Physics Education - (Ed extended footage)
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- เผยแพร่เมื่อ 12 พ.ย. 2012
- Extended interview footage with Ed Copeland.
Main video at: • Problems with High Sch...
All the extras at: bit.ly/SO4Hrh
Test Tube by video journalist Brady Haran for the University of Nottingham.
More at www.test-tube.org.uk/ - วิทยาศาสตร์และเทคโนโลยี
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I don't know why but these videos always calm me down
its because he overuses extreme closeups
Pootie Tang It’s because he’s telling you Fairytale, Babies like it and gullible adults also.
Cymoon RBACpro get back into the loony bin
" i don't care, i just want to solve it" basically all mathematician
I was hoping Ed talking about how mathematics and physics came together as a package would inspire Brady to begin putting more mathematics in the videos.
i think the point is that you physically cant understand physics without maths especially at a higher level
I think it's because he wants to force them to try to explain stuff without equations, exactly for people who don't know that type if math. But yes, sometimes it would be nice with a bit of math 😁
Loving the cheeky D1 reference when he's talking about Further Maths XD
I love the way Ed explains things.
I have watched Sixty Symbols videos for a long time now and have always admired every professor featured in the videos. Ed Copeland seems so relaxed and I admire how much he seems to truly care about his field of study. I have always loved Physics and I plan to study it further, and this is just one of the many great influences that I have come across. I also loved the cheeky "lets get more sport back in there" comment on education. Thank you so much for these videos, and the inspiration to continue pursuing my dream of becoming a Physicist.
We've got memorise chapters and past papers - literally the recipe for A levels.
Physics A level is a joke, there’s a bigger emphasis on practicals and practical skills than there is for maths, which is completely outrageous.
Darwin I love ed, hes so calm.
Like a physics yoda or something
As a returning student (starting an electrical engineering degree at 30), I can vouch for the weakness in math and physics in the US school system. I hardly ever touched calculus, and certainly didn't do anything with physics in high school.
Add to that a gap of over a decade, and things get really difficult. Despite that, though. It's been a fantastic school year. I've gone from watching videos like these, to understanding calculus and basic mechanics.
@@existenceisillusion6528 can you describe what kind of pain please ?
10:55 I can totally confirm and agree with this. The teaching method now seems to be get by the test then your fine. It's not understanding the material, its understanding the test.
I hated doing surfaces of revolution, was poorly explained in the text book I had.
"You've just got to go and do it."
Profound words.
Thank you for being so comprehensive and helpful with your uploads, Brady. I really appreciate it!
I wish I had done further :/ sigh Im teaching it to myself and most of its okay, but occasionally I get a problem wrong and I don't have a teacher to explain where I've gone wrong so I can't correct my mistakes
Further maths also has the more enjoyable topics in my opinion: complex numbers, matrices, hyperbolic functions...
Really valuable contributions from Tony , again. Ty very much because access to expert-level university professors telling it how it is is available to almost anyone globally with access to the net and English. This may help more enter this vital field in the future . It is of interest to anyone in education and the lay viewer too.
Brady, your ask the most pertinent questions!
I feel as though you always ask the same questions I would have asked if I were to to have the opportunity to interview these professors.
In school, besides from the inevitable distraction from other students messing around, I found that I was always looking for a reason why something like "y^2 - 4y -8 = 5y +28" made sense.
I didn't just want to GET the answer. I wanted the reason for that answer. Perhaps I didn't have the insight to explain it to myself. I just found it really tough to not think about how poorly it was taught.
Ny mental arithmetic is fine. I just can't justify these algebraic equations logically. I am extremely passionate about physics and the pursuit of science in general. I just wish I understood the underlying mathematics.
Old comment I know but lemme try to explain :) Your equation simplifies to y^2 - 9y = 36 which is a tad complicated for an example so let's say you have a quadratic equation like x^2 - x = 0. From either factorisation or the quadratic formula you know that x =0 or x=1.
What does that *really* mean though? Well consider a funcion x^2 - x = y. Many know that this is a parabola that "opens" upwards. So what does x^2 - x = A mean (where A is a number)? This means we are looking for points where the parabola crosses the line y = A. So if x^2 - x = 0 we are looking for points where the parabola intersects with the x-axis, and those points happen to be x= 1 and x=0
That gives geometric intuition about the equation we dealt with. When the equations get more complicated (and we dont have 2-d curves anymore) it's a bit harder to visualize but most of the times we think of points where two or more graphs meet :)
@@dankaxon4230 it's unnecessarily complicated for the purpose of the example I gave. The quadratic itself isn't complicated but I can't be arsed to get off my phone and take a piece of paper to work out the zeroes for the equation so I used a more simple example.
