The difference between a 2:1 and a First with regards to career opportunities?
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Original post by Jake22
Model solutions are awful - they don't tell you if there is a flaw in your proof, they tell you here is someone else's proof and 99% of the time people just believe it without checking it. They teach you nothing and detract from your mathematical education.
Model solutions are awful - they don't tell you if there is a flaw in your proof, they tell you here is someone else's proof and 99% of the time people just believe it without checking it. They teach you nothing and detract from your mathematical education.
That really does depend on how you use them. I try to solve example questions on my own. If I succeed, I read the model solution to see if there was a different way about it. If it's the same as my method, I can use the model solution to look for a better way of phrasing the ideas behind the answer.
If I get stuck with a question, I can skim the first bit of the model solution to try to pick up the first idea. Then I try and fill in the rest. Sometimes I will still be unable to do it, in which case I learn the ideas of the model solution and try to come back to it another time.
If your instinctive reaction to having a list of solutions available is to read them without trying to solve the question on your own, then you will find a maths degree tricky.
Original post by IrrationalNumber
That really does depend on how you use them. I try to solve example questions on my own. If I succeed, I read the model solution to see if there was a different way about it. If it's the same as my method, I can use the model solution to look for a better way of phrasing the ideas behind the answer.
If I get stuck with a question, I can skim the first bit of the model solution to try to pick up the first idea. Then I try and fill in the rest. Sometimes I will still be unable to do it, in which case I learn the ideas of the model solution and try to come back to it another time.
If your instinctive reaction to having a list of solutions available is to read them without trying to solve the question on your own, then you will find a maths degree tricky.
If I get stuck with a question, I can skim the first bit of the model solution to try to pick up the first idea. Then I try and fill in the rest. Sometimes I will still be unable to do it, in which case I learn the ideas of the model solution and try to come back to it another time.
If your instinctive reaction to having a list of solutions available is to read them without trying to solve the question on your own, then you will find a maths degree tricky.
Yes but I think the majority (especially the majority that complain about the absence of model solutions) use them as per your last sentence. I still think the practice of actually looking up something similar somewhere in a book etc. is actually better for you.
Original post by Physics Enemy
Once you're cornered to forking out money to jump through hoops, when you know full well you could self learn for little cost, then it becomes a job factory in the eyes of many. I pay the money, I expect the goods; if you don't want to provide, then abolish the fees and/or get rid of employer's banal middle-class requirements.
This is exactly my point. I hate the direction new labour took us with this starting in the late nineties. I think they may have destroyed something brilliant.
It is also worth noting that the employers' banal requirements are totally linked in with the high uptake of university. All this business of this mysterious collective of 'employers' requiring every man and his dog to take an economics degree or whatever is part of the same propoganda machine set forth to ensure that 50% of school leavers go to university which, let's face it, was a temporary measure to reduce unemployment.
This is why I distanced myself from the student protests about fee increases - I can't agree with them because I just fundamentally disagree with the whole system of funding and fees and the changes that have been enacted since 1997.
(edited 13 years ago)
Original post by Kaloo
For maths modules you need past papers. You could learn everything about a topic to a first class level, but find yourself unable to spot what the question is trying to get you to do in the exam or how to apply what you know then you're not going to do very good.
Only if you are either a weak student in which case you shouldn't be there in the first place or should be naturally weeded out by the exam process OR you are a capable student but you can't be bothered to try and understand the point of a course or the material within. Or perhaps you are an otherwise potentially great student who has been misled into thinking that the point of university is anything other than to improve one's knowledge, understanding and capacity to learn.
Original post by Jake22
This is exactly my point. I hate the direction new labour took us with this starting in the late nineties. I think they may have destroyed something brilliant.
It is also worth noting that the employers' banal requirements are totally linked in with the high uptake of university. All this business of this mysterious collective of 'employers' requiring every man and his dog to take an economics degree or whatever is part of the same propoganda machine set forth to ensure that 50% of school leavers go to university which, let's face it, was a temporary measure to reduce unemployment.
This is why I distanced myself from the student protests about fee increases - I can't agree with them because I just fundamentally disagree with the whole system of funding and fees and the changes that have been enacted since 1997.
It is also worth noting that the employers' banal requirements are totally linked in with the high uptake of university. All this business of this mysterious collective of 'employers' requiring every man and his dog to take an economics degree or whatever is part of the same propoganda machine set forth to ensure that 50% of school leavers go to university which, let's face it, was a temporary measure to reduce unemployment.
