How much Maths does one need in Particle Physics?

[MarcAlexander]

Hi, I'm Marc. I'm 14, from the UK and I love Particle Physics and Nuclear Physics. I was just wondering about how much Maths and what areas of Maths I would need to accumulate the knowledge for, in order to do A-level and eventually University Physics, specifically Particle Physics.

Could anyone shed some Photons on my situation?

 

[Pythagorean]

the field theory has classical roots in differential equations (which follows from calculus), the quantum mechanical part of it is mostly group theory and linear algebra (matrices and eigenstuffs).

 

[nickbob00]

If you do maths GCSE and get an A, then do A level Maths and get an A, that's all the maths you need to get into an undergraduate course. Ideally, you would do A level Further maths and also do additional maths GCSE or something like that, if it is offered at your school. At 14, you don't need to be teaching yourself much.

On an undergrad physics degree, you will do lots and lots of maths, much of which will be required rather than optional.

 

[MarcAlexander]

If you do maths GCSE and get an A, then do A level Maths and get an A, that's all the maths you need to get into an undergraduate course. Ideally, you would do A level Further maths and also do additional maths GCSE or something like that, if it is offered at your school. At 14, you don't need to be teaching yourself much.

On an undergrad physics degree, you will do lots and lots of maths, much of which will be required rather than optional.

Well I'm just wondering if Chemistry is more my thing. :\

You see, I'm personally very interested in particles, their sub-atomic particles, their elementary particles and so on. I have reason to believe this area of Science comes under Particle Physics. My dilemma is that I:
1) Don't really care about the rest of Physics besides the particle aspect, e.g.I couldn't give a damn about light refraction or thermal conduction.
2) I'm not a great fan of 'pointless' Maths, if you get were I'm coming from.

I'm starting to think maybe it's Chemistry I should be loured towards as that's pure particles with the odd metamorphic rock or two. Also I enjoy writing and reading Chemical formulae as it is short and simple. But my dilemma is that Chemistry seems to be more about how the atoms bond to form molecules rather than matter and anti-matter.

Physics or Chemistry??

 

[Awesomesauce]

Well I'm just wondering if Chemistry is more my thing. :\

You see, I'm personally very interested in particles, their sub-atomic particles, their elementary particles and so on. I have reason to believe this area of Science comes under Particle Physics. My dilemma is that I:
1) Don't really care about the rest of Physics besides the particle aspect, e.g.I couldn't give a damn about light refraction or thermal conduction.
2) I'm not a great fan of 'pointless' Maths, if you get were I'm coming from.
...

"The best of the golds at the bottom of the barrels of crap" - Randy Pausch
The 'rest of physics' does not come optional (un)fortunately. You can't just jump into the deep end without teaching yourself to tread water.

 

[MarcAlexander]

"The best of the golds at the bottom of the barrels of crap" - Randy Pausch
The 'rest of physics' does not come optional (un)fortunately. You can't just jump into the deep end without teaching yourself to tread water.

It's not that I find the rest of Physics wrong, it's just I have no particular interest in them. I guess I'm just going to have to learn all the 'crap' in order to reach the 'gold'.

Thanks guys.

 

[Functor97]

Well I'm just wondering if Chemistry is more my thing. :\

You see, I'm personally very interested in particles, their sub-atomic particles, their elementary particles and so on. I have reason to believe this area of Science comes under Particle Physics. My dilemma is that I:
1) Don't really care about the rest of Physics besides the particle aspect, e.g.I couldn't give a damn about light refraction or thermal conduction.
2) I'm not a great fan of 'pointless' Maths, if you get were I'm coming from.

I'm starting to think maybe it's Chemistry I should be loured towards as that's pure particles with the odd metamorphic rock or two. Also I enjoy writing and reading Chemical formulae as it is short and simple. But my dilemma is that Chemistry seems to be more about how the atoms bond to form molecules rather than matter and anti-matter.

Physics or Chemistry??

You do realize that those fundamental particles are pieces of "pointless" mathematics? No one can draw or see an electron let alone a quark... The more fundamental you go, the more mathematical it gets.

 

[MarcAlexander]

You do realize that those fundamental particles are pieces of "pointless" mathematics? No one can draw or see an electron let alone a quark... The more fundamental you go, the more mathematical it gets.

You could see an electron or quark under an electron-microscope. But I acknowledge your point.

 

[Kevin_Axion]

You could see an electron or quark under an electron-microscope. But I acknowledge your point.

