction. I got an offer of AAA for Maths from Oxford nearly two weeks ago. When I was applying, I wanted all the information and help I could get so I thought I’d do everyone who is applying next year a favour and tell you (just about) everything I know. Actually, I’m really writing it because some people I talked to at interview had 100 people applying from their year at school and were getting all sorts of seminars and interview preparation, whilst others got nothing. At my school (independent) we get practically sod all, so I was tempted to be all “ I can find this stuff for myself, so anyone else can too” but hey, I need the rep. I’m writing it now because I can still actually remember it and because next year, I probably won’t care about applicants any more.
And there’s already a thread for 2007 applicants so some of you must be keen.Secondly, a disclaimer. I have an offer. I have not made my offer and may well not get the grades. I may get the grades, go to Oxford, decide I hate Maths, fail all my exams and be back here warning you all against it. I could go, love it but be crap at Maths and get kicked out. Hopefully not, but what I mean is don’t give anything I’ve said too much respect.
Ok, so attached should be:
• Some advice someone gave me
• A report someone on TSR wrote about their Cambridge interview (I hope they don’t mind me posting it!)
• Other people’s personal statements
• My personal statement
• What I wrote on the OAF
• A document with 100 (
) interview questions from http://www.oxbridge-admissions.org.uk/• Other, verbal interview questions (as opposed to mathematical problems)
• An article on the Philosophy of Maths (random)
• The Oxford, Cambridge and Imperial reading lists
• And various notes, some of which are posts from the TSR Maths forum
Some other stuff…
Books I read:
o A Very Short Introduction to Mathematics - Timothy Gowers
o The Man Who Loved Only Numbers – Paul Hoffman
o A Mathematician’s Apology – GH Hardy
o 1089 And All That – David Acheson
o (Some of) The Pleasures Of Counting – TW Körner
o (Some of) The Foundations of Mathematics – Stewart & Tall
o (Some of) The Music of the Primes – Marcus du Sautoy
o (Some of) The Emperor’s New Mind – Roger Penrose
Would I say that any of these were useful? My first thought would be no, most, if not all of my preparation was totally needless. However, at my interviews we did discuss Euclid’s proof of the infinitude of the primes (in 1089 And All That and A Very Short Introduction to Mathematics) and Cantor’s diagonal argument (in The Pleasures Of Counting). Also, they introduced me to concepts I couldn’t now imagine not knowing, like Euclid’s proof and proof by induction. So, these books specifically? Probably not that much (although most of them are on the reading lists) But being generally (mathematically) well-read? Definitely. A lot can be found on the internet
Useful Websites:
http://meikleriggs.org.uk
www.mathshelper.co.uk
http://www.mathsexams2.tk
http://www.nrich.maths.org
http://www.cut-the-knot.org
http://www.plus.maths.org
www.mathsexams.ukteachers.com
http://www.maths-exams.com
http://mathworld.wolfram.com/
http://en.wikipedia.org/wiki/Main_Page
http://www.maths-exams.com/
http://www.stepmaths.tk/
http://www.rugbyschool.net/sl/academic/departments/maths/oxbridge.htm
http://www.maths.ox.ac.uk/prospective-students/undergraduate/background/
http://www.maths.ox.ac.uk/prospective-students/undergraduate/sutton/lecture2.pdf
http://www.maths.ox.ac.uk/prospective-students/undergraduate/sutton/lecture1.pdf
http://www.mat.bham.ac.uk/maths_extension/
http://www.thepaperbank.co.uk/
http://integrals.wolfram.com/index.jsp
http://www.bmoc.maths.org/home/bmo.shtml
http://www.srcf.ucam.org/~apd35/STEP/
I know my preparation may seem extensive but it wasn’t really like that. More a case of “I’m bored, let’s see what’s on TSR. Hmm Maclaurin’s series. What are they. Let’s check Mathworld. Hmm, that looks like that question I was trying to do earlier about sketching
…etc.” Interviews: so people said to me you can’t really prepare for them. Evidently, I didn’t believe them, but once you get down there and meet the tutors and everything, it just doesn’t seem like they would care about all of the minutiae that everyone thinks is so important (e.g. OAF).
In general, they were quite fun actually. My advice is as follows:
Sort out any problems, however small, with your Maths teacher.
Look at the proofs of things that are blindly asserted in class / in textbooks.
Have an area of interest to talk about.
Get the Siklos STEP booklet.
Do some of the old Oxford Maths Tests from the 80's on www.mathsexams2.tk as well as obviously the ones on the Oxford website.
Be comfortable doing questions which look hard but are on things you know eg. differentiating e^e^cosx^e^x. It's just using the chain rule 3 times rather than one.
Also, knowing how to prove basic number theory is invaluable. There are tricks which you must learn like, proof by induction, contradiction, considering the cases of odd and even, modular arithmetic, writing odds as 2k+1 and evens as 2k etc. etc.
My advice would be to prepare as much as is going to make you feel most confident. Also, be calm. Most of the questions aren’t that hard.
EDIT: If you're applying to Oxford, the written test is really important to some tutors, they may place A LOT of emphasis on it.
Lastly, don’t just copy any of the personal statements or do any of the stuff I’ve done just for the sake of it. For a start, I only did this stuff because I enjoyed it (oh, how revision for C2 in January is making me realise that!!!). Secondly, I’m not even that good at Maths, there are some far better people on here than me (e.g. KaiserMole, Chewwy, even though he’s a year below me and loads more) and people much better placed to give you advice (e.g. Wrangler, RichE, Alphanumeric, ElChueco, Neapolitan and others) Everyone will tell you that you’ll only read stuff because it interests you. That’s not true, you’ll only remember stuff if it interests you. So do what you enjoy doing. Hopefully that should be loads of (but not too much!) Maths.