@@dankaxon4230 Ain't you the brightest
Further maths is my favourite subject by far! Love it!
I really enjoy watching all of the professors and scientists at Nottingham speak, but above all, Professor Copeland always has a calm amd inviting demeanor.
Ed was in university in the late seventies? Assuming 1980 and 20 years old, that makes him 52. Still looks like he's in his 30's to me when I'm not paying attention. And when I look closer, 40's.
For the first year of my Physics degree, we had two lectures a week dedicated to maths, had a tutorial sheet every week and it got everyone to the same level. We started with A level maths and then went onto differential equations, complex numbers, vectors etc. We also had two maths lectures a week in second year, covering vector calculus and some higher order differential equations. There are some problems with matching the maths to the physics, but it is improving.
What's with the aversion to "maths"? Math is easily the most important subject in school. It's the language of money and trade. Realistically, there is almost no field where you won't be using math regularly. Now, to be fair, I feel I have a much more intuitive grasp of math and logic, but are concepts like algebra and geometry really that difficult to grasp by high school graduation?
I will say, the education system is kind of broken in how time is the metric for advancing, not actual completion or understanding. I fear too many students are pushed into the next level because it's the end of the semester, not because they grasp the subject.
To be honest, they should put a large amount of focus into three main maths topics; Calculus, Statistics and Algebra(Inclusive of Linear Algebra)
Three most important topics for doing physics or, practically, any course in university. Everything else like number theory or combinatorics should be done as well but not so much of.
Discrete mathematics
@TheSpecialistGamerX2 you're right
i´m simply an accountant, and.... i just cannot stop admire these kind of very smart and humble people...
Great. I enjoyed hearing him talk about maths.
Thanks so much it really helped me realise that my decision to do fmath is worth it!
Yes, I totally agree with what Ed says. I did Further Maths at 'A' level before going on to do Astrophysics at the University of Leicester (back in 1992). Although I struggled with quite a few of the concepts in Further Maths and didn't get a particularly good grade I found that when I got to Leicester I was way ahead of most of my fellow students when it came to the maths so I was glad I did it. A lot of the maths used I'd encountered before so I knew quite a few of the "tricks"!
Further Maths was the best A-Level I did. It's both very interesting, but also challenging and really gives you a lot of what you need to do some proper physics.
Great video, like the fact there is such a difference in opinion, between Ed and Phil
Wow Thanks Brady
Please! Please more stuff with Ed :D
Despite the looming doom of my final further exams in a couple of days, I'm really happy I do further maths in preparation for engineering at uni.
I so agree with Ed's comments: my first calculus course when I've started studying mechanical engineering was indeed on the imaginary numbers... and than I understood I still had to learn a lot before I could even try to start to learn the engineering stuff. The only way I was able to learn the math is just do it. It's no magic, its just gaining enough experience to see the how you can solve equations efficient. After you've done enough maths, you start to recognise the problems and you don't have you try X amount different approaches to solve a problem, but pick the right way in your first pair of attempts.
From a personal viewpoint, there's two familiar learning techniques, by doing and by rote memorization, and the current system is set up like a factory that has the non-physical, low cost, memorization preferences. Learning by doing is better for hands-on physical experimentation, but only in conjunction with the broad spectrum of background information most quickly aquired by rote for specializations in research.
The branching across fields seems to be what is the result of complexity, and it leaves the teaching of broad spectrum approaches a bit confused. What is the new scene of self-teaching skills and science courses online having on the economy? (Should be effective?)
Ed is a great man, i would love to be in one of his lectures. Greetings from Balkan.
Calculus and matrices too are probably particularly useful in economics as well :) I discovered something online the other day called "tensor calculus".
a great educator!
im in 11th year of physics and i want to become a physics proffesor its my big dream. this has helped me jnderstand the level of maths im going to need and il prepared for it.
You should see higher secondary maths and physics textbooks (India)
Hi.
Amazon.co.uk has a large library of books and e-books about all sorts of mathematics. You can check out the reviews to find out if one is worthwile. I'd suggest single-variable math analysis and linear algebra tot start off with.
This is so true!
Hello Brady! Maybe you can do one on Chemistry education in schools too! Would love to hear about it too (if there is anything much to say...) Yay thanks:D
right??!?!? he's always been my favorite! but dont dispair all you other guys, youre great too!
It's....acutally pretty much the same here. We don't have compter sciences or civil engineering (at least until university) but we do have technical and industrial production (fixing cars and opperating heavy machinery) and electrical engineering. We also have agricalture, fishing and forestry (farming); design, arts and crafts; building and construction; health and sosial studies (nursing); media and coms.(creating ads and taking pictures); and service and transport.
