Is this correct? inequalities

[becomingagodo]

Well, I'm have just started doing further pure mathematics 1 college, so I can do a full alevel next year. Which is really good as then I can apply to cambridge and get in.

Anyway, then I looked at the textbook heres a review from amazon.
I tried to use this book alone, without a teacher. I was totally disapointed. The theory was far from well-explained, there were only few examples to illustrate the theory,the exercises were too difficult to handle with such a poor explanation. Having used all the other books of the series, this book didn't live up to my expectations at all.
http://www.amazon.co.uk/Heinemann-Modular-Maths-Edexcel-Further/dp/0435511092

I have to agree with this person. The book sucks and explains nothing, it kind of like do this and then lots of question(which are impossible to do because the explanation is poor). Anyway, so I might be asking alot of questions on this forum about further pure 1.

Anway, how do you solve
3/(x-1)>1
the book says solve it normally i.e.
3/(x-1)-(1(x-1))/(x-1)>0

(-x+4)/(x-1)>0
Now how do you find the critical points. You solve to make zero so x=4 and x=1. However, how do you know if it in the form of 1<x<4 or X<1 and x>4?

I draw the grap, but it doesn't help.

By trial and error. Is it true that you just draw horizontal lines at x=1 and x=4 then you look at the inequality and see if it asking if it above the x-axis or below. If it below and you can colour it in continously then is the anwser
1<x<4, however if it asked for above line there is no place you can colour in the graph so you say the anwser is x>4 and x<1.

Can someone explain?

[drkitten]

Well, I'm have just started doing further pure mathematics 1 college, so I can do a full alevel next year. Which is really good as then I can apply to cambridge and get in.

Well, you can apply, anyway. I suspect the chances of your getting in are slim.




Now how do you find the critical points. You solve to make zero so x=4 and x=1. However, how do you know if it in the form of 1<x<4 or X<1 and x>4?

The easiest way is to evaluate the function at various points. Since f(0) = -3,
you know that the range x<1 is out. Since f(2) = 3, the range 1<x<4 is in.


I draw the grap, but it doesn't help.

How can it not help? If you draw the graph of 3/(x-1), then anywhere the function value is >1 is the region where 3/(x-1) > 1.

Questions like this are a significant part of the reason I doubt you can read math at Cambridge.

[becomingagodo]

The easiest way is to evaluate the function at various points. Since f(0) = -3,
you know that the range x<1 is out. Since f(2) = 3, the range 1<x<4 is in.

Okay I think I understand. Thanks you solved alot of problems.
Well, you can apply, anyway. I suspect the chances of your getting in are slim.
3to5 is not slim. That the odds of getting into to trinity if you do further mathematics.

Questions like this are a significant part of the reason I doubt you can read math at Cambridge.
Rome was not built in a day.

[Thing]

3to5 is not slim. That the odds of getting into to trinity if you do further mathematics.
With those odds it hardly seems worth making too much effort to study for it.

By the way, that question I asked you a while ago about finding which was bigger out of e^pi and pi^e without a calculator? I got it from a, now retired, Cambridge Professor who used it on interview days on students who seemed a bit too fluent at differentiating x^x (the standard interview question in those days). You might just want to give it a moment's thought...

[Modified]

For this simple case, true where:

(x - 1 > 0 and -x + 4 > 0) or (x - 1 < 0 and -x + 4 > 0)

(x > 1 and x < 4) or (x < 1 and x > 4)

(x > 1 and x < 4)

1 < x < 4

[69dodge]

For this simple case, true where:

(x - 1 > 0 and -x + 4 > 0) or (x - 1 < 0 and -x + 4 > 0)

The last inequality is backwards. It should be "-x + 4 < 0".
(Just a typo, obviously, because what follows is right.)

(x > 1 and x < 4) or (x < 1 and x > 4)

(x > 1 and x < 4)

1 < x < 4

[69dodge]

Is it true that you just draw horizontal lines at x=1 and x=4 [...]

A horizontal line at x = 1 or at x = 4? What does that mean? A horizontal line consists of points with the same y-coordinate and different x-coordinates.