This is why I distanced myself from the student protests about fee increases - I can't agree with them because I just fundamentally disagree with the whole system of funding and fees and the changes that have been enacted since 1997.
I totally agree with you on all points. University is a place where one pays fees, gets drunk, rote learns model answers to pass the exams; all in order to jump through banal employer hoops (only adopted to cull application numbers, rather than necessity) and for the middle-class student experience.
I laugh at these 'any degree' jobs that are now so prevelant. A nice way of saying that little to no specific skills/ability are required, but they want to see a generic (yet expensive) piece of paper anyway. They could just take people who are middle class based on their school/area and be done with it.
(edited 13 years ago)
Jake22
x
I disagree: I, like IrrationalNumber, use examples etc to understand and check my own working and in that sense they are necessary. Face it; the people who write these things are experts, anyone who has self taught will tell you it can be very difficult to comprehend something without a methodology clearly displayed. Add in actual teaching and it becomes 10x easier. Plus I find it hard to believe someone who is willing to study maths at uni will effectively cheat
Original post by Jake22
Only if you are either a weak student in which case you shouldn't be there in the first place or should be naturally weeded out by the exam process OR you are a capable student but you can't be bothered to try and understand the point of a course or the material within. Or perhaps you are an otherwise potentially great student who has been misled into thinking that the point of university is anything other than to improve one's knowledge, understanding and capacity to learn.
DFranklyn was saying something about how Cambridge exams are so hard in the past that there was no easy marks. No marks for bookwork(which would be rewarded by just doing past papers and reading notes). He said that was wrong and that he knew someone who was really bright and failed because of that.
I don't think it will be better to have a exams like that. Although, I wouldn't be disadvantaged by it. However, I know some bright people that do well because they do a ton of example sheets and do past papers a lot.
This is exactly my point. I hate the direction new labour took us with this starting in the late nineties. I think they may have destroyed something brilliant.
It is also worth noting that the employers' banal requirements are totally linked in with the high uptake of university. All this business of this mysterious collective of 'employers' requiring every man and his dog to take an economics degree or whatever is part of the same propoganda machine set forth to ensure that 50% of school leavers go to university which, let's face it, was a temporary measure to reduce unemployment.
This is why I distanced myself from the student protests about fee increases - I can't agree with them because I just fundamentally disagree with the whole system of funding and fees and the changes that have been enacted since 1997.
It is also worth noting that the employers' banal requirements are totally linked in with the high uptake of university. All this business of this mysterious collective of 'employers' requiring every man and his dog to take an economics degree or whatever is part of the same propoganda machine set forth to ensure that 50% of school leavers go to university which, let's face it, was a temporary measure to reduce unemployment.
This is why I distanced myself from the student protests about fee increases - I can't agree with them because I just fundamentally disagree with the whole system of funding and fees and the changes that have been enacted since 1997.
You can't blame everything on labour. Certainly, all conservatives are doing is increasing them.
That is twisting words. The point was that 50% had some extra training more like apprenticeships. Also, uni in the past sucks as you would have to be rich. Paul Dirac was refused entry into Cambridge the first time round because he couldn't afford tuition fees, you really want something like that again.
What would you replace it with? No fees? Only rich going to uni? Only people who you consider smart going to uni?
Original post by Simplicity
DFranklyn was saying something about how Cambridge exams are so hard in the past that there was no easy marks. No marks for bookwork(which would be rewarded by just doing past papers and reading notes). He said that was wrong and that he knew someone who was really bright and failed because of that.
Well it was harder back then, and ideally academia should be hard. He either didn't study enough, or did study enough but wasn't as bright as the other students (but still obv very bright to be doing Maths at Cam).
Original post by Simplicity
I don't think it will be better to have a exams like that. Although, I wouldn't be disadvantaged by it. However, I know some bright people that do well because they do a ton of example sheets and do past papers a lot.
If someone does well only because they rote learn model solutions and notes, they aren't bright. Any talentless grafter or nerd can do that. I doubt you could do the 'clever thinking type Maths' either, you've only done bookwork exams and Maths. If you could, why didn't you go to Cambridge or MIT like DFranklin?
Original post by Simplicity
You can't blame everything on labour. Certainly, all conservatives are doing is increasing them.
Irrespective of what Conservatives do or don't, he can still blame Labour if he makes credible points.