In Austria we can attend profession specific highschools. You can choose computer science, electrical engineering, civil engineering, commercial highschools, etc. You do get a general education there, but you also learn a real profession and then in case you go to university you have an advantage in your area. There is of course also the option for a very general highschool (Gymnasium), but I think that's maybe a waste of time. The only thing you are qualified after that is to go to university.
8 years later and there is no more AS exam but there is a UCAS exam to get predicted grades to receive uni offers...
Most of the more fun stuff it an optional module at the end of the second year, you choose 1 from five choices or it is chosen for you.
Sounds like he's talking about what'd be Calc 2 here in the states.
Trig Substitution was brutal for me to get through at the time.
In Norway in the first year of high school you take a test that determines how much you remember from last year. You then get placed in P1 or T1. P=practical math (easy) and T=Theoretical math (harder). The next year, if you have P1, you can choose P2 or S1 (Social math: for economics ect.). And if you had T1 you get either S1 or R1 (Sciences Math) which is the type of math you need to become an engineer and/or move on to University level physics, chemistry and math. I think it's a good system.
Im in linear algebra now and its pretty painful. it has such a abstract architecture. hard to wrap your mind around.
You were talking about i in the first physics lesson? What was the lesson on? (Physics 1 here in the US is typically mostly mechanics and dynamics, which.. doesn't use i.
Any recommended book on Mathematics for understanding topics like Tensors,Eigen values,Differential Equations in a bit of depth ?
You mean like the books "Calculus: a complete course" & "Linear Algebra and its applications"? You can get them where pirates lay anchor ;)
+Akhilesh Kumar calculus and linear algebra
Essentially, yes, or you could do these at college ('college' is not university, college is another thing here where you do AS and A levels). I've just started Maths, Further Maths, Physics and Chemistry AS levels myself.
I sense a numberfile series coming along... A level maths extension for transition to university!
What is the point of finding a diagonal matrix? I study further maths and have finished the FP3 syllabus but am struggling to see the point of finding a Diagonal Matrix, in terms of physics. I understand where Eigenvectors and Eigenvalues come into Quantum Mechanics but is there a special reason for it or is it just a matrix that contains all the Eigenvalues?
matricies are tool to determine linear relations of bunch of systems. They are used widely in wave or field theories. Look, you have this law, that bunch of indepandant vectors ( one from another) can describe certain "n-dimantional space", so they use this sh**t to determine does the equasion system can create or descrive "n-dimentional space of possible answers". Idk if its accurate or not, but this is the direction. I make a headace to my lecturer of calculus eqations and physics by same questions and i get the feeling that they dont know the answers themselves hiding behid "dont asq such questions! learn it now as it is, youll anderstant later....", but the problem is i cant learn something without knowing, even remotly, its purpose.
I 100% agree with Professor Copeland, as a further mathematician myself, I agree that the normal maths syllabus is not good enough to prepare students to a mathematical related degree. Further maths covers so much more content than the normal maths syllabus, and is a lot more fulfilling.
Since the subject came up... I wonder if you get any Canadian students...and how do they stack up?
I did Decision Maths last year in my AS Maths, and my god it was a nightmare. It ended up okay but I would have much rather done mechanics :) Anyway, I don't do Further Maths at A level (although nowadays I wish I did), would it be wise for me to get a textbook or a different source to look at for introductions to the sort of stuff necessary to know for the Physics courses at University? If so what would anyone recommend? :)
if you have some calculus and vector experience it's not much more you need. 1st year uni is mostly just getting everyone up to scratch. I didnt do further maths and I got 75% in my first year :)
No one from the UK says Sophomore, I have no idea what year that is.
Nine years later, time for an update on Ed's daughter.
Anyone here, do you know if the further maths that Ed is talking about is more in depth than Advanced Higher maths in Scotland? I know we do complex numbers and calculus with quite complicated equations and some general relativity in AH physics but I don't know what the courses in England and Wales have in them.
+Scott Boyd It is around the same things. But some exam boards in England are above the AH maths in Scotland.
+Nathan GggSteels Here in Australia we do 2 different high level maths courses, being Methods and Specialist. In Methods we do integration and differentiation, but for the rest of the year we are going to do statistics and stuff which I hardly think will contribute very much to my aspiration of becoming an engineer. The requirement for getting into methods is not quite as high as that of specialist so I got into that but I wasn't allowed to do specialist, which goes into vectors and complex numbers, things which are abundant in engineering. I think a potential problem is also the idea of prerequisites in high schools which can prevent people from achieving what they need as easily.