[Matt the Poet]

By the way, that question I asked you a while ago about finding which was bigger out of e^pi and pi^e without a calculator? I got it from a, now retired, Cambridge Professor who used it on interview days on students who seemed a bit too fluent at differentiating x^x (the standard interview question in those days). You might just want to give it a moment's thought...

Well that's me not getting any work done this afternoon.

Damn.

[drkitten]

With those odds it hardly seems worth making too much effort to study for it.

Yeah, well, normally it's because the people who are as bad at math as BAGO don't bother to apply to Trinity for maths.

Similarly, normally people who sign up for scuba training pass. But that's because people who can't swim wouldn't sign up in the first place. A certified non-swimmer would be unable to pass, regardless of the overall pass rate statistics.

[becomingagodo]

I tried pluging in values and it worked for very simple equation, however not for more complex ones. However I realized you have to draw both graphs(seriously don't make some funny comment about that being obvious, as the book explains nothing) then it became easy.
Yeah, well, normally it's because the people who are as bad at math as BAGO don't bother to apply to Trinity for maths.
Based on what evidence.

Anyway, I might ask some help later, as I am starting the number theory chapter.

[Professor Yaffle]

BAGO - you are aware that to have a chance at getting into Cambridge, you will also have to do very well in your other (non maths) A-levels too?

[drkitten]

I tried pluging in values and it worked for very simple equation, however not for more complex ones. However I realized you have to draw both graphs(seriously don't make some funny comment about that being obvious, as the book explains nothing) then it became easy.

Based on what evidence.

Based on the evidence of your mathematical talent and work ethic, as presented in the discussions here on the Randi forum.

Basically, you have no mathematical intuition whatsoever -- sarcastic comments or no, a Cambridge-level mathematician should have found the graph interpretation to be "obvious." That's a handicap ("obviously" it's easier to do a subject if you have an intuitive feel for it), but not a show-stopper. One can get by in mathematics on simple hard work.

... but, you don't have that capacity either. You get frustrated too easily when your intuitions don't mesh with the findings, and instead of sitting down and working your way logically from first principles, you just start blowing off major areas of study that you dislike. (Case in point : "The ZF set theory is rubbish. Espically Naive set theory." As was pointed out earlier, not only is ZF not rubbish, it's also entirely different from naive set theory and arose as a response to the problems of naive set theory. Another example is your glib dismissal of calculus, or of Cramer's Rule and the usefulness of set determinants.)

Basically, you don't have the native talent to pick math up easily. You don't have the work ethic to pick it up by slogging through the problems. And you even lack the fundamental maturity to avoid insulting the people who genuinely do understand the material and are trying to teach it to you.

That detailed enough for you?

[aggle-rithm]

Basically, you don't have the native talent to pick math up easily. You don't have the work ethic to pick it up by slogging through the problems. And you even lack the fundamental maturity to avoid insulting the people who genuinely do understand the material and are trying to teach it to you.

That detailed enough for you?

Ow!

[drkitten]

Ow!

Have you seen his prior postings? Search on the forum for "becomingagodo" and "calculus" and see what comes up. I won't post excerpts myself lest I be accused of poisoning the well and of cherry-picking.

[andyandy]

3to5 is not slim. That the odds of getting into to trinity if you do further mathematics.
.

this misunderstanding of basic probability doesn't bode too well ;)

first you need (almost certainly)


Exceptional promise in GCSE - 6A*s +
A in maths
A in further maths
A in another subject

(projected, or achieved.....)

next you need to impress enough to get an interview....

and if you get an interview you (if all things were equal which they're not) would have a (roughly i think) 1/3 chance of an offer....

lots of people who take further maths don't get an A, and even those that do will certainly require strong A-levels as support......Es and Fs in physics i'm afraid aren't good enough.....

by all means chase a dream, but be realistic not presumptious about the chances of realisation.....

just my 2 cents :)

[ben m]

BAG, it often sounds like you enjoy reading about famous mathematicians, but almost all of your posts about actual mathematics---how to do calculus, how to interpret a graph, whether calculus is important or not, whether analysis is important, whether proofs are important---has expressed frustration and lack of understanding.

Have you considered trying for a degree in history of mathematics rather than mathematics itself? Then you'd spend more time, e.g., reading about Euler and Gauss, and less time worrying about when you'll become Euler or Gauss.

Just an idea.