No, you can't. And I think the play on words is alluding to the fact that fundamental particles are points, and also QFT plays on group theory (abstract algebra), partial differential equations, differential geometry/topology etc.

 

[MarcAlexander]

No, you can't. And I think the play on words is alluding to the fact that fundamental particles are points, and also QFT plays on group theory (abstract algebra), partial differential equations, differential geometry/topology etc.

Could you explain to me what QFT is? I know what it stands for: Quantum Field Theory. I just don't know what relevance it has in Particle Physics, like S=D/T has in calculating velocities based on the distance and the time it took them to accomplish that distance. What does QFT tell us or prove to us?

 

[Kevin_Axion]

Could you explain to me what QFT is? I know what it stands for: Quantum Field Theory. I just don't know what relevance it has in Particle Physics, like S=D/T has in calculating velocities based on the distance and the time it took them to accomplish that distance. What does QFT tell us or prove to us?

I'll go through it really quickly since I have to go:

1. First we begin with classical mechanics and that includes Newtonian, Lagrangian and Hamiltonian mechanics. This field of physics studies the motion and dynamics of classical object i.e planets, balls etc. The objects follow trajectories in gravitational fields and can be modeled precisely in position and time.

2. Secondly we have relativistic mechanics. That is, the study of classical objects in high velocities or as v\rightarrow c. In this we are introduced to space-time or Minkowski space-time. We see that objects in an inertial frame experience time, distance and causality different then others.

3. Thirdly we have quantum mechanics, QM is the study of objects at the atomic level. Here, objects don't follow the rules of classical objects, everything has uncertainty. For instance there is an uncertainty between time and energy and an uncertainty between position and momentum etc. QM uses Hilbert spaces to define the state of a particle and uses non-commutative operators to describe uncertainty.

4. Now we have QFT. QFT is the combination of relativity and quantum mechanics and it forms relativistic quantum mechanics or the study of quantum mechanical objects in accelerated or inertial reference frames as v\rightarrow c. Here we see that the fundamental objects in nature are fields and particles are the local excitations of these fields. This is the most accurate depiction of nature so far.

 

[BloodyFrozen]

2) I'm not a great fan of 'pointless' Maths, if you get were I'm coming from.

Much of physics requires MATH

MATH IS APPARENTLY THE LIFE.

 

[MarcAlexander]

I'll go through it really quickly since I have to go:

1. First we begin with classical mechanics and that includes Newtonian, Lagrangian and Hamiltonian mechanics. This field of physics studies the motion and dynamics of classical object i.e planets, balls etc. The objects follow trajectories in gravitational fields and can be modeled precisely in position and time.

2. Secondly we have relativistic mechanics. That is, the study of classical objects in high velocities or as v\rightarrow c. In this we are introduced to space-time or Minkowski space-time. We see that objects in an inertial frame experience time, distance and causality different then others.

3. Thirdly we have quantum mechanics, QM is the study of objects at the atomic level. Here, objects don't follow the rules of classical objects, everything has uncertainty. For instance there is an uncertainty between time and energy and an uncertainty between position and momentum etc. QM uses Hilbert spaces to define the state of a particle and uses non-commutative operators to describe uncertainty.

4. Now we have QFT. QFT is the combination of relativity and quantum mechanics and it forms relativistic quantum mechanics or the study of quantum mechanical objects in accelerated or inertial reference frames as v\rightarrow c. Here we see that the fundamental objects in nature are fields and particles are the local excitations of these fields. This is the most accurate depiction of nature so far.

Is Quantum Physics for Dummies a good book?

Also what would be a good(simple) book for Physics in Maths be?

 

[MarcAlexander]

Much of physics requires MATH

MATH IS APPARENTLY THE LIFE.

I apologise if i pulled a 'heart string'. What I meant was that throughout school I am constantly taught Mathematics that seems to have no practical use like Median, Prime Factors, HCF, LCM etc. Personally I love Algebra.

 

[BloodyFrozen]

I apologise if i pulled a 'heart string'. What I meant was that throughout school I am constantly taught Mathematics that seems to have no practical use like Median, Prime Factors, HCF, LCM etc. Personally I love Algebra.

Yes, I agree that mathematics in Highschool may be boring, but learn it. And then study on your own

 

[MarcAlexander]

Yes, I agree that mathematics in Highschool may be boring, but learn it. And then study on your own

I completely agree. I just wish I'd had an interest in Physics from the start; maybe I'd have tried harder with Maths but, I was only a kiddie back then, now I'm doing my GCSEs. Are there any books that teach everything about Maths from baby stuff to high level stuff which would ultimately prepare me for Quantum Mechanics? And would Calculus be necessary?
If so then what is Calculus?