Original post by Simplicity
That is twisting words. The point was that 50% had some extra training more like apprenticeships. Also, uni in the past sucks as you would have to be rich. Paul Dirac was refused entry into Cambridge the first time round because he couldn't afford tuition fees, you really want something like that again.
Extra training in totally unecessary and unrelated disciplines though, and to a declining standard as well. Rendering it a waste of time and money, especially with the recession. I agree that uni in the past was too money orientated, but it isn't a whole lot different now. It's a middle class job factory effectively.
Original post by Simplicity
What would you replace it with? No fees? Only rich going to uni? Only people who you consider smart going to uni?
Courses that can and ideally are best self taught don't need to exist in these overly large and costly campuses. We may need smaller unis for engineering and doctors etc. I think exam centres should exist where people can sit any exam they like, at a set fee, when they're ready and willing. GCSE, A-Level, whatever.
Original post by Physics Enemy
Well it was harder back then, and ideally academia should be hard. He either didn't study enough, or did study enough but wasn't as bright as the other students (but still obv very bright to be doing Maths at Cam).
Ask DFranklyn. He was convinced that the person couldn't have worked harder. I was sort of hoping he would have posted in here, pretty sure he watches this thread.
If you looked at the history of the tripos it wasn't good. Hardy wrote something like he was going to drop out and that he was rote learning how to do questions. If you really want the full text I can get you it. But, he was talking about how he had to learn tricks and jump through hoops.
Original post by Physics Enemy
If someone does well only because they rote learn model solutions and notes, they aren't bright. Any talentless grafter or nerd can do that. I doubt you could do the 'clever thinking type Maths' either, you've only done bookwork exams and Maths. If you could, why didn't you go to Cambridge or MIT like DFranklin?
I disagree. Surely learning is a important part of intelligence. Talentless grafters are better than wasted so called geniuses.
I remember a thread like this. Was you arguing that STEP was the greatest thing ever? As I can quote Warwick professor not being able to do Olympiad problems.
Why I didn't apply for Cambridge is because I made a lot of mistakes in the past and I'm 2 years older than everyone else in my position I.e. applying to uni at 19 instead of 17. I originally planned to do art.
Original post by Physics Enemy
Irrespective of what Conservatives do or don't, he can still blame Labour if he makes credible points.
Extra training in totally unecessary and unrelated disciplines though, and to a declining standard as well. Rendering it a waste of time and money, especially with the recession. I agree that uni in the past was too money orientated, but it isn't a whole lot different now. It's a middle class job factory effectively.
Courses that can and ideally are best self taught don't need to exist in these overly large and costly campuses. We may need smaller unis for engineering and doctors etc. I think exam centres should exist where people can sit any exam they like, at a set fee, when they're ready and willing. GCSE, A-Level, whatever.
Extra training in totally unecessary and unrelated disciplines though, and to a declining standard as well. Rendering it a waste of time and money, especially with the recession. I agree that uni in the past was too money orientated, but it isn't a whole lot different now. It's a middle class job factory effectively.
Courses that can and ideally are best self taught don't need to exist in these overly large and costly campuses. We may need smaller unis for engineering and doctors etc. I think exam centres should exist where people can sit any exam they like, at a set fee, when they're ready and willing. GCSE, A-Level, whatever.
I don't see his point. Just some rant about labour.
Don't see how training is bad. The uni's of the past were crap. I see fees like this as the optimum way.
That's stupid. Again, I've learnt a lot from lecturers by talking to them and other students. Granted, I have to pay for it, but that's okay.
(edited 13 years ago)
Original post by alexs2602
I disagree: I, like IrrationalNumber, use examples etc to understand and check my own working and in that sense they are necessary. Face it; the people who write these things are experts, anyone who has self taught will tell you it can be very difficult to comprehend something without a methodology clearly displayed. Add in actual teaching and it becomes 10x easier. Plus I find it hard to believe someone who is willing to study maths at uni will effectively cheat
My point was to differentiate between a worked example and model solutions to homework questions. I think it would do people better to have to go to the library and find a similar worked example in a book and modify it to their problem rather than just have solutions to exercises.
I think it is great practice for mathematics, in particular for building confidence to just try the exercises and see what you can do. Otherwise, there is too much sniffing at spelt out lecture notes and past exams and not enough actual, god forbid, thinking going on
Original post by Simplicity
Ask DFranklyn. He was convinced that the person couldn't have worked harder. I was sort of hoping he would have posted in here, pretty sure he watches this thread.