[mijopaalmc]

BAG, it often sounds like you enjoy reading about famous mathematicians, but almost all of your posts about actual mathematics---how to do calculus, how to interpret a graph, whether calculus is important or not, whether analysis is important, whether proofs are important---has expressed frustration and lack of understanding.

Have you considered trying for a degree in history of mathematics rather than mathematics itself? Then you'd spend more time, e.g., reading about Euler and Gauss, and less time worrying about when you'll become Euler or Gauss.

Just an idea.

Don't you need a basic understanding of mathematics at a post-secondary level to study the history of mathematics, much like you need a similar background in science to study the philosophy of science?

[ddt]

Well, I'm have just started doing further pure mathematics 1 college, so I can do a full alevel next year. Which is really good as then I can apply to cambridge and get in.

Can someone explain?
Your math problem has already been explained, but your question rises another question with me.

When I went to school in Holland, this was 3rd year grammar school stuff. At most. You want to apply for Cambridge next year?

[mijopaalmc]

Your math problem has already been explained, but your question rises another question with me.

When I went to school in Holland, this was 3rd year grammar school stuff. At most. You want to apply for Cambridge next year?

You did algebra when you were 8 or 9 years old?

At least that's how third year grammar school translates to this untrained American.

[sol invictus]

You did algebra when you were 8 or 9 years old?

At least that's how third year grammar school translates to this untrained American.

I went to public schools in the US, and I remember doing basic algebra at this level (or maybe a little below) in 4th grade. That was in the top tier math class (out of three). By my junior year in high school I was taking calculus at the local state university, along with a few other students.

While I don't know much about the British secondary school system, I do know Cambridge pretty well - and I'd be surprised if you (the OP that is) could get it with what seems to be your level in math. Certainly you'd have no chance at a top US university, absent something else really compelling in the application.

[mijopaalmc]

I went to public schools in the US, and I remember doing basic algebra at this level (or maybe a little below) in 4th grade. That was in the top tier math class (out of three). By my junior year in high school I was taking calculus at the local state university, along with a few other students.

I too took calculus my junior year in high school, but I was only doing my multiplication tables in third grade. It wasn't until sixth and seventh grade that I started doing algebra (an this was the top tier math class out of two at my grade school).

[jimbob]

Your math problem has already been explained, but your question rises another question with me.

When I went to school in Holland, this was 3rd year grammar school stuff. At most. You want to apply for Cambridge next year?

I'd guess that this wasn't...

Thank you, I understand it now.
2.5 how do you turn this into a improper fraction? I forgot the rule again.


Another word, Professor Yaffle has already mentioned this, but hey.

Matriculation.

[ddt]

When I went to school in Holland, this was 3rd year grammar school stuff. At most. You want to apply for Cambridge next year?
You did algebra when you were 8 or 9 years old?

At least that's how third year grammar school translates to this untrained American.

Sorry - school systems are so widely different that confusion had to arise. Grammar school in British usage, AFAIK, is a secondary school geared for an academic track after that. So that would be around 14 years old.

[becomingagodo]

Well, if you would like to hear. I figured out how to do this now, you just have to draw the graph then use the inspection method.

Well, I think my the probabillity of getting into a top university is 100%, I'm thinking about going to bristol. However, I think the odds in cambridge is about 75%.
Thank you, I understand it now.
2.5 how do you turn this into a improper fraction? I forgot the rule again.

Another word, Professor Yaffle has already mentioned this, but hey.
Thats was a year ago.

Anyway, if I don't try to get into cambridge then I won't get into cambridge, it becomes a self furfilling profecy. So I guess you can only try. Even Ramanujan makes mistakes, so you really can't judge someones mathematical abillity.

Certainly you'd have no chance at a top US university,
This must be a joke. As the things I have heard about US mathematics is depressing.

You people are seriously not getting it, I am the greatest mathematician ever. Also, don't use the what have you done defense.

[ben m]

This must be a joke. As the things I have heard about US mathematics is depressing.

Given that you thought Galois, Fermat, and Gauss are stupid, this leaves a lot of room for US math to be spectacular.

Seriously, US high school students on average are pretty bad, but the average ones aren't applying to college to get math degrees. Our math BS, MS, and Ph.D educations are just fine, thank you.