I apologise for so many questions. It's just I have no one else to ask really.

 

[micromass]

I completely agree. I just wish I'd had an interest in Physics from the start; maybe I'd have tried harder with Maths but, I was only a kiddie back then, now I'm doing my GCSEs. Are there any books that teach everything about Maths from baby stuff to high level stuff which would ultimately prepare me for Quantum Mechanics? And would Calculus be necessary?
If so then what is Calculus?

I apologise for so many questions. It's just I have no one else to ask really.

Yes of course calculus would be necessary. Calculus is one of the most important theories around and is absolutely fundamental if you want to study any science.

Calculus basically allows you to analyze continuous functions and graphs in an easy way. It allows you to find areas under graphs, volumes, rate of change. And it can be used to solve optimization problems.

 

[BloodyFrozen]

I completely agree. I just wish I'd had an interest in Physics from the start; maybe I'd have tried harder with Maths but, I was only a kiddie back then, now I'm doing my GCSEs. Are there any books that teach everything about Maths from baby stuff to high level stuff which would ultimately prepare me for Quantum Mechanics? And would Calculus be necessary?
If so then what is Calculus?

I apologise for so many questions. It's just I have no one else to ask really.

Well, as micromass already explained, Calculus would be extremely useful, but you can either take it in your high school (if they offer it) or learn it by yourself.

I recommend getting a good grasp in HS Algebra and Precalculus/Trigonometry. As for textbooks, I can't really say. You could always ask to borrow a Precalc/Alg II book from a school teacher. Nearly any would suffice. As for Calculus texts, I'd ask someone else.

 

[micromass]

Start with the excellent book "Basic mathematics" by Serge Lang. It consist of everything you need to know of high school mathematics (not including calculus). If you're done with that, then perhaps take a light calculus book like "practical analysis in one variable" by Estep. After that, you should take a fun book like Spivak or Apostol.

 

[MarcAlexander]

I've just purchased "Quantum Physics for Dummies" of Amazon.

 

[brocks]

Are there any books that teach everything about Maths from baby stuff to high level stuff which would ultimately prepare me for Quantum Mechanics?

Yes, there is one. It's called "The Road to Reality" by Roger Penrose. If you read it cover to cover, and understand everything in it, you will know all you need to know to be a great physicist.

One caveat: in order to do that without previous exposure to the material, you will have to be the smartest person who ever lived. An IQ of 400 or so would be about right.

Assuming that you are not the smartest person who ever lived, you will just have to take your math classes in sequence, like the rest of us. One or two math classes at a time, spending a minimum of 12 hours a week for a full semester on each class. Calculus is only the beginning, and if you are not taking it by your freshman year of college at the latest, then you will be behind most people who will eventually get a PhD in physics.

Why don't you assume that the people who run universities are not idiots or sadists, and actually require prerequisites for good reasons? Then pick a few schools that you might want to attend, or just go to the MIT OCW website, and see what they require for a physics degree. The websites of most physics departments have the required math and physics courses all laid out, year by year. That's what you have to take. It's a lot of work, and there are no short cuts.

If you don't like that idea, then you will have to be content with reading books *about* science, where authors try to make things simple enough for housewives to understand. Sorry, but that's the way it is.

 

[BloodyFrozen]

I've just purchased "Quantum Physics for Dummies" of Amazon.

I'd highly recommend following micromass' suggestion and learn the maths required first.

Going along with the idea of learning high school mathematics, I'd also recommend reading a geometry book by Harold Jacobs.


It'd be helpful if we know what math courses you've already taken.

 

[micromass]

I've just purchased "Quantum Physics for Dummies" of Amazon.

Reading such a book is near to useless. It won't teach you what actual quantum physics is.
By all means: read the book if it's interesting. But if you are really serious about going into particle physics, then you'd be far better of with spending your time doing math.

 

[MarcAlexander]

Yes, there is one. It's called "The Road to Reality" by Roger Penrose. If you read it cover to cover, and understand everything in it, you will know all you need to know to be a great physicist.

One caveat: in order to do that without previous exposure to the material, you will have to be the smartest person who ever lived. An IQ of 400 or so would be about right.

Assuming that you are not the smartest person who ever lived, you will just have to take your math classes in sequence, like the rest of us. One or two math classes at a time, spending a minimum of 12 hours a week for a full semester on each class. Calculus is only the beginning, and if you are not taking it by your freshman year of college at the latest, then you will be behind most people who will eventually get a PhD in physics.