If you looked at the history of the tripos it wasn't good. Hardy wrote something like he was going to drop out and that he was rote learning how to do questions. If you really want the full text I can get you it. But, he was talking about how he had to learn tricks and jump through hoops.
If you looked at the history of the tripos it wasn't good. Hardy wrote something like he was going to drop out and that he was rote learning how to do questions. If you really want the full text I can get you it. But, he was talking about how he had to learn tricks and jump through hoops.
To me it just sounds like the Tripos was really hard. There's always going to be an element of rote learning that can save you a bit, but the 'best' exams don't really depend on that, since they're supposed to test other things. IMO anyway.
Simplicity
I disagree. Surely learning is a important part of intelligence. Talentless grafters are better than wasted so called geniuses.
Better in the sense they do the work, instead of lazing about and wasting their ability, but not because they're smarter or more likely to solve a hard problem. If a system was adopted to reward IQ and innovative flashes of brilliance, then they wouldn't even be seen as better in any light. And in many areas, that is what is rewarded infact. You're right I've had this discussion before.
Simplicity
I remember a thread like this. Was you arguing that STEP was the greatest thing ever? As I can quote Warwick professor not being able to do Olympiad problems.
As usual, often when people try and make a counter-claim, the cheap tactic is to overstate my point until it sounds ridiculous (not you, happened in the other thread). My point was that talent and raw ability should be valued more, and I was fully in favour of things like AEA, STEP, BMO, IMO etc which tests 'clever thinking Maths' as I call it, that really stretch people and identify the clever ones. Not the bookwork/slog type of exams that test hours spent memorising.
If the Warwick professor can't do Olympiad problems (which very bright teens / young adults can do), then I think that speaks volumes. Perhaps he's stuck at Maths long enough and learnt enough material to get a Masters, PhD etc but maybe doesn't have that raw ability and high intelligence to figure out the really hard problems. I don't see why he should be excused on the basis of other credentials that don't test the same things; if he's good enough then he should be able to do the problems.
Simplicity
Why I didn't apply for Cambridge is because I made a lot of mistakes in the past and I'm 2 years older than everyone else in my position I.e. applying to uni at 19 instead of 17. I originally planned to do art.
That's fair enough, but there's nothing stopping you applying to Cambridge at age 19. It's not like it's a big difference in the grand scheme of things, or in the eyes of tutors. If you're good enough you'd get a STEP offer and then hopefully get the 1, 1. My point is, it's quite arrogant to assume you wouldn't be phased by very hard Maths Qs and thinking type stuff, when they're meant to stretch the brightest. The least you should do is have a legit go (ideally in exam conditions!) before commenting.
Simplicity
I don't see his point. Just some rant about labour.
Probably that it's resulted in universities becoming a job factory for the middle classes, rather than an arena for education. Education has been devalued, and now uni is just a hoop you need to jump through to meet an employer's tick-box criteria. Well, that's how it's perceived by the masses anyway. But then these make up the numbers.
Simplicity
That's stupid. Again, I've learnt a lot from lecturers by talking to them and other students. Granted, I have to pay for it, but that's okay.
You shouldn't need to pay thousands to talk to people. You aren't paying anyone on here. I doubt DFranklin would charge you to skype with him. Or RichE.
(edited 13 years ago)
Original post by Physics Enemy
To me it just sounds like the Tripos was really hard. There's always going to be an element of rote learning that can save you a bit, but the 'best' exams don't really depend on that, since they're supposed to test other things. IMO anyway.
Nah, you misread. GH Hardy said the exam was based only on tricks and that the best Mathematician didn't get the highest grades. http://www.vukutu.com/blog/2010/11/hardy-on-the-tripos/
Granted, I'm sure Cambridge has reformed itself.
Original post by Physics Enemy
Better in the sense they do the work, instead of lazing about and wasting their ability, but not because they're smarter or more likely to solve a hard problem. If a system was adopted to reward IQ and innovative flashes of brilliance, then they wouldn't even be seen as better in any light. And in many areas, that is what is rewarded infact. You're right I've had this discussion before.
Huh?
Original post by Physics Enemy
As usual, often when people try and make a counter-claim, the cheap tactic is to overstate my point until it sounds ridiculous (not you, happened in the other thread). My point was that talent and raw ability should be valued more, and I was fully in favour of things like AEA, STEP, BMO, IMO etc which tests 'clever thinking Maths' as I call it, that really stretch people and identify the clever ones. Not the bookwork/slog type of exams that test hours spent memorising.