You people are seriously not getting it, I am the greatest mathematician ever. Also, don't use the what have you done defense.

Take a look at some typical questions from a Trinity maths entrance interview: http://www.trin.cam.ac.uk/show.php?dowid=4

[Thing]

Take a look at some typical questions from a Trinity maths entrance interview: http://www.trin.cam.ac.uk/show.php?dowid=4
I'd certainly like to know the greatest mathematician ever's answers to these, perhaps he could post a few here. Number 3 will be child's-play to him, since he finds calculus so easy.

ETA: A further thought: if I were interviewing maths candidates I'd give them this sheet to study for two minutes and then ask them to tell me which is the easiest problem and which is the hardest, with reasons. Perhaps BAD or others might like to try.

[Thing]

Well that's me not getting any work done this afternoon.

Damn.
I'll take it over to the puzzles section.

[Chris Haynes]

...


This must be a joke. As the things I have heard about US mathematics is depressing.

You people are seriously not getting it, I am the greatest mathematician ever. Also, don't use the what have you done defense.

My younger son will be applying to several universities next year. So far his list includes California Polytechnic, Colorado School of Mines and the local university as a fallback application (he has received literature from Columbia Univ., Rensselaer Polytechnic Institute, Kettering Univ., Case Western and others). Unlike you, he does understand calculus, and is willing to do the work to understand the concepts.

This year he is studying AP Calculus AB, and next year he will take AP Calculus BC. Both of which are described in detail here, with sample questoins:
http://www.collegeboard.com/prod_downloads/ap/students/calculus/ap-cd-calc-0708.pdf

(to be honest, I know I could answer those questions 32 years ago when I was taking calculus, but now I would have to do a bit of work to do that... but I do remember that to differentiate means to take the slope of the curve and to integrate is to find the area under the curve! ---- though I have used those concepts at work --- but mostly using Euler's Identity, eiπ + 1 = 0, and eix = cos(x) + isin(x)), the Laplace transform, and matrix algebra (Cramer's Rule rules!) to solve the nonlinear multi-variable second order differential equations that are used to describe vibration characteristics of vehicles with rubber wheels).

According to the wiki on this course, http://en.wikipedia.org/wiki/AP_Calculus , over 200000 students in the USA and Canada took the AP Calculus AB test, with over half getting a score (3) sufficient to earn college credit. I would say that math instruction for those students was quite adequate. How does your own math education measure up?

Mathematics requires some natural affinity, and work, work and more work. It is a good thing to ask questions, but try to understand the answers.

Stupidest math question I ever asked in class was "who was Eigen?". I mean there is Laplace, Euler, Lagrange, Cramer and a bunch of other math names, how was I supposed to know that "eigen" was German for "proper"?

[Chris Haynes]

Well that's me not getting any work done this afternoon.

Damn.

pssst... it has to do with the power of raising a number to a power... the difference between values of those two very important transcendental values is not much (3.14159-2.71728=.42331), so an equivalent question would be which is higher: 33.5 or 3.53 .

[sol invictus]

This must be a joke. As the things I have heard about US mathematics is depressing.

Interesting, considering the best math departments in the world are all there. Cambridge is good, but... take a look a this list of Fields medalists, and see how many are at Princeton (for example).

http://mathworld.wolfram.com/FieldsMedal.html

[Chris Haynes]

Interesting, considering the best math departments in the world are all there. Cambridge is good, but... take a look a this list of Fields medalists, and see how many are at Princeton (for example).

http://mathworld.wolfram.com/FieldsMedal.html

Cool, one of my college classmates studied at Princeton (only slumming with us for a few quarters because his dad taught at our university... they used to go to Las Vegas together with their own Blackjack scheme).

Hmmm... looking at the list, one of son's friends is considering UC Berkeley (edit to add: that young man is also considering CalTech, he is one of those scary smart kids, he scored a "5" in an AP test last spring, a test my son only got a "2" in). I will suggest he look there (he is trying to decide between physics and mechanical engineering).

[sol invictus]

Cool, one of my college classmates studied at Princeton (only slumming with us for a few quarters because his dad taught at our university... they used to go to Las Vegas together with their own Blackjack scheme).

Hmmm... looking at the list, one of son's friends is considering UC Berkeley. I will suggest he look there (he is trying to decide between physics and mechanical engineering).