Why don't you assume that the people who run universities are not idiots or sadists, and actually require prerequisites for good reasons? Then pick a few schools that you might want to attend, or just go to the MIT OCW website, and see what they require for a physics degree. The websites of most physics departments have the required math and physics courses all laid out, year by year. That's what you have to take. It's a lot of work, and there are no short cuts.

If you don't like that idea, then you will have to be content with reading books *about* science, where authors try to make things simple enough for housewives to understand. Sorry, but that's the way it is.

Did I not in my original post state that I was from the UK. Also your sarcasm was not appreciated, but I do understand the point you were trying to get across. I've canceled the order for the Quantum Physics book and I think I'm going to get that "Basic Mathematics" book by Serge Lang.

My question is: does QM cover the maths aspect of Particle Physics or the whole of Particle Physics (and more?)?

 

[Greg Bernhardt]

Reading such a book is near to useless. It won't teach you what actual quantum physics is.
By all means: read the book if it's interesting. But if you are really serious about going into particle physics, then you'd be far better of with spending your time doing math.

However at 14 maybe what he needs is a concept overview to motivate and wet his pallet. At his age, I was just beginning Algebra/Geometry (not that I know much now). I don't think he's going to be getting too involved any time soon. No one should be too serious in anything at 14.

 

[BloodyFrozen]

Did I not in my original post state that I was from the UK. Also your sarcasm was not appreciated, but I do understand the point you were trying to get across. I've canceled the order for the Quantum Physics book and I think I'm going to get that "Basic Mathematics" book by Serge Lang.

My question is: does QM cover the maths aspect of Particle Physics or both?

Check if you can borrow that book from your local library. Take your time learning. Better to learn it correctly.

 

[MarcAlexander]

Check if you can borrow that book from your local library. Take your time learning. Better to learn it correctly.

Good suggestion. :)

 

[micromass]

However at 14 maybe what he needs is a concept overview to motivate and wet his pallet. At his age, I was just beginning Algebra/Geometry (not that I know much now). I don't think he's going to be getting too involved any time soon. No one should be too serious in anything at 14.

True, somehow I forgot that he was 14

To the OP: yes, reading such a quantum physics book could be benificial and you might find it interesting. But don't fool yourself into thinking that you're doing actual physics. You need a whole lot a prerequisites to be able to do actual physics.
Also, pop sci books are made to get people interested in physics. And what often happens is that they find the actual physics to be a lot more boring than what the books describe.

Do get the "quantum physics for dummies" book, you'll have fun reading it! But by all means, don't neglect your math!

 

[Phyisab****]

You have a solid 8 years of math and physics background before you can start to think about particle physics. Here is a free copy of a QFT book, maybe it will give you an idea of why you need to learn so much background before you can do particle physics.

http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf

 

[brocks]

Did I not in my original post state that I was from the UK.

Yes, you did. But other than using units of furlongs per fortnight, UK physics is pretty much the same as US physics.

Also your sarcasm was not appreciated, but I do understand the point you were trying to get across.

I was not being sarcastic; I was trying to give you a dose of reality. At fourteen, you are excused for not knowing what classes you should concentrate on for a career in particle physics, but IMO you should not be excused for asking for a book that covers math from junior high to graduate level. Your posts are extremely well written, which makes it hard to believe that you are as clueless as you pretend, but if you really are, then it's past time for you to start getting serious about math, instead of just wishing you could be a physicist without doing the work.

My question is: does QM cover the maths aspect of Particle Physics or the whole of Particle Physics (and more?)?

We are trying to make you understand that you cannot do much in *any* field of physics without math through at least vector calculus, diff eq, and linear algebra. Yes, there are freshman classes in physics that are done without calculus, but they will make you about as fluent in physics as a year of Spanish will make you fluent in Spanish, i.e. a six-year old kid raised in Spain would run rings around you. And they are terminal classes --- if you want to take anything else in physics, you will have to go back and repeat freshman physics, but this time using a calculus-based text.

You probably won't get an undergraduate degree in physics without taking elementary classes in both QM and particle physics, and you will almost certainly not take an undergraduate math class that is not useful in all areas of physics. If you are 14 now, then that takes you through the next seven or eight years.

By then, when you are applying for an advanced degree, you can decide what you want to specialize in, and you will know what extra math you need for it. And I still think the best way to get a preview is to look at the websites of several physics departments. Buying the first book recommended by a stranger is going to give hit or miss results. A book that a PhD thinks is great may not be the right one for you.