I agree. I feel that if in the younger years of maths I wasn't taught it as in depth as it could have been. It would have greatly benefited me later on.
But the math behind all of this is even more fascinating.
Anyone know what exam board is he talking about for maths? They tend to vary a tad
+mbk3986 That sounds like Edexcel to me, or at least when I did it we covered core, decision and stats
Exactly the same for me brother
Best. Idea. Ever. Let's hope its a saturday :P
fear of new students or sadness due to the lack of modern physics in his days? 06:03
anyway, really really really good initiative, sixtysymbols is the best!
thanks to you all guys and thanks to internet for all those wonders
In sum, remove exams? ;-)
I'm really regretting not taking further maths... I think that might have made uni a lot easier for me
I was not prepared for college science. I had no idea. The thing is, I am not a math person. But I could still do a lot of it, juuust enough to make myself think I was ready when I really wasn't and, to be honest, didn't really want to be. It wasn't wasted, by any streatch. But I'm a humanities guy. I could have developed that more.
For people who aren't going onto specifically a University physics track, is it more important for them to get a firm grounding in Classical Greek/Newtonian physics?
Even mechanical and civil (and maybe even chemical) engineers need more thermodynamics than quantum dynamics.
guys do help me out here. i am starting college this year and my final goal has always been theoretical physics. does that imply directly that i should do my BSc , or could i do engineering now (kinda like a back up plan) and then return to pure physics in my masters. jeez i need help, folks.
Do the BSc in Physics. If Physics fails Physics BSc can go on to get a MSc in engineering.
I think that it is frames, not fractions of a second.
I agree with you on the pop stars. :)
Brady's first question is genius.
Actually the ending with er and not re is the correct way there are just some people called british that don't know that it should end with er as everyone but british people end with er. So for the last time it's not metre it's meter.
You could say maths is.... *puts on sunglasses*
... Integral to Physics.
YEAAAAAAHHH!!!!
the first youtube video i've seen with no dislikes!
can you suggest some books to help us reach expectations.
sincerely
a student in a stupid education system.
If they want more depth from their undergraduates all you need to do is make Further Maths compulsory, BUT unfortunately not all schools make this option readily available to all students.
Here in the U.S, high school generally goes through what I'd call Algebra II, or maybe Pre-calc and Trigonometry (the pre-calc part is just limits...), and Calculus is considered a college level course, although if you're lucky you can take Calculus in high school. Generally the introductory physics courses CAN be taken concurrently with Calculus, but it's easier if you take it ahead of time.
Also the whole maths instead of math is messing me up :D
Completely off topic but what's going on with that clock at the bottom? Is the right hand unit 25ths of a second? Whaaaaaaaaat?
It's a 25 frame-per-second camera, so it's counting the frames.
***** Oooh, thank you. That would make a lot of sense :P
The A and As level exams are taken at ages 16 - 18 years old.
Without adequate mathematics (at least Calculus) Physics rapidly becomes a waste of time.
Mathematics is not physics for “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. “ so Said Einstein .
We say mathematics. However, I think the problem is the way we derive all course nicknames. We call Calculus calc. Biology Bio, Chemistry chem, etc. I think it is more based on the fact that Mathematics is a field so we shorten it and drop the "s." It's just another one of those things that we do differently like in the US we end words with "er" and not "re."
problem is that the maths O-level was emptied for the GCSE, and and the stuff that was removed had to be taught in addition to the A-level syllabus ... which overloads them at A-level. the group theory from O-level is gone; the calculus is gone; the proper linear algebra is gone. and this is bad news for anyone wishing to do a degree in maths, physics or engineering.
i would give anything to learn physics from mr copeland. its funny, a good professor can be like a godsend, while a bad professor can be the worst thing imagineable.
Maybe I'm misunderstanding something but the way he has to explain integration seems like they don't teach calculus in the UK. Is that correct? In the US calculus definitely isn't required but anybody looking to pursue a physics degree would have probably taken it, and integration is almost the entire focus of the 2nd semester of calculus. At least in my experience
Calculus is taught in the UK but usually not until about the age of 16/17 when you do a levels
that awesome moment when you read the most rated comment and is the exact same idea that you have in mind
I'm not saying that this is the way to go, I just wanted to show what systems there are.
The funny thing is that I probably learnt more physics by taking engineering than I did in the physics class,,,
We learnt all the simple stuff like forces and energy equations, all the electricity formula and theory.
We even touched on displacement, harmonic motions, imaginary numbers.
There is the old argument of breadth vs depth.
Now I'm curious, what do you guys think about Brazilians? Are we good scientists? Ps.: I'd love to study in Nottingham!