Princeton is probably the best math department in the world, especially when you add the Institute for Advanced Study (which is not part of the university, but is very nearby and easily accessible).

But I'm not sure excellence in research is really the best way to choose a school, particularly for an undergrad. If he's interested in physics or engineering, I'd say look at Stanford, Cal Tech or MIT over Princeton.

[Complexity]

You people are seriously not getting it, I am the greatest mathematician ever. Also, don't use the what have you done defense.


I've been taking a mental-health break from Bago for several weeks, but enough time has passed that I'm no longer depressed by his existence.

I'm back.

First, my lad, you are not and never will be the greatest mathematician ever.

You are not a mathematician.

You are never going to be a mathematician.

You're not going to do enough work to become even a bad mathematician.

Also, it would be the 'What have you ever done' offense. Words matter.

[Complexity]

Which is really good as then I can apply to cambridge and get in.


Don't start packing.

Sorry, dude, but you're not cut out for mathematics.

Many years of serious study might get through high school mathematics with a passing score, but that's about it, and you'll never put in the work needed to do even that.

[Chris Haynes]

.... If he's interested in physics or engineering, I'd say look at Stanford, Cal Tech or MIT over Princeton.

Those are all on the dream list, but only if he gets scholarships, also known as the "dream-on" list. The idiot boy took the PSAT test with very little sleep and no breakfast and ended up with a 89%tile. No scholarship at that level. Despite getting straight "A"s in chemistry, physics and calculus, and his lowest grades are in Latin and social studies (next year as a senior he plans to take AP Chemistry and advanced physics, since he took his biology requirement in a summer at a community college).

Actually, I would think those three schools may be better for graduate school. Something he may end up doing (he is an excellent swim teacher, and he may actually make a very good engineering professor... but that is just a parental dream).

By the way, one of my high school friends went to MIT. His dad offered him the choice between a Porsche car or MIT, he chose MIT (even though he still likes little bitty sports cars). He wrote me a letter while he was there, and from what I understood was that taking speed was the norm to survive (late 1970s). He did survive enough to get an engineering Master's and is now a manager at a consumer electronics company.

An anecdote... but still, he may apply just to see if he can get in.

(oh, crud... I just dragged out my college transcript. What was I thinking? I left high school with a 3.82 GPA. out of 4.. yet I got all these "C"s in college. I got a C in physics and differential equations! Both are subjects I used at work on a daily basis. Aargh! I graduated with a 2.97 out of 4.0 grade point average... though looking at it, my best grades were in Math. From a low of 2.5 for Linear Algebra (Cramer's Rule!) to a 4.0 in Advanced Calculus... with a 3.6 in Analytical Methods in Engineering, an applied math course. I guess I am not so smart.)

[Chris Haynes]

Don't start packing.

Sorry, dude, but you're not cut out for mathematics.

Many years of serious study might get through high school mathematics with a passing score, but that's about it, and you'll never put in the work needed to do even that.

Dude, that is harsh!

But, true.

[Thing]

pssst... it has to do with the power of raising a number to a power... the difference between values of those two very important transcendental values is not much (3.14159-2.71728=.42331), so an equivalent question would be which is higher: 33.5 or 3.53 .
pssst...no it wouldn't. See http://forums.randi.org/showthread.php?t=106642 for the ongoing discussion of this puzzle.

[Chris Haynes]

pssst...no it wouldn't. See http://forums.randi.org/showthread.php?t=106642 for the ongoing discussion of this puzzle.

Oh, crud... I will have to check it out. I looked and looked at it, and just figured on the values!

[becomingagodo]

Take a look at some typical questions from a Trinity maths entrance interview:
I would anwser them for you, however I have seen them before.
This year he is studying AP Calculus AB, and next year he will take AP Calculus BC.
AP calculus is nothing compared to further mathematics.
How does your own math education measure up?
Better, much better.
Interesting, considering the best math departments in the world are all there. Cambridge is good, but... take a look a this list of Fields medalists, and see how many are at Princeton (for example).
Field medals are trivial, Perelmann did not except his field medal. Now solving a big millenium problem, thats something.
Since 1994 there has only been three. Even then one was Russian and moved there. Even Cambridge has two, one less then Princeton.
First, my lad, you are not and never will be the greatest mathematician ever.
I will be. I guess you have no vision.
Many years of serious study might get through high school mathematics with a passing score, but that's about it, and you'll never put in the work needed to do even that.
I am a A student. You know I am going to get a A. I can give my result for C1 exam in march, and it will be like 94%.