For now, take all the math you can. If you can take calculus in high school, do it. Go ahead and read books for Dummies and the like, because that's all you're ready for now, and they may motivate you to learn more, but realize that if you can't solve the problems in the real textbooks for physics majors, then you don't really understand the subject; you've just learned a few buzzwords.

 

[MarcAlexander]

Yes, you did. But other than using units of furlongs per fortnight, UK physics is pretty much the same as US physics.



I was not being sarcastic; I was trying to give you a dose of reality. At fourteen, you are excused for not knowing what classes you should concentrate on for a career in particle physics, but IMO you should not be excused for asking for a book that covers math from junior high to graduate level. Your posts are extremely well written, which makes it hard to believe that you are as clueless as you pretend, but if you really are, then it's past time for you to start getting serious about math, instead of just wishing you could be a physicist without doing the work.



We are trying to make you understand that you cannot do much in *any* field of physics without math through at least vector calculus, diff eq, and linear algebra. Yes, there are freshman classes in physics that are done without calculus, but they will make you about as fluent in physics as a year of Spanish will make you fluent in Spanish, i.e. a six-year old kid raised in Spain would run rings around you. And they are terminal classes --- if you want to take anything else in physics, you will have to go back and repeat freshman physics, but this time using a calculus-based text.

You probably won't get an undergraduate degree in physics without taking elementary classes in both QM and particle physics, and you will almost certainly not take an undergraduate math class that is not useful in all areas of physics. If you are 14 now, then that takes you through the next seven or eight years.

By then, when you are applying for an advanced degree, you can decide what you want to specialize in, and you will know what extra math you need for it. And I still think the best way to get a preview is to look at the websites of several physics departments. Buying the first book recommended by a stranger is going to give hit or miss results. A book that a PhD thinks is great may not be the right one for you.

For now, take all the math you can. If you can take calculus in high school, do it. Go ahead and read books for Dummies and the like, because that's all you're ready for now, and they may motivate you to learn more, but realize that if you can't solve the problems in the real textbooks for physics majors, then you don't really understand the subject; you've just learned a few buzzwords.

I'm not as clueless as you may interpret, I just want to make sure the information I accumulate is clarified. :)

 

[GregJ]

Mathematics is essential for physics, just as wheels are essential for cars (at least for now hehe).

Pick up some good books on Algebra, Trigonometry and Geometry. Get those under your belt then start looking at Precalculus or Calculus. Do your best and who knows, you may actually begin to like it.

From there you should be ready. Most of all, have fun ;)

 

[MarcAlexander]

Mathematics is essential for physics, just as wheels are essential for cars (at least for now hehe).

Pick up some good books on Algebra, Trigonometry and Geometry. Get those under your belt then start looking at Precalculus or Calculus. Do your best and who knows, you may actually begin to like it.

From there you should be ready. Most of all, have fun ;)

Now that's the most positive post I've heard all day. Good for you kiddo. ;)

 

[yenchin]

This spells out what you need to know eventually: http://www.staff.science.uu.nl/~hooft101/theorist.html

 

[MarcAlexander]

This spells out what you need to know eventually: http://www.staff.science.uu.nl/~hooft101/theorist.html

Thanks!

 

[Lavabug]

I have the same question as the OP, but my situation is different: I'm a 3rd year student and I've finished all my math courses (linear algebra(weak on theory), year's worth of multivariable calculus, ODEs, PDEs, complex variables and integral transforms). Which means I have no option of taking more math in my 3rd and 4th years unless I spend my 4th year abroad and manage to take something.

My university used to offer an elective introductory course on tensors, integral equations and group theory with applications to physics in the 3rd year. I managed to get the notes on the subjects but they're pretty condensed/summarized. Can anyone recommend a good book on these subjects that's accessible for self-study/fun? Because it sounds like it would be extremely relevant to any sort of advanced physics in particular HEP.

Is rigor really important at this level? Or is it more important to get familiarized with applying these areas of math to physics than having an "epsilon-delta analysis" emphasis?

 

[FeDeX_LaTeX]

I apologise if i pulled a 'heart string'. What I meant was that throughout school I am constantly taught Mathematics that seems to have no practical use like Median, Prime Factors, HCF, LCM etc. Personally I love Algebra.

I'm assuming you mean GCSE Mathematics. Yes, your GCSE Maths years (14-16) will be incredibly boring. Start learning some AS topics; it couldn't hurt. You could do what I did and get your school to enter you for some AS modules early if you're confident enough to; that will be a starting point into calculus. One of the most intimidating things about mathematics can often be notation for some students.

