Theoretical Physics - Prerequisites

sponsoredwalk

Hi I have a question regarding the Theoretical Physics course in Trinity. I've read all the info on the website and it seems that nothing more than a moderate introduction to calculus and physics is necessary but i'd like to know if this is true. From my study I've found calculus based physics far more easier than leaving cert physics due to the intuition as opposed to learning blind facts on faith so I think I'd be capable of doing well but, I wonder how fast the pace is in the class itself.
If by next year I had a thorough understanding of Linear Algebra, Multivariable Calculus and a reasonable understanding of electromagnetism would the first year be still sufficiently challenging or would I have the peace of mind to study ahead.
Please let me know your thoughts, Gatias Tibi Ago

antiselfdual

Sorry are you planning on doing the course or teaching yourself at home, I'm a bit confused... But in any case:

Seeing as everyone who does the course starts off having done Leaving Cert maths/physics/applied math they don't expect anything more from you. Having done some linear algebra, calculus and electromagnetism couldn't but help you out as in first year tp you do a linear algebra course, (mostly single variable) analysis and a bit of electromagnetism/waves (under the wonderful title of "Seeing and Hearing", God bless the School of Physics)... but they're not a "prerequisite" for the course which is supposed to teach you those things itself.

I'm not entirely sure what you mean by the "peace of mind to study ahead," there's no way I can reasonably evaluate how your self-taught knowledge will compare to what's expected in the first year courses (which have changed a little since I did them). I've never heard of anyone being so damn good at first year that it was mostly trivial to them. Out of interest what books are you using/thinking of using at the moment?

sponsoredwalk

Well, I am self-teaching myself physics using loads of different sources. My best sources are sitting down with the books though and hammering through the questions. I've used the online MIT courses a bit, but only for clarification purposes in calculus and am beginning to use it for linear algebra.For physics I hammered through all 52 lectures of The Mechanical Universe though this was as I was beginning calculus so it was more of an introduction and now i have fundamentals of physics -8th edition which is brilliant so far. I hear it's very thorough for an intro to E&M too. As I'll have to wait for the mature student option to attend the class (should I choose to do so) I have a year free so I'd like to just be sure that I'm doing the right work as opposed to spending a year on doing work which is ok but not up to the level required. I suppose any links etc... could be very useful if anyone has any. My main worries are as follows;

Hyperbolic geometry - in special relativity is it used as the basis or is it taught ala algebra? I find it very hard to understand Leonard Susskind's version of special relativity on youtube (Stanford Lectures) using the light cone and hyperbolic geometry and haven't found a sufficient link to teach it to me so far. I'd like to be able to understand Euler's e to the i theta version of trig with complex numbers but I have no links or books to do so.

Advanced Calculus - on tcd's website it looks like calculus 2, i.e. gradient, curl, beginning ode's. is it similar to this course, say were I to be sufficient in all of these aspects of calculus by next year would i have much work to do?
http://ocw.mit.edu/OcwWeb/Mathematics/18-02Fall-2007/VideoLectures/index.htm
http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/VideoLectures/index.htm

I'll post more questions in due course. thanks a lot for your time gratias!

Fringe

There's no need to do any of that although it would probably help a bit. We've all started from scratch. Linear algebra is a bit difficult at the moment and mechanics would be a lot harder if I didn't do applied maths. The rest is reasonably easy although that is all at the moment. It could all go downhill in a few months when we start other topics. If you went in with all that already learned, you wouldn't have a problem at all.

antiselfdual

Okay well the level you're aiming for is beyond what you'll do in first year TP, not that that's a criticism.

With regards to some of the points:

Special relativity in first year is very basic - see here. A little more is done in 2nd yr and a little in 3rd, mostly learning the use of [latex]x^{\mu}[/latex] style notation.

The MIT links you posted seem similar to the content of 2nd year methods, see here. Obviously if you can do all that before first year you'll be very well prepared indeed.

For a general approximation of some courses, go here

I think the essential point is that your main worries are issues only encountered by students of TP several months or years into the degree, so don't worry...