[sol invictus]

Those are all on the dream list, but only if he gets scholarships, also known as the "dream-on" list. The idiot boy took the PSAT test with very little sleep and no breakfast and ended up with a 89%tile. No scholarship at that level. Despite getting straight "A"s in chemistry, physics and calculus, and his lowest grades are in Latin and social studies (next year as a senior he plans to take AP Chemistry and advanced physics, since he took his biology requirement in a summer at a community college).


Well, Berkeley is excellent as well. But what makes the three I mentioned special is the emphasis on undergrad education. Especially at the two techs - students there are really kind of coddled. Not in the sense that it's easy, but in the sense that they get tons of personal attention.

Another option is a small college, maybe one with a 3/2 program if he decides to do engineering. That will in general get him better teaching, but less access to advanced courses.

[Complexity]

Dude, that is harsh!

But, true.


I put Bago on ignore for a few months. I needed a rest.

Coddling him will accomplish nothing. Trying to help him hasn't worked.

We've already tried nearly everything except for cold, harsh reality.

That's all I have left for him, and he'll get it in spades.

[Complexity]

I would anwser them for you, however I have seen them before.


Answer them or say nothing more. Do not use any books, reference materials, calculators, software, or the internet while you answer them.


AP calculus is nothing compared to further mathematics.


You don't know any calculus yet, and I don't think you ever will.

You still need to spend a good amount of time on high school algebra.

Quit deluding yourself.


I will be. I guess you have no vision.


Quit deluding yourself. You have no future in mathematics. None.

[becomingagodo]

Answer them or say nothing more. Do not use any books, reference materials, calculators, software, or the internet while you answer them.

I really can't anwser them. As these are question that need further maths 2 and 3, also study of step papers. The point is in a year when I take step O will be able to anwser them.
You don't know any calculus yet, and I don't think you ever will.

You still need to spend a good amount of time on high school algebra.
Actually I do know calculus, however I haven't done the chain rule and I will be doing PD's soon.
Quit deluding yourself. You have no future in mathematics. None.
Your never going to solve RH. The fact is you won't even learn complex analysis. Seriously, I would rather have no future in mathematics then have a poor one, ten years and no proof. You may be happy, however I would rather be unhappy and have a proof.

[LostAngeles]

I've been taking a mental-health break from Bago for several weeks, but enough time has passed that I'm no longer depressed by his existence.

I'm back.

First, my lad, you are not and never will be the greatest mathematician ever.

You are not a mathematician.

You are never going to be a mathematician.

You're not going to do enough work to become even a bad mathematician.

Also, it would be the 'What have you ever done' offense. Words matter.

Don't start packing.

Sorry, dude, but you're not cut out for mathematics.

Many years of serious study might get through high school mathematics with a passing score, but that's about it, and you'll never put in the work needed to do even that.

Seriously.

I'm barely cut out for mathematics even when I'm not a shambling wreck and I'm still substantially better off mathematically than BAGO.

I really can't anwser them. As these are question that need further maths 2 and 3, also study of step papers. The point is in a year when I take step O will be able to anwser them.

Actually I do know calculus, however I haven't done the chain rule and I will be doing PD's soon.

Your never going to solve RH. The fact is you won't even learn complex analysis. Seriously, I would rather have no future in mathematics then have a poor one, ten years and no proof. You may be happy, however I would rather be unhappy and have a proof.

You're never going to solve RH either. The chain rule is so... funda-***********-mental that if you aspired to any mathematical glory, you'd already be working on it. Chain rule is what you do after the power rule. Seriously.

I'm learning complex analysis. It sucks and I should just drop it and take it over again, but I'm learning it. Do you know any complex analysis?

Say BAGO, what's the integral over Western Europe?

[Chris Haynes]

Well, Berkeley is excellent as well. But what makes the three I mentioned special is the emphasis on undergrad education. Especially at the two techs - students there are really kind of coddled. Not in the sense that it's easy, but in the sense that they get tons of personal attention.