Yes, there is one. It's called "The Road to Reality" by Roger Penrose. If you read it cover to cover, and understand everything in it, you will know all you need to know to be a great physicist.

Road to Reality is a great book, but it is no easy read. Despite what some reviews and the blurb may suggest, you do need to do a lot of background research when it comes to the harder chapters. I doubt anyone can use this book alone to teach themselves the mathematics of the book, particularly the manifolds chapters (and the Lie algebra chapter, I think?). Although this book is cheap, it certainly is not for the scientific layperson. I disagree with Penrose's view that you don't have to look at the equations in detail to understand what is going on. Simply put, if you don't have the sufficient mathematical background to learn some of these topics, you won't learn much from this book. I recommend that you make an attempt (because it can be a very rewarding read) but don't become discouraged if you make almost no progress with it. Don't be fooled by the cover; this book will have a lot of mathematics in it. There are exercises at the bottom of most pages for you to verify your learning, but they aren't easy.

I've canceled the order for the Quantum Physics book and I think I'm going to get that "Basic Mathematics" book by Serge Lang.

I think the best thing for you to do is actually just to get an AS textbook. You can even get them for free online these days from a quick Google search. Get the Edexcel ones; there's one for each of the 18 modules; C1-4, M1-5, FP1-3, D1-2, S1-4. Start working your way up through the core modules and do some of the mechanics and further pure ones (stats couldn't hurt too much either). I think the D1/D2 books are pretty bad though; they do teach the content, but they are terrible representations of Discrete Mathematics (the manner in which it is taught it notoriously dull). Get the newer textbooks (2008 onwards); they make the stuff easy to understand and have lots of exercises. Not only that, but the way in which these textbooks are laid out means your knowledge shouldn't atrophy, especially as you're going to be sitting those papers pretty soon anyway!

Also take a look at the NRICH website (nrich.maths.org). There are lots of problems on there for you to solve. Despite its colourful look, some of those problems are very tough; if you find a problem really easy, you can consider possible extensions of the problem and consider the notion of proof.

I also recommend taking some time out every now and then. Do you like problem-solving? Seeing as you're in the UK (like me) and at that age where you start to become 'better' at mathematics (for me, anyway), it wouldn't hurt to try experimenting with some of the mathematics you've learned already. You might thing that some of the GCSE stuff is completely pointless, but they are fundamental prerequisites for A-level topics (mostly -- there is some stuff in the GCSE spec that you'll never need for AS/A2/STEP, ever). For instance, at your age, I wondered why you could only find natural-number derivatives (1st, 2nd, 3rd, etc.), but with some experimentation for a day or two I found that you could extend it to other sets of numbers (e.g. it became possible to find the (3+2i)th derivative of some function). Experiment with what you have, and try to solve some problems (NRICH); it'll be very rewarding. Unless you hate maths with a passion.

I'm hearing a lot of things from people like "take precalc, trig, algebra II, (...)". In the UK you probably won't know what those topics entail, so I think it's easier if I just say which modules to look at: Pre-calc stuff is higher-end GCSE-level and covered in C1-C4; same for trig. I'm tempted to say not to waste too much time with C1 since half of it is GCSE stuff, but its foundations are important.

I was in your situation just two years ago; volunteer for masterclasses where they are offered, look at online lectures (KhanAcademy, PatrickJMT, Dr Chris Tisdell (sp?), and there's a guy that does lots of Topology stuff too, but look at that when you're in your AS year). I started off with Edugratis (whose website is sadly no longer working) who introduced me to calculus at 13-14. That led me to "Paul's Online Math Notes". Take your time and work through it slowly.

And don't neglect your other subjects!

If you need resources or have any queries, you can PM me if you wish. I'm 16 and doing my A-levels and (hopefully) can give you a bit of guidance.

 

[dalcde]

Don't really care about the rest of Physics besides the particle aspect, e.g.I couldn't give a damn about light refraction or thermal conduction.

I'm with you.

 

[MarcAlexander]

I'm assuming you mean GCSE Mathematics. Yes, your GCSE Maths years (14-16) will be incredibly boring. Start learning some AS topics; it couldn't hurt. You could do what I did and get your school to enter you for some AS modules early if you're confident enough to; that will be a starting point into calculus. One of the most intimidating things about mathematics can often be notation for some students.