You didn't answer the last thread. But, STEP, AEA, BMO, IMO are testing crappy knowledge. Even if someone was great at them if they was only tested on that they would be reinventing the wheel. As was said doing STEP is unlikely to lead the person to invent topology. The problem is that Maths is so advanced now that learning or as you call it memorization is a key skill. Certainly, it stupid being a genius at group theory and not knowing for example about symmetrical groups because you are lazy to learn it.
Original post by Physics Enemy
If the Warwick professor can't do Olympiad problems (which very bright teens / young adults can do), then I think that speaks volumes. Perhaps he's stuck at Maths long enough and learnt enough material to get a Masters, PhD etc but maybe doesn't have that raw ability and high intelligence to figure out the really hard problems. I don't see why he should be excused on the basis of other credentials that don't test the same things; if he's good enough then he should be able to do the problems.
http://www.warwick.ac.uk/~masbm/PCAPP/Events/Discussion/ma4.html
I would wager that few if any Warwick students without quite some prior training in solving IMO style problems could solve this within a week of seeing it. (I tend not to wager ever unless I am absolutely confident of winning the wager - I am a mathematician after all.)
I think such a course would be doomed to failure, and certainly would not be seen by the students as either "fun" or "easy".
(As an aside, at the institution where I did my undergraduate degree, the vast majority of the professional mathematicians there were unable to solve such problems without a full day's work - olympiad participants are given about 1.5 hours per problem. :-) )
I think such a course would be doomed to failure, and certainly would not be seen by the students as either "fun" or "easy".
(As an aside, at the institution where I did my undergraduate degree, the vast majority of the professional mathematicians there were unable to solve such problems without a full day's work - olympiad participants are given about 1.5 hours per problem. :-) )
Olympiad problems are garbage with little relevance to real Mathematics. It's stupid to define raw talent on it. As said above Warwick students would have trouble doing them, but Warwick is the 3rd Best uni for Maths with student who have done STEP. It's stupid to judge talent on stupid competition.
Original post by Physics Enemy
That's fair enough, but there's nothing stopping you applying to Cambridge at age 19. It's not like it's a big difference in the grand scheme of things, or in the eyes of tutors. If you're good enough you'd get a STEP offer and then hopefully get the 1, 1. My point is, it's quite arrogant to assume you wouldn't be phased by very hard Maths Qs and thinking type stuff, when they're meant to stretch the brightest. The least you should do is have a legit go (ideally in exam conditions!) before commenting.
Might try and get into it for PhD. Their was other factors, like messing up on D1 and being predicted stupid grades(B for further maths, note I got an A in this). I doubt they produce the brightest(it's sort of like producing a diet plan for a tall skinny women model for them to lose weight, you can't really go wrong). To be fair, I doubt the uni matters you should do most of the stuff by yourself. On Maths Qs, I don't see Maths that way it isn't a problem or sort of prove this, more like developing ideas and being creative. Not can you do this stupid problem. Technically, I'm really weak student(in the sense problem solving skills are really crap) and I rely more on logic and deducing stuff from simpler stuff or axioms, even worse I purposely forget stuff.
Original post by Physics Enemy
Probably that it's resulted in universities becoming a job factory for the middle classes, rather than an arena for education. Education has been devalued, and now uni is just a hoop you need to jump through to meet an employer's tick-box criteria. Well, that's how it's perceived by the masses anyway. But then these make up the numbers.
You shouldn't need to pay thousands to talk to people. You aren't paying anyone on here. I doubt DFranklin would charge you to skype with him. Or RichE.
You shouldn't need to pay thousands to talk to people. You aren't paying anyone on here. I doubt DFranklin would charge you to skype with him. Or RichE.
You really don't believe in education, you believe in some sort of romantic genius idea.
That's different. To be fair, I learn weird(like not being able to read Langs algebra, then suddenly a month later I understand it), however for the average person a structured approach of tutorials and doing example sheets, plus a exam is the best way. For the average person, not your so called romantic ideal that is like 0.0000000001% of the population.
(edited 13 years ago)
Original post by Simplicity
Nah, you misread. GH Hardy said the exam was based only on tricks and that the best Mathematician didn't get the highest grades. http://www.vukutu.com/blog/2010/11/hardy-on-the-tripos/
What else is an exam meant to be on? It's either book work or spotting clever ways of answering tricky Qs (or a combo of the two). What else did he expect? I don't get why the 'best mathmo' wouldn't be able to do this like the other best students. If he can't, maybe re-think the idea of 'best'?