That sounds like a change for 30 years ago when my high school friend went there. In his letter to me then it seemed that speed was a required substance.

Another option is a small college, maybe one with a 3/2 program if he decides to do engineering. That will in general get him better teaching, but less access to advanced courses.

Well, compared to the state schools (Cal Berkeley, Cal Poly, etc), Cal Tech is a small school.

Thanks a bunch. I was actually thinking of starting a thread on college choices for geeky mechanical/physics boy, but this works. He is going to apply for a summer fellowship for a high student to work in a research lab at the local university (again, one of those large state research universities).

By the way, he has taken classes at the community college, and the level of teaching with the smaller class sizes is very nice compared to the same courses at the large university (biology class has 30 students, not 150!).

[Nancarrow]

Say BAGO, what's the integral over Western Europe?

Is it zero? I assume the reasoning is the same I heard to answer the question 'why is the contour integral around Germany zero?'.

BAGO, please do apply to Trinity, Cambridge. You won't get in, but if by some miracle you did, it would finally inspire me to go visit my old stomping ground. I imagine you would be very... identifiable.

[LostAngeles]

Is it zero? I assume the reasoning is the same I heard to answer the question 'why is the contour integral around Germany zero?'.

BAGO, please do apply to Trinity, Cambridge. You won't get in, but if by some miracle you did, it would finally inspire me to go visit my old stomping ground. I imagine you would be very... identifiable.

Yes, it is and I assume the reasoning is the same.

[Complexity]

I imagine you would be very... identifiable.


I think the sock will be a dead giveaway.

[aggle-rithm]

Have you seen his prior postings? Search on the forum for "becomingagodo" and "calculus" and see what comes up. I won't post excerpts myself lest I be accused of poisoning the well and of cherry-picking.

Oh, I have no doubt he had it coming. But, still...Ow!

Fortunately, he appears to have a thick skin. Or skull, whichever.

[Almo]

Have you considered trying for a degree in history of mathematics rather than mathematics itself? Then you'd spend more time, e.g., reading about Euler and Gauss, and less time worrying about when you'll become Euler or Gauss.

Just an idea.

History of Math and Physics is terribly interesting. All the reasons why people thought the wrong things they did. Like when Copernicus said "Sun middle!" and many said, "eh, I don't know." It was because he was still using circular orbits, so his model didn't make better predictions than the geocentric model of the time. If your theory doesn't make better predictions, why accept it? It may have been attractive to some as it was more elegant, but that's not enough.

Western Europe integral is a joke:
It's zero, because if there are any Poles, they are removeable.

[sol invictus]

Western Europe integral is a joke:
It's zero, because if there are any Poles, they are removeable.

That's only true if Western Europeans are analytic. Given the reasoning skills displayed by the OP in this thread, I'm skeptical. :)

[LostAngeles]

History of Math and Physics is terribly interesting. All the reasons why people thought the wrong things they did. Like when Copernicus said "Sun middle!" and many said, "eh, I don't know." It was because he was still using circular orbits, so his model didn't make better predictions than the geocentric model of the time. If your theory doesn't make better predictions, why accept it? It may have been attractive to some as it was more elegant, but that's not enough.

Western Europe integral is a joke:
It's zero, because if there are any Poles, they are removeable.

Ah, I heard it as all the Poles are in Eastern Europe

[DazzaD]

Anyway, then I looked at the textbook heres a review from amazon.



I have to agree with this person. The book sucks and explains nothing, it kind of like do this and then lots of question(which are impossible to do because the explanation is poor).

I am familiar with those books, many of my students use them.

They are not intended to be a "bible" of mathematics, they cannot be given the amount of material they are expected to cover and the limited space. Personally I think they do quite a good job given the limited space and scope.

If you want to have a slightly better insight into the origins and uses of the material you might be better off with a good undergraduate introductory calculus book, I recommend:

Calculus - second edition by Finney and Thomas
ISBN 0-201-59120-0

The thing is no book is ever going to replace a good teacher. Most of that material in the FP1 book should be well within the capabilities of a good A Level student, if they have been taught (and learnt and practised) properly.

You may be surpised how much of that material was on courses for younger children some 10, 20 or 100 years ago.