Road to Reality is a great book, but it is no easy read. Despite what some reviews and the blurb may suggest, you do need to do a lot of background research when it comes to the harder chapters. I doubt anyone can use this book alone to teach themselves the mathematics of the book, particularly the manifolds chapters (and the Lie algebra chapter, I think?). Although this book is cheap, it certainly is not for the scientific layperson. I disagree with Penrose's view that you don't have to look at the equations in detail to understand what is going on. Simply put, if you don't have the sufficient mathematical background to learn some of these topics, you won't learn much from this book. I recommend that you make an attempt (because it can be a very rewarding read) but don't become discouraged if you make almost no progress with it. Don't be fooled by the cover; this book will have a lot of mathematics in it. There are exercises at the bottom of most pages for you to verify your learning, but they aren't easy.



I think the best thing for you to do is actually just to get an AS textbook. You can even get them for free online these days from a quick Google search. Get the Edexcel ones; there's one for each of the 18 modules; C1-4, M1-5, FP1-3, D1-2, S1-4. Start working your way up through the core modules and do some of the mechanics and further pure ones (stats couldn't hurt too much either). I think the D1/D2 books are pretty bad though; they do teach the content, but they are terrible representations of Discrete Mathematics (the manner in which it is taught it notoriously dull). Get the newer textbooks (2008 onwards); they make the stuff easy to understand and have lots of exercises. Not only that, but the way in which these textbooks are laid out means your knowledge shouldn't atrophy, especially as you're going to be sitting those papers pretty soon anyway!

Also take a look at the NRICH website (nrich.maths.org). There are lots of problems on there for you to solve. Despite its colourful look, some of those problems are very tough; if you find a problem really easy, you can consider possible extensions of the problem and consider the notion of proof.

I also recommend taking some time out every now and then. Do you like problem-solving? Seeing as you're in the UK (like me) and at that age where you start to become 'better' at mathematics (for me, anyway), it wouldn't hurt to try experimenting with some of the mathematics you've learned already. You might thing that some of the GCSE stuff is completely pointless, but they are fundamental prerequisites for A-level topics (mostly -- there is some stuff in the GCSE spec that you'll never need for AS/A2/STEP, ever). For instance, at your age, I wondered why you could only find natural-number derivatives (1st, 2nd, 3rd, etc.), but with some experimentation for a day or two I found that you could extend it to other sets of numbers (e.g. it became possible to find the (3+2i)th derivative of some function). Experiment with what you have, and try to solve some problems (NRICH); it'll be very rewarding. Unless you hate maths with a passion.

I'm hearing a lot of things from people like "take precalc, trig, algebra II, (...)". In the UK you probably won't know what those topics entail, so I think it's easier if I just say which modules to look at: Pre-calc stuff is higher-end GCSE-level and covered in C1-C4; same for trig. I'm tempted to say not to waste too much time with C1 since half of it is GCSE stuff, but its foundations are important.

I was in your situation just two years ago; volunteer for masterclasses where they are offered, look at online lectures (KhanAcademy, PatrickJMT, Dr Chris Tisdell (sp?), and there's a guy that does lots of Topology stuff too, but look at that when you're in your AS year). I started off with Edugratis (whose website is sadly no longer working) who introduced me to calculus at 13-14. That led me to "Paul's Online Math Notes". Take your time and work through it slowly.

And don't neglect your other subjects!

If you need resources or have any queries, you can PM me if you wish. I'm 16 and doing my A-levels and (hopefully) can give you a bit of guidance.

Thank you. Finally someone who realizes that things in America have different naming conventions as of that in the UK. I know how to do Trigonometry and I enjoy 'problem solving', I just dislike graphs very much as I have never really found a use for them besides the obvious uses. I shall pursue my research into these areas of Mathematics but mainly focus on current studies on it(GCSE ones). I'm going to go do my Chemistry homework, will take a few hours or so, I'm going to say: live long and prosper.

 

[FeDeX_LaTeX]

Thank you. Finally someone who realizes that things in America have different naming conventions as of that in the UK. I know how to do Trigonometry and I enjoy 'problem solving', I just dislike graphs very much as I have never really found a use for them besides the obvious uses. I shall pursue my research into these areas of Mathematics but mainly focus on current studies on it(GCSE ones). I'm going to go do my Chemistry homework, will take a few hours or so, I'm going to say: live long and prosper.

What has been your experience of trigonometry so far? If it's just the stuff in the GCSE syllabus, make sure you remember all of it for A-level. You'll need them for M1-5 and C2.