Fringe

Yeah you're definitely doing way too much for first year. If by advanced calculus, you mean the module called advanced calculus, it is incredibly boring. The module is more focused on techniques rather than theory. The first few lectures have only been leaving cert level. I counted a few people sleeping on Thursday. I think you're worrying a bit too much. You don't need to learn anything beforehand(although there's nothing stopping you) as all classes start from scratch and assume you do not know anything.

Aoibheann

sponsoredwalk wrote: »

Hi I have a question regarding the Theoretical Physics course in Trinity. I've read all the info on the website and it seems that nothing more than a moderate introduction to calculus and physics is necessary but i'd like to know if this is true. From my study I've found calculus based physics far more easier than leaving cert physics due to the intuition as opposed to learning blind facts on faith so I think I'd be capable of doing well but, I wonder how fast the pace is in the class itself.
If by next year I had a thorough understanding of Linear Algebra, Multivariable Calculus and a reasonable understanding of electromagnetism would the first year be still sufficiently challenging or would I have the peace of mind to study ahead.
Please let me know your thoughts, Gatias Tibi Ago

Tbh, you'll be fine without doing any of that - if you knew Linear Algebra well, where would the real maths challenge come from? :P The calculus module so far is grand, as are analysis and mechanics - and hopefully they won't get too bad. Linear algebra is fascinating, and it's a lovely feeling just getting the concept there and then - if you knew it already it'd be no fun!

I can't say really anything about the physics lectures as we've only had one real one so far and it was beyond easy. Waves, a bit of simple harmonic motion.. handy stuff like. I'm sure it'll get tough at some point (well, I hope it's not quite this easy :P) but I'd say it'll never get unmanageable. With physics, the labs and tutorial stuff count for a good bit so you'll be going into the exams with close to a pass under your belt already if you go about things the right way.

Fringe wrote: »

There's no need to do any of that although it would probably help a bit. We've all started from scratch. Linear algebra is a bit difficult at the moment and mechanics would be a lot harder if I didn't do applied maths. The rest is reasonably easy although that is all at the moment. It could all go downhill in a few months when we start other topics. If you went in with all that already learned, you wouldn't have a problem at all.

Exactly this. Well, mechanics would be a lot easier if I could HEAR what was going on. :pac: But otherwise it's grand.

dog_pig

I seriously have little clue as to what is going on in mechanics - I'm not sure whether that's down to me being stupid or the fact that I've no idea what he's saying in the lectures.

sponsoredwalk

Lol, that's the thing about Linear Algebra - It does become a challenge quickly. I got freaked out by all the eigenvectors and Hermitians and I would usually do a stupid thing like ignore them, naturally, but they are really important for Quantum Mechanics so you gotta know it all cold.

SImple Harmonic Motion - well that's the kind of stuff I like to know, but the intuition is hard to keep. Think about motion, from calculus you can use the equation x=x_0 + v_0t + 1/2at^2 to derive so much. I try to find ways in all aspects of physics that stick together easily like that, "try" being the key word

Aoibheann

dog_pig wrote: »

I seriously have little clue as to what is going on in mechanics - I'm not sure whether that's down to me being stupid or the fact that I've no idea what he's saying in the lectures.

Well if you can simultaneously hear something that quiet and fast, write everything down AND understand what's going on, it'd be amazing. I understand mechanics, I just don't understand the lectures.. :pac:

sponsoredwalk wrote: »

Lol, that's the thing about Linear Algebra - It does become a challenge quickly. I got freaked out by all the eigenvectors and Hermitians and I would usually do a stupid thing like ignore them, naturally, but they are really important for Quantum Mechanics so you gotta know it all cold.

SImple Harmonic Motion - well that's the kind of stuff I like to know, but the intuition is hard to keep. Think about motion, from calculus you can use the equation x=x_0 + v_0t + 1/2at^2 to derive so much. I try to find ways in all aspects of physics that stick together easily like that, "try" being the key word

But it's lovely! And if I'd covered it before I started TP, there'd be nothing to really sink my teeth into. I'm really looking forward to it becoming challenging, in a weird way. It'll be fun!

Haha, know what you mean! It's good to note where things come up again and again in different areas, so you don't label something as specifically one section that would NEVER come up elsewhere. It's too limiting, and it makes people think in horribly set ways..