Original post by Simplicity
Huh?
Working hard and ability are two different things, in short.
Original post by Simplicity
You didn't answer the last thread. But, STEP, AEA, BMO, IMO are testing crappy knowledge. Even if someone was great at them if they was only tested on that they would be reinventing the wheel. As was said doing STEP is unlikely to lead the person to invent topology. The problem is that Maths is so advanced now that learning or as you call it memorization is a key skill. Certainly, it stupid being a genius at group theory and not knowing for example about symmetrical groups because you are lazy to learn it.
What do you mean by crappy knowledge? The beauty of Maths lies in solving a huge array of complex problems with relatively basic Maths, relying on intuition and ingenuity in applying it. I don't see the point of learning Maths (or anything) if you can't apply it well, and in unfamiliar situations. And indeed can't solve tricky problems using Maths you already know, or is 'easier' than the current material you know. What's the point? Doesn't make you a better Mathematician.
Yes I read it. That goes to show how hard IMO problems are, even using relatively basic Maths. It's not about material. Anyone can rote learn stuff or remember formulae. The ingenuity in applying is the real discriminator.
Original post by Simplicity
Olympiad problems are garbage with little relevance to real Mathematics. It's stupid to define raw talent on it. As said above Warwick students would have trouble doing them, but Warwick is the 3rd Best uni for Maths with student who have done STEP. It's stupid to judge talent on stupid competition.
This doesn't make any sense. A problem is a problem, people either solve it or they don't. Hard problems have more credibility for the obvious reason that they're hard. It's not a qualitative thing. And trying to pick and choose what problems to solve is a very cheap and easy copout from running from the tough problems. In no other discipline I can think of, is there any dream in running away from the things people find hard. Tackling it is usually the aim.
Warwick students couldn't do them in a week (as the guy describes) because these types of problems are designed for the best students, and they're the ones at Cambridge and MIT, the top ones at these unis, not just the 'average' Cam Mathmo either. I think it's good though that Warwick are trying to incorporate IMO problems in their course though (if they are?). Thumbs up if true.
Original post by Simplicity
You really don't believe in education, you believe in some sort of romantic genius idea.
I see education as equipping someone with skills, so they become 'enhanced', mentally. So helping someone to think better outside the box, or developing intuition and flair, developing good insight into solving problems, clarity of thought and expression, strong focus, etc. So not really material per se, but moreso skills. I also believe in stretching and competition, hence why I have respect for those types of papers. I think a Professor (or anyone) who can't solve certain difficult Maths problems but goes on to rubbish them, is in denial.
Simplicity
That's different. To be fair, I learn weird(like not being able to read Langs algebra, then suddenly a month later I understand it), however for the average person a structured approach of tutorials and doing example sheets, plus a exam is the best way. For the average person, not your so called romantic ideal that is like 0.0000000001% of the population.
That's learning to pass exams for the sake of passing exams. If they went on holiday for a few months, and you asked them to answer those Qs again, they wouldn't know what to do. That's called memorization, not understanding/skills.
Original post by Jake22
Only if you are either a weak student in which case you shouldn't be there in the first place or should be naturally weeded out by the exam process OR you are a capable student but you can't be bothered to try and understand the point of a course or the material within. Or perhaps you are an otherwise potentially great student who has been misled into thinking that the point of university is anything other than to improve one's knowledge, understanding and capacity to learn.
Maybe you do a degree in pure maths and your questions pretty much tell you what operations to do. In my maths based exams I have to find the link between the case and the theory before I can even think about answering the question. This takes time and is the only reason why it is beneficial to do past papers for me... so I can gauge what is expected from me in a question straight away. I'm not talking about simple differentiation/matrix type stuff.
Original post by Kaloo
Maybe you do a degree in pure maths and your questions pretty much tell you what operations to do.
No, maths exams aren't just calculations. Your knowledge of the material and experience of it (plus general mathematical maturity) guides you as to which techniques may be beneficial in answering a given question.
Original post by Physics Enemy
What else is an exam meant to be on? It's either book work or spotting clever ways of answering tricky Qs (or a combo of the two). What else did he expect? I don't get why the 'best mathmo' wouldn't be able to do this like the other best students. If he can't, maybe re-think the idea of 'best'?
Working hard and ability are two different things, in short.