I'm not sure what you mean by 'graphs'. If you mean the standard y = mx + c and y = ax^2 + bx + c graphs they teach you at GCSE, there is a lot more to it than just that, especially in statistics (t-distributions, probability density function, continuous and cumulative distribution functions, etc. -- these are all S1-4 topics). What is it that you don't like about graphs? Is it the notation that is confusing ( i.e. f(x) )?

After studying C1 you will probably like graphs a bit more. Have you heard of limits?

 

[neutrino']

marcalexander. if you know the famous particle physicist Richard Feynman, he had alredy mastered calculus by the age of 15 which means that it is time for you to start enlighten yourself of calculus. He discuses in his autobiography that his mastery of calculus at young age helped him at undergrad school (at MIT), which is clear that his success in QED and other researchs arises from his mastery of calculus. He studied calculus using the book "Calculus for the practical man" buy it or google it for ... as FeDeX_ LaTeX said a quick googling ;).

your consideration for your future career is appreaciable.

 

[FeDeX_LaTeX]

Just out of interest -- what constitutes a 'mastery of calculus'?

 

[MarcAlexander]

What has been your experience of trigonometry so far? If it's just the stuff in the GCSE syllabus, make sure you remember all of it for A-level. You'll need them for M1-5 and C2.

I'm not sure what you mean by 'graphs'. If you mean the standard y = mx + c and y = ax^2 + bx + c graphs they teach you at GCSE, there is a lot more to it than just that, especially in statistics (t-distributions, probability density function, continuous and cumulative distribution functions, etc. -- these are all S1-4 topics). What is it that you don't like about graphs? Is it the notation that is confusing ( i.e. f(x) )?

After studying C1 you will probably like graphs a bit more. Have you heard of limits?

I mean bar charts and median etc. I love linear algebra. ;)
No, I have not heard of this 'limits'.

 

[MarcAlexander]

marcalexander. if you know the famous particle physicist Richard Feynman, he had alredy mastered calculus by the age of 15 which means that it is time for you to start enlighten yourself of calculus. He discuses in his autobiography that his mastery of calculus at young age helped him at undergrad school (at MIT), which is clear that his success in QED and other researchs arises from his mastery of calculus. He studied calculus using the book "Calculus for the practical man" buy it or google it for ... as FeDeX_ LaTeX said a quick googling ;).

your consideration for your future career is appreaciable.

A well spoken post. ;)

As soon as I have 'remembered' all of my previous Mathematical education(i.e.revised it), then I shall look into Calculus and maybe even start learning it. :)

 

[neutrino']

Just out of interest -- what constitutes a 'mastery of calculus'?

understanding ("mastery") of differential and integral calculus. and then partial differentiation and so forth. also mastering multivariable differentiation.

FeDeX_ LaTeX what r u trying to pull?


and marc, I should have mentioned that mastering precalulus (having a solid background on trig, matrix...) is important. Take a look at this book:
Precalculus, Larson
it is a very nice book with practical application of knowledge of each chapter.

 

[FeDeX_LaTeX]

I wasn't trying to "pull" anything; merely trying to see what it takes to 'master' calculus. Given the amount of different topics in calculus that does seem like a difficult task.

C1 will teach you how to differentiate and integrate a basic function in the form of kxⁿ.
C2 and M2 will open you up to applications of differentiation.
C3 will teach you how to differentiate almost every common function.
C4 will teach you methods of integration and implicit differentiation which can then be applied in M3.

 

[neutrino']

I wasn't trying to "pull" anything; merely trying to see what it takes to 'master' calculus. Given the amount of different topics in calculus that does seem like a difficult task.

C1 will teach you how to differentiate and integrate a basic function in the form of kxⁿ.
C2 and M2 will open you up to applications of differentiation.
C3 will teach you how to differentiate almost every common function.
C4 will teach you methods of integration and implicit differentiation which can then be applied in M3.

Excuse me fedex. I shouldn't have said that. Since I don't live in the UK, I want to know if you are given Calculus in the age 14-17?

 

[MarcAlexander]

Excuse me fedex. I shouldn't have said that. Since I don't live in the UK, I want to know if you are given Calculus in the age 14-17?

Calculus is not available until you reach A-level/University, I think. I do not possesses access to learning Calculus at school, yet.

 

[neutrino']

so A-level means university? i have uk physics books. so what does O- level mean?

 

[GregJ]

GCSEs followed by O-Levels. After those are A-Levels (can be thought of as university entrance level). Although I started school in the UK, I did not finish so I am not 100% sure.