I DID have a bad year early on. In T1 I got the equivalent of a D and this year I got my first B in maths in a longe time. However I am only one person so I can't really base it on anything, and the numbers show that about half of all high school fail math so it's not tha great for everyone (obviously). I'm just saying that having a system like this is better than having the US system where everyone does the same thing for another 3 years and you don't get to specialize untill University.
It's weird that your Professors, who seem to have done 'A' level about 1979, all seem to have been left ignorant of imaginary and complex numbers. I did (JMB) 'A' level maths in 1975 and we certainly were introduced to both.
Rob Fenwitch Possibly different exam boards. We did imaginary numbers at my school as well at A-Level ( circa 1981 )
his ears a reminiscent of yoda :D
Brady, can you please ask them if the average level of freshmen knowing 'untaught knowledge' required for university has risen since the periodic video's and sixty symbols started?
the idea that physics students don't realize physics is a mathematical subject is crazy to me, at my age now 30+.... I'm not sure I really understood what physics was when I was in early highschool though
I have had imaginary numbers explained to me, and I understand that they are a number line that is at a right angle to real numbers, but I have no clue what THAT means.
that's a way of representing them? a complex number on that system is a number which is composed of a wholly real part and a wholly imaginary part. Once you have that you can subject these complex numbers to geometry and algebra and prove a whole bunch of stuff linking the two which are really cool. The imaginary bit is just a placeholder for the square root of minus one and so "ni" for n=real multiples, i=sqrt-1. The uses of the complex numbers and i are huge and wide reaching. My favourite result is the fact that wavefunctions are wholly complex and so the wavefunction its self isn't a physical wave, it isn't real. You need to do some stuff with it to get physical, meaningful things out of it
Complex numbers are not complicated. "Complex" just means that they are not "simple", i.e., they consist of *two* parts: a real part and an imaginary part (or a length and an angle).
You already know numbers that consist of two parts and which come with their own special rules for addition, subtraction, multiplication, division, equality.
They are called fractions.
Complex numbers are no more complicated than fractions: they are also just pairs of ordinary numbers + a set of rules for how to add, multiply, etc.
The rules are made so things work out "nicely": there is something that works a lot like a normal 1 when you multiply, something that works a lot like a normal 0 when you add, commutativity ("swaps": a+b = b+a, a*b = b*a) work the way you expect, etc.
A few things are weird (for both fractions and complex numbers) compared to "simple" numbers. For fractions, it is equality: (2,3) = (4,6) = (10,15) etc. For complex numbers it is relative comparisons (ordering) that at first glance isn't a problem but things don't work the way you expect them to when you scale the numbers you compare (multiply them with normal numbers).
But in both cases you get to keep almost all the math you are used to! And both extensions of the normal numbers are useful!
And why are they extensions? Because they can represent all the numbers you are used to -- and then some. Examples with fractions: 5 = (5,1), 11 = (11,1). Examples with complex numbers: 5 = (5,0), 11 = (11,0).
It so happens that you can do something more with complex numbers than you could with normal numbers, namely have a nicer square root function. With normal numbers, you can't always take the square root. With complex numbers you can (but the result may turn out not to be a normal number). You can, in fact, give a meaning to sqrt(-1)... just not one you can represent with normal numbers.
This is nice, because we really don't like exceptions in math, or places where our normal operations break down. That's why we invented negative numbers in the first place: doing addition backwards (=subtraction) didn't always work. It's also why we invented fractions: doing multiplication backwards (=division) didn't always work. Doing squaring backwards (= taking square roots) taught us that fractions weren't enough, so we invented real numbers. It turns out that roots teach us something more, namely the necessity for complex numbers.
With complex numbers, all these exceptions disappear except for one: we still can't divide by zero.
Calculus is all about how we can *almost* divide by zero anyway.
Oh, by the way, it also turns out to be useful to think of complex numbers as points in a plane (2D coordinate system). It's a nice representation, that's all.
Multiplication within complex numbers turns out to be different from what you are used to: it is a combination of a rotation and a scaling. You can see a small shadow of that with the normal numbers, namely when you multiply by negative numbers. As it turns out, multiplying by -1 is exactly the equivalent of a 180° rotation. That is precisely why multiplying two negative numbers gives you a positive result.
Complex analysis is what happens if you take complex numbers *really* seriously and it let's you patch up even more holes and exceptions for various functions where they tend to go towards positive or minus infinity.
Eric Taylor they don't have to be at a 90 degree level. Any imaginary basis for the complex plane can be chosen as long as the following analysis is consistent with that choice of basis.
Additional maths for O level teaches us logarithms,calculus, trigonometry