What do you mean by crappy knowledge? The beauty of Maths lies in solving a huge array of complex problems with relatively basic Maths, relying on intuition and ingenuity in applying it. I don't see the point of learning Maths (or anything) if you can't apply it well, and in unfamiliar situations. And indeed can't solve tricky problems using Maths you already know, or is 'easier' than the current material you know. What's the point? Doesn't make you a better Mathematician.
Yes I read it. That goes to show how hard IMO problems are, even using relatively basic Maths. It's not about material. Anyone can rote learn stuff or remember formulae. The ingenuity in applying is the real discriminator.
This doesn't make any sense. A problem is a problem, people either solve it or they don't. Hard problems have more credibility for the obvious reason that they're hard. It's not a qualitative thing. And trying to pick and choose what problems to solve is a very cheap and easy copout from running from the tough problems. In no other discipline I can think of, is there any dream in running away from the things people find hard. Tackling it is usually the aim.
Warwick students couldn't do them in a week (as the guy describes) because these types of problems are designed for the best students, and they're the ones at Cambridge and MIT, the top ones at these unis, not just the 'average' Cam Mathmo either. I think it's good though that Warwick are trying to incorporate IMO problems in their course though (if they are?). Thumbs up if true.
I see education as equipping someone with skills, so they become 'enhanced', mentally. So helping someone to think better outside the box, or developing intuition and flair, developing good insight into solving problems, clarity of thought and expression, strong focus, etc. So not really material per se, but moreso skills. I also believe in stretching and competition, hence why I have respect for those types of papers. I think a Professor (or anyone) who can't solve certain difficult Maths problems but goes on to rubbish them, is in denial.
That's learning to pass exams for the sake of passing exams. If they went on holiday for a few months, and you asked them to answer those Qs again, they wouldn't know what to do. That's called memorization, not understanding/skills.
Working hard and ability are two different things, in short.
What do you mean by crappy knowledge? The beauty of Maths lies in solving a huge array of complex problems with relatively basic Maths, relying on intuition and ingenuity in applying it. I don't see the point of learning Maths (or anything) if you can't apply it well, and in unfamiliar situations. And indeed can't solve tricky problems using Maths you already know, or is 'easier' than the current material you know. What's the point? Doesn't make you a better Mathematician.
Yes I read it. That goes to show how hard IMO problems are, even using relatively basic Maths. It's not about material. Anyone can rote learn stuff or remember formulae. The ingenuity in applying is the real discriminator.
This doesn't make any sense. A problem is a problem, people either solve it or they don't. Hard problems have more credibility for the obvious reason that they're hard. It's not a qualitative thing. And trying to pick and choose what problems to solve is a very cheap and easy copout from running from the tough problems. In no other discipline I can think of, is there any dream in running away from the things people find hard. Tackling it is usually the aim.
Warwick students couldn't do them in a week (as the guy describes) because these types of problems are designed for the best students, and they're the ones at Cambridge and MIT, the top ones at these unis, not just the 'average' Cam Mathmo either. I think it's good though that Warwick are trying to incorporate IMO problems in their course though (if they are?). Thumbs up if true.
I see education as equipping someone with skills, so they become 'enhanced', mentally. So helping someone to think better outside the box, or developing intuition and flair, developing good insight into solving problems, clarity of thought and expression, strong focus, etc. So not really material per se, but moreso skills. I also believe in stretching and competition, hence why I have respect for those types of papers. I think a Professor (or anyone) who can't solve certain difficult Maths problems but goes on to rubbish them, is in denial.
That's learning to pass exams for the sake of passing exams. If they went on holiday for a few months, and you asked them to answer those Qs again, they wouldn't know what to do. That's called memorization, not understanding/skills.
I've noticed lots of olympiad people have ridiculous postcounts on Nrich. The only possible entertainment you could get on that site is maths. If there's any humour or personality, it's terrible. The site looks very boring, and the main sections are all maths, most of the others are maths related. Lots of their posts are also on olympiad problems. It's also easy to find textbooks and past papers geared towards preparing for these competitions, and lots of these posters mention these books.
A post on that site from someone who's actually studied properly for olympiads claimed that the inequalities were "monkey see, monkey do": you're just copying the techniques in the solution to a similar inequality a lot of the time.
If you'd seen "Beautiful Young Minds", you'd know that one competitor in IMO claimed "this has been my life for the last" however many "years".
If that's not a "bookwork nerd", I don't know what is.
This argument that uni would test intelligence better if you weren't "spoonfed" doesn't work. If you weren't given the stuff to learn, the people getting the high grades would just be the hard working nerds who would spend their own time looking stuff up, while the intelligent but lazy people wouldn't bother so would get low grades.
