What are the math prerequisites?

[moe darklight]

I've searched the internet and can't find this information. I need to know what are the different math requirements, and in what order they should be learned so I don't get lost again and waste time (I've had to pause physics and calculus because I was starting to get lost; then I found out there's stuff I hadn't learned that I didn't know comes before).

so what are the usual prerequisites for Physics I & II?

when do linear algebra, differential equations, and tensors come into play in physics and in what order? (are those needed for the early stuff?)

what would come first, GR or Quantum?

... I'd ask more, but this should hold me for like the next decade

 

[robphy]

What does your school's [hopefully well-planned] curriculum suggest?
Are you following the curriculum?

 

[moe darklight]

What does your school's [hopefully well-planned] curriculum suggest?
Are you following the curriculum?

I'm not in school for anything even remotely math or physics related (I start university this fall, and am going to major in literature/creative writing— I got the letter that I got accepted just yesterday actually ).

In high school I was an idiot and dropped out of math in grade eleven, figuring I wouldn't need it, so I don't even have that to go by.

Just this past year I've gained an interest in physics and math and have been spending a little time every day studying. My biggest problem has been that I don't know what comes when, so I'll start a topic and then get lost only to find out that there is something that comes before it... which gets really annoying (just to give you an idea: one of the first book I bought was "A first course in general relativity" ... it said "a first course" so I figured it'd be really basic well, needless to say, there it is: sitting on my shelf after I got lost within the first 30 pages).

so right now I'm right back to the basics with precalculus and algebra (I got schaum's precalculus); figured I'd start from that very start and make sure I don't miss anything— I guess I'm doing fine since I get most answers to the questions right.— that's why I ask; because, since I don't have a school to tell me what to take, I don't want to unknowingly skip a major step and find myself lost again.

 

[robphy]

Here's an example:
http://apps.carleton.edu/curricular/physics/handbook05_06/major/

 

[symbolipoint]

I'm not in school for anything even remotely math or physics related (I start university this fall, and am going to major in literature/creative writing— I got the letter that I got accepted just yesterday actually ).

In high school I was an idiot and dropped out of math in grade eleven, figuring I wouldn't need it, so I don't even have that to go by.

Just this past year I've gained an interest in physics and math and have been spending a little time every day studying. My biggest problem has been that I don't know what comes when, so I'll start a topic and then get lost only to find out that there is something that comes before it... which gets really annoying (just to give you an idea: one of the first book I bought was "A first course in general relativity" ... it said "a first course" so I figured it'd be really basic well, needless to say, there it is: sitting on my shelf after I got lost within the first 30 pages).

so right now I'm right back to the basics with precalculus and algebra (I got schaum's precalculus); figured I'd start from that very start and make sure I don't miss anything— I guess I'm doing fine since I get most answers to the questions right.— that's why I ask; because, since I don't have a school to tell me what to take, I don't want to unknowingly skip a major step and find myself lost again.

If you are able to adequately study PreCalculus, then this is good. Study Trigonometry either within your current PreCalculus book, if it is contained there, or from a good Trigonometry book in case your Precalculus book does not contain it. After your PreCalculus with Trigonometry, next do in order: Calculus 1, 2, 3(being "Intermediate" Calculus), and you'll want an introduction to Linear Algebra and some study of Differential Equations.

The typical lower division fundamental Physics courses require Calculus 1 and 2, very little Linear Algebra, sometimes a little bit of differential equations; and Algebra and Trigonometry throughout. Maybe some things had changed during last several years but maybe someone else can comment on whether the typical lower level Physics courses use much Intermediate Calculus (third semester Calculus).

 

[Poop-Loops]

The following route is pretty standard:

Algebra -> Geometry (nothing hardcore, just regular High-School geometry) -> Trigonometry -> Calculus (Stewart's Calculus is a standard text. I liked it a lot.) -> Linear Algebra -> Differential Equations.

That's all the math classes I've taken. The rest of the math I need I learned in mathematical physics (Boas' book is standard) and in the various physics courses that the math is needed to advance.

 

[moe darklight]

cool, thanks guys that clears things up.

 

[muppet]

Also, as far as physics goes: in UK universities you'll often start QM in your first year (as you've done partial differentiation by the time you leave school), wheras you might do general relativity in your third year but more likely wouldn't cover it until fourth year. So I'm afraid there's a bit of a gap between popsci and introductory courses

 

[Brad Barker]

if there is a course offered on general relativity for undergrads, it is likely an elective, whereas quantum mechanics is typically (universally?) a requirement for a physics degree.

in my experience, i took linear algebra the semester after differential equations. fairly interchangeable.

 

[Poop-Loops]

Same for me, but LA was definitely easier for me than Diff EQs, so I listed it first.

 

[cristo]

Also, as far as physics goes: in UK universities you'll often start QM in your first year (as you've done partial differentiation by the time you leave school),

Bloody hell.. what school did you go to? I hadn't see partial differentiation until I got to university.