And that's it.
Good Luck next year!
PS – someone else can bump this later, when it becomes more relevant time-wise.
EDIT: Popa Dom's Personal Statement. I hope he doesn't mind me stealing it.
[INDENT]The idea of proof has always held a real fascination for me. The process of starting from a simple set of axioms and deriving almost any mathematical truth (putting Godel to one side) is what truly separates Mathematics from any other subject. It is the closest we can ever get to absolute truth, and therein lies its sheer beauty and the reason it is the only subject for me. Of course, it's also a good deal of fun.
I have tried to extend my Maths as much as possible beyond the classroom, and whenever I do so I uncover either some completely new and intriguing area of Mathematics or a very neat trick I hadn't thought of in more familiar territory. One example of this is my attendance at weekly lectures given by the department of Mathematics at Bristol University, covering topics from the Mathematics of juggling to quantum mechanics, although some of my favourites have been those on the less exotic "inequalities", which taught me a lot about thinking about problems creatively. I also attended a summer school run by the National Academy of Gifted and Talented Youth at the University of Durham, where I spent two weeks being introduced to various approachable first year undergraduate topics such as proof by induction, Markov chains and using Maple. This experience not only allowed me to discover areas of Mathematics I would not otherwise have encountered, but also gave me a small taste of university life, as there was a large number of us living in one of the colleges. I am also involved in the UKMT mentoring scheme, whereby each month I am given a sheet of questions in areas not touched on at A level, such as geometry and number theory, giving me a good opportunity to explore new mathematical ideas myself, and gain a much deeper appreciation of the interconnections within Mathematics and the creation of proofs. I am a member of the school's Maths team and we are regularly successful in competing against teams from other schools in the area. I also attend STEP sessions at local schools when available, as I find the questions much more interesting than the standard A level ones, and thinking about how to solve them has greatly improved my rigour in approaching problems.
Among the mathematical books I have read, I enjoyed "Godel, Escher, Bach", which gives a good grounding in axiomatic reasoning and formal systems, whilst at the same time pointing out their major flaw. I also liked "To infinity and beyond" by Eli Maor, which deals with the concept of infinity, its implications and its paradoxes, both in Maths and elsewhere.
I particularly enjoy the pure side of the A level syllabus, especially trigonometry and calculus, as they involve a certain degree of proof and introduce new concepts. I believe my other academic subjects all complement Mathematics as they are about finding ways of describing reality, be it through language in French or through equations and models in Physics and Chemistry. I find Critical Thinking especially relevant as it is about the construction of sound logical arguments, an art lying at the heart of Mathematics in proof. I have acheived an A grade in all modules across all my subjects.
In my spare time, I practise kickboxing, and have competed in various local competitions. As a volunteer, I am involved in a year seven Maths mentoring scheme and help at a homeless shelter. I enjoy travelling, and will be going to Nicaragua for a month after my A levels to help in a small village, explore the local jungles and volcanoes and practise my Spanish. I lived in France from the ages of 9 to 12, and learnt to adapt to a new language and culture.
I very much look forward to exploring the new ideas of University level Mathematics, and playing a full part in University life.
[/INDENT]
e-unit
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There seems to be no attachment in this post.
Neapolitan
There seems to be no attachment in this post.
Cheers. It's added now, I hope it works. I also added you to my post. I knew I was forgetting one of the senior mathematicians.
www.stepmaths.tk is another good link.
A book that I enjoyed and found helpful which wasn't on the reading list was Prime Obsession: The History of the Greatest Unsolved Problem in Mathematics by John Derbyshire. This is a book about the Reimann Hypothesis which alternates a history of it with a mathematical explanation of why mathematicians care about it and its relationship to prime numbers. It's a good read and accessible with AS (I think) level maths but reaches a long way with that maths. It also provides a number of little tidbits of maths if you're asked to say something you've studied in an interview, such as proving ∑(1/ns)=π(1-p-s)-1 (this is the Euler Product formula, where n are the natural numbers and p are the primes, and is the first step to deeper results about the Reimann Zeta Function (which is what the Reimann Hypothesis is about) and the primes.
Ben
Ben
Jonny W
www.stepmaths.tk is another good link.
I'd say that http://www.maths-exams.com/ is also an extremely good resource and has many more papers.
fabulous stuff, Wikipedia and Mathworld are excellent reference sites too....other than that I am keeping quiet for the time being, will have to see what the postman brings!
AlphaX
Good luck with everything! I hope you get what you want!
cheers
- Here's hoping (hehe, my names mentioned in the thread, makes me feel a bit bashful)
AlphaX
happy mathmo
With luck KM will out-happy you with tomorrow's post!
Hiho, hihocinders1288
thread starter you are my hero! i love you to bits! fantastic advice!
rep coming up right now
rep coming up right now
Oooh. A revival. How exciting.
Anyone else can add stuff if they feel like it, and I'll edit it into the original post.
A decent website i found only days after finishing mods exam (which included loads of real analysis)
http://web01.shu.edu/projects/reals/reals.html
This link covers 3 of the 15 first year courses, and is easy to follow so would be a massive help to anyone coming in october.
Edit: This post is targeted towardsm oxford students, i dont know other uni courses
http://web01.shu.edu/projects/reals/reals.html
This link covers 3 of the 15 first year courses, and is easy to follow so would be a massive help to anyone coming in october.
Edit: This post is targeted towardsm oxford students, i dont know other uni courses
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