Someone getting higher grades than you in maths class where you've both been trained equally (say at school) probably does mean they're more intelligent. But I think you can say less at uni or with olympiads, since the effort you put in in spare time plays more of a role, and attendance at lectures and tutorials isn't taken so seriously. I don't think lecture attendance at my uni is monitored. I reckon you could potentially have the brightest person getting a 2:1 at an average uni, precisely because there isn't enough "spoonfeeding" (note: I'm not at an average uni, and I'm not heading for a 2:1 right now, so I'm not trying to cover for myself here).
(edited 13 years ago)
Original post by schoolstudent
I've noticed lots of olympiad people have ridiculous postcounts on Nrich. The only possible entertainment you could get on that site is maths. If there's any humour or personality, it's terrible. The site looks very boring, and the main sections are all maths, most of the others are maths related. Lots of their posts are also on olympiad problems. It's also easy to find textbooks and past papers geared towards preparing for these competitions, and lots of these posters mention these books.
A post on that site from someone who's actually studied properly for olympiads claimed that the inequalities were "monkey see, monkey do": you're just copying the techniques in the solution to a similar inequality a lot of the time.
If you'd seen "Beautiful Young Minds", you'd know that one competitor in IMO claimed "this has been my life for the last" however many "years".
If that's not a "bookwork nerd", I don't know what is.
This argument that uni would test intelligence better if you weren't "spoonfed" doesn't work. If you weren't given the stuff to learn, the people getting the high grades would just be the hard working nerds who would spend their own time looking stuff up, while the intelligent but lazy people wouldn't bother so would get low grades.
Someone getting higher grades than you in maths class where you've both been trained equally (say at school) probably does mean they're more intelligent. But I think you can say less at uni or with olympiads, since the effort you put in in spare time plays more of a role, and attendance at lectures and tutorials isn't taken so seriously. I don't think lecture attendance at my uni is monitored. I reckon you could potentially have the brightest person getting a 2:1 at an average uni, precisely because there isn't enough "spoonfeeding" (note: I'm not at an average uni, and I'm not heading for a 2:1 right now, so I'm not trying to cover for myself here).
A post on that site from someone who's actually studied properly for olympiads claimed that the inequalities were "monkey see, monkey do": you're just copying the techniques in the solution to a similar inequality a lot of the time.
If you'd seen "Beautiful Young Minds", you'd know that one competitor in IMO claimed "this has been my life for the last" however many "years".
If that's not a "bookwork nerd", I don't know what is.
This argument that uni would test intelligence better if you weren't "spoonfed" doesn't work. If you weren't given the stuff to learn, the people getting the high grades would just be the hard working nerds who would spend their own time looking stuff up, while the intelligent but lazy people wouldn't bother so would get low grades.
Someone getting higher grades than you in maths class where you've both been trained equally (say at school) probably does mean they're more intelligent. But I think you can say less at uni or with olympiads, since the effort you put in in spare time plays more of a role, and attendance at lectures and tutorials isn't taken so seriously. I don't think lecture attendance at my uni is monitored. I reckon you could potentially have the brightest person getting a 2:1 at an average uni, precisely because there isn't enough "spoonfeeding" (note: I'm not at an average uni, and I'm not heading for a 2:1 right now, so I'm not trying to cover for myself here).
You make some very good points, which I agree with. Regarding uni, if they changed the system they'd have to change the nature of the papers, making the nerds flounder as they couldn't wrote learn it. You're right about a lot of the IMO competitors, and it definitely put a dampener on things. I guess the Q "Why can't he just be normal and have friends and a nice GF, but be really clever and do the IMO" kept cropping up in my mind. If it's down to hard work moreso than intelligence, I think that's a shame. I still reckon most of them, if not all, are very clever though.
(edited 13 years ago)
Original post by Physics Enemy
I still reckon most of them, if not all, are very clever though.
The ones I met are both clever and remarkably normal people. I think the post above is unfair - they do have a life, even if they like maths.
Original post by IrrationalNumber
The ones I met are both clever and remarkably normal people. I think the post above is unfair - they do have a life, even if they like maths.
Sigh ... it was just a Q that cropped up when watching the Beautiful Minds program. It wasn't a blanket statement by any means. They should be normal, I see no reason why they shouldn't be. I wonder whether the IMOers are treated like celebrities at Cambridge. Free entry and drinks at parties/clubs, girls swooning, etc. It could be the high life, and rightly so.
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