But yes, I agree that quantum mechanics is usually taught earlier that GR. (I'm not sure why GR was asked about as opposed to SR; that latter is of course normally mentioned in first year).

 

[muppet]

Hehe.. actually come to think of it you're right cristo; I was getting it confused with implicit I think! My bad. I think people who do full further maths A2 do PDEs though (at least I remember my ex telling me about them).
And just to reiterate: you can't call it a physics degree unless it has quantum mechanics in but most physicists will never study general relativity, although nearly all will study special relativity, to some extent anyway.

 

[cristo]

Hehe.. actually come to think of it you're right cristo; I was getting it confused with implicit I think! My bad. I think people who do full further maths A2 do PDEs though (at least I remember my ex telling me about them).

Yea, that's more likely. I never did further maths: my teacher asked me at the time, but I said I "didn't want to study maths all week." It's funny how things turn out!

 

[muppet]

Hah... I nearly didn't do physics A-level because I thought the teacher was crap, and flatly refused to do further maths A-level because I was bored by my GCSE maths teacher. That Hawking and his Brief History have a lot to answer for...

 

[moe darklight]

But yes, I agree that quantum mechanics is usually taught earlier that GR. (I'm not sure why GR was asked about as opposed to SR; that latter is of course normally mentioned in first year).

O I see. yea that's why I asked: every textbook I see for physics talks about SR and contains an introduction to QM, yet I'd never seen one with even an introduction to GR, and wondered why that is... I didn't know it wasn't standard. I was just asking about it because I don't really know much about it but from the little I've heard it sounds interesting and wanted to know when it's usually taught (namely: when, if ever, I'll be able to understand that damn book I bought — it cost me like 30 bucks and I'm not one to waste that kind of money. I'll get through it if it's the last thing I do!

me vs. complicated GR book I don't understand
round 1​

do you think it's even possible to learn this stuff on my own? I'm handling algebra and all that well, but that's just the beginning; some of the math I see on the more advanced forums and textbooks like on tensors make me dizzy I don't really see myself being able to learn stuff like that ... I guess I'll just have to find out on my own what my limit is.

 

[cristo]

GR is definitely interesting! Which GR book did you buy, moe?

 

[MathematicalPhysicist]

O I see. yea that's why I asked: every textbook I see for physics talks about SR and contains an introduction to QM, yet I'd never seen one with even an introduction to GR, and wondered why that is... I didn't know it wasn't standard. I was just asking about it because I don't really know much about it but from the little I've heard it sounds interesting and wanted to know when it's usually taught (namely: when, if ever, I'll be able to understand that damn book I bought — it cost me like 30 bucks and I'm not one to waste that kind of money. I'll get through it if it's the last thing I do!

me vs. complicated GR book I don't understand
round 1​

do you think it's even possible to learn this stuff on my own? I'm handling algebra and all that well, but that's just the beginning; some of the math I see on the more advanced forums and textbooks like on tensors make me dizzy I don't really see myself being able to learn stuff like that ... I guess I'll just have to find out on my own what my limit is.

The latest edition of wheeler and taylor (spacetime physics), has an introductory chapter on GR, but it's better to read the book from start to finish before starting tackling GR, for GR you need differential geometry,differential forms and other nice mathematical tools which I'm unaware of at the moment.

 

[moe darklight]

GR is definitely interesting! Which GR book did you buy, moe?

"A First Course In General Relativity." is it good? it was in the batch of physics books I got when I thought physics might be interesting and figured I'd check it out. I didn't know it was so advanced!

first, it said "a first course." also, general relativity, to my untrained ear, sounded like it would be easier than special relativity (lke, you know: this is just the general idea; nothing special ). "this looks like a perfect starting point!" I thought when I saw the book — needless to say, I didn't know the first thing about physics a year ago. I had read only a little on special relativity, which I found really cool— I called my dad really excited that I could tell him how much younger than everyone else he was for driving two hours to work every day... it came to like billionths of a second in about 30 years of driving from that day (assuming everyone else he knows stays in an inertial point of reference).
he didn't find it as exciting as I thought he would .

when did you learn GR? are you still studying or are you done?

 

[cristo]

"A First Course In General Relativity." is it good? it was in the batch of physics books I got when I thought physics might be interesting and figured I'd check it out. I didn't know it was so advanced!

By Schutz? It's a good book, but may be a little too advanced right now. The book suggested above is good, though (Taylor and Wheeler). That seems like it would be a good place to start.

first, it said "a first course." also, general relativity, to my untrained ear, sounded like it would be easier than special relativity (lke, you know: this is just the general idea; nothing special ). "this looks like a perfect starting point!" I thought when I saw the book — needless to say, I didn't know the first thing about physics a year ago.

That's quite a common mistake; however the theories are called what they are because special relativity is a special case of general relativity; that is, it only discusses inertial frames of reference.

when did you learn GR? are you still studying or are you done?

I first learned GR properly a couple of years ago, and I took two courses on it in my undergrad days. I still use GR quite a bit, and know nothing like the amount that the experts do, so I'd say I was still learning!