The problem with most of A Level maths is that the teachers are forced to press a simple button in students minds in order that they grasp the mechanism of getting the answer, practice and move on. They have a limited timescale and are not really encouraged to derive results or explore ideas or sit and wonder in fascination at how certain things are related or put together.

A shame really.

[drkitten]

I really can't anwser them. As these are question that need further maths 2 and 3, also study of step papers. The point is in a year when I take step O will be able to anwser them.

Perhaps. Given your track record, a certain degree of suspicion is warranted.

For example:

Actually I do know calculus, however I haven't done the chain rule

Given how simple, obvious, and fundamental the chain rule is to calculus, one might suggest that if you haven't done the chain rule, you haven't done calculus.

I've noticed a tendency of yours to overstate your accomplishments --- such as in this very thread, where you announced glibly that you "would" answer the Trinity questions and then when pressed admitted that you don't have the background. Similarly, in another thread, you announced that you could learn calculus in twenty minutes, but were unable to solve a simple polynomial max/min problem.

I don't think you have any realistic idea of what you can and can't do in mathematics. It's very easy to read a book about Gauss and imagine yourself to be him --- oh, sorry, Gauss was an idiot, wasn't he? (smirk) --- but quite another thing to actually be able to do the mathematics yourself. Your questions bespeak a level of mathematical ignorance that my eleven-year old niece would be embarrassed to show (even she knows how to graph a function and determine whether its value is above or below 1), and I rather seriously doubt that in a year you can teach yourself what is literally six or seven years worth of material.


Seriously, I would rather have no future in mathematics then have a poor one.

Well, that's good. Congratulations. Your wish has been granted.

[Fredrik]

Take a look at some typical questions from a Trinity maths entrance interview: http://www.trin.cam.ac.uk/show.php?dowid=4
I should kick your ass for posting that. :) I took me a looong time to solve them all, and I had more important things to do. These problems must be very, very hard for someone who has only studied high school mathematics. Is this really a test for students who haven't even started studying mathematics at the university yet? How much time do they get to complete this test?

[Yllanes]

I should kick your ass for posting that. :) I took me a looong time to solve them all, and I had more important things to do. These problems must be very, very hard for someone who has only studied high school mathematics. Is this really a test for students who haven't even started studying mathematics at the university yet? How much time do they get to complete this test?
I don't see anything that requires techniques unavailable to high school graduates, but they certainly would be difficult and very long to solve for them. Maybe it's not a conventional test, in the sense that they are not supposed to be able to solve everything. It simply says that they would use whatever you respond as a basis for an interview, I don't think they grade the exam in a conventional manner.

[drkitten]

I should kick your ass for posting that. :) I took me a looong time to solve them all, and I had more important things to do. These problems must be very, very hard for someone who has only studied high school mathematics. Is this really a test for students who haven't even started studying mathematics at the university yet?

Not in the sense that the tests are scored and the people who score the highest are accepted. They're more like mathematical Rorshach tests, in that your answers will provide a degree of insight into the background that you have, your approach to solving (difficult) mathematical problems. your level of creativity, and so forth.

For instance, what they'd really like to see is not a student who solves all the problems. What they'd like to see is a student who comes up with a unique, novel, and promising approach to all the problems -- whether she solves them or not. ("Wow! I never thought of using the Fundental Theorem of Arithmetic to derive the Poisson distribution!")

[sago]

Its been a long time since I went for this kind of interview, but when I did (late 80s) you got a pretty short amount of time to do the questions (I remember about half-an-hour - could be wrong).

Then in the interview you got asked why you picked the questions you did. What approaches you'd taken. If you did manage to actually get through to a solution, you'd be asked variations on the spot.

My intuition was that I was being asked to display my natural sense of mathematics, rather than any ability to manipulate equations or know particular formulae. The better conversations sparked off from some of the harder questions. Its also a good idea to ask questions of the interviewers to show you're passionate about learning more.

Ahh those A-level days... absolutely bloody stressful...

As someone who spent my A-level further maths cruising through the classwork and trying to prove the prime number theorem in my spare time, I really think the OPer has no clue of the math skills of those he's competing with. I could have comfortably done the OP's question at 13-14, but I was still nowhere near the best mathematician in my freshman class.