Theoretical Physics in TCD?

sponsoredwalk

Hi I've been browsing the course contents periodically over the past few
months as I've been getting better & better @ math & physics & I think
it's time I asked some of you who know the course well some specifics
on what you actually go through in the course.
Btw, I'm not starting in September but am hoping to start the following
year so will study as often as I can over the following year while I do
other things...

I'll stick with first year for now;

Mathematics:

Michaelmas term

• MA1111 Linear algebra I
• MA1121 Concepts of analysis
• MA1131 Advanced calculus
• MA1241 Mechanics I (PDF description of MA1241)

Hilary term

• MA061 Practical computing I]0 credits[/I
• MA1212 Linear algebra II
• MA1122 Analysis on the real line
• MA1242 Mechanics II

Alright, the Linear Algebra class does not give a recommended text but I'll
assume this linear algebra course is going to be more theoretical than say
a Gilbert Strang book? I find those books that skip the motivation
more challenging.
I'm currently reading Serge Lang's "Introduction to Linear Algebra" to
prepare for his more theoretical "Linear Algebra"., this book just
gives you the secrets behind L.A. that other books I've read just ignore!
Would that book be enough to withstand first year L.A. in TCD?
I have a lot to read but if I finish these books fast enough I would crack
into Axler's Linear Algebra Done Right as well, what do you think?

As for Analysis, well before I begin the year I am going to have completed
Walter Rudin's Principle's of Mathematical Analysis
(I'm doing the pre-requisites now to get ready for this book & will be using
Apostol's Mathematical Analysis along with it as backup).
There is no recommended text on the page but I would guess that being
able to cope with Rudin would be enough for the whole year, right?

As for Advanced Calculus well that's just multivariable calculus &
by the beginning of term I'll have read Serge Lang's Multivariable Calculus
and both volume's of Apostol's Calculus 1 & 2 so I think that will be
enough. If not, let me know!

As for Mechanics, well I have given up University Physics by
Young/Freedman & gone back to the first edition of Alonso & Finn's
Fundamental University Physics because they actually use calculus in
this book properly (according to physicsforums.com anyway!) so that I'll be able to
read Kleppner/Kolenkow along with the Berkeley physics course properly.
I think having read these books will be enough for the course.

I'll asume practical computing would be Ordinary Differential Equations,
would that be correct? Well I can kind of fake my way through some of
those already but I've got two Diff Eq. books that I'm going to focus
on later in the coming months to get a grip with these babies...

Physics:

I'm pretty confused by the page here because
they've made it out as though they jump straight into special relativity.
I don't think that's a good idea at all, I mean at all!
Anyway, whatever way the course is layed out I'll have read Alonso & Finn,
Kleppner/Kolenkow, The Mechanics & E&M Berkeley physics books &
if I can fit them in I'll do the old Taylor/Wheeler Special Relativity book &
Gregory's Classical Mechanics (It flirts with Lagrangians!!!).



Some of this may be over-preparation but they way I have things
constructed I'll need to be over-prepared so I would like some
input on whether or not I'll need to do more, i.e. will the course ask more
that the above books do of a student?

Thanks, I await your replies

ZorbaTehZ

sponsoredwalk wrote: »

Alright, the Linear Algebra class does not give a recommended text but I'll
assume this linear algebra course is going to be more theoretical than say
a Gilbert Strang book?

Semester 1: Anton & Rorres
Semestor 2: Gelfand

I'm currently reading Serge Lang's...
Would that book be enough to withstand first year L.A. in TCD?

Yes,.

I have a lot to read but if I finish these books fast enough I would crack
into Axler's Linear Algebra Done Right as well, what do you think?

From the perspective of the course, it's unnecessary.

As for Analysis, well before I begin the year I am going to have completed
Walter Rudin's Principle's of Mathematical Analysis

Lecturer provides all the notes, but Spivak or Rudin would be the best choice for more exercises/exposition etc.

As for Advanced Calculus well that's just multivariable calculus &
by the beginning of term I'll have read Serge Lang's Multivariable Calculus
and both volume's of Apostol's Calculus 1 & 2 so I think that will be
enough. If not, let me know!

Not familiar with those, but the course is very easy. Double integrals, significance of grad etc.

As for Mechanics, well I have given up University Physics by
Young/Freedman & gone back to the first edition of Alonso & Finn's
Fundamental University Physics because they actually use calculus in
this book properly (according to physicsforums.com anyway!) so that I'll be able to
read Kleppner/Kolenkow along with the Berkeley physics course properly.
I think having read these books will be enough for the course.

Leaving-cert calculus is more than sufficient for K&K. Their is another very good book by Morin which you can take a look it too.

I'll asume practical computing would be Ordinary Differential Equations,
would that be correct? Well I can kind of fake my way through some of
those already but I've got two Diff Eq. books that I'm going to focus
on later in the coming months to get a grip with these babies...

Unfortunately no. It's a joke class where they begin some C++.

I'm pretty confused by the page here because
they've made it out as though they jump straight into special relativity.
I don't think that's a good idea at all, I mean at all!

Why is it a bad idea? The fundamentals of SR are not difficult to grasp at all really. A.P. French is the text if you're wondering (excellent book)

Some of this may be over-preparation but they way I have things
constructed I'll need to be over-prepared so I would like some
input on whether or not I'll need to do more, i.e. will the course ask more
that the above books do of a student?

It depends on the student, specifically whether or not you're willing to do consistent work , and judging by your post, I think you will have no problem with the course.

myfatherrsson

woah....chill
the stuff isnt so terribly complicated you have to read half the books in the library before going in! Although i might as well be p!ssin into the wind sayin that, i can tell you're the kind of person who'll enjoy reading them all cover to cover....you'll fit in nicely with the tp's

sponsoredwalk

myfatherrsson wrote: »

woah....chill
the stuff isnt so terribly complicated you have to read half the books in the library before going in! Although i might as well be p!ssin into the wind sayin that, i can tell you're the kind of person who'll enjoy reading them all cover to cover....you'll fit in nicely with the tp's

Ha thanks, I think you gotta focus mostly on the math though & be well
prepared.

I watched this lecture by Steven Weinberg & he was talking about how he
discovered some of his equations back in the 60's and, well, he basically
talks about how he discovered some weird Lagrangian equation through
use of Modern Algebra techniques & I as just floored :eek: You gotta be able
to do it all if you want to have a hope - at least that's my thinking now

The A.P. French book is from a slightly more modern Berkeley physics
series so I'm sure it'll be like the one in the course I'm going to do - well
we'll see how things go but the Taylor/Wheeler one has to be read!

antiselfdual

You've got this so well planned out that I'm worried the course is just going to interfere with your education...

You can get a presumably accurate idea of what the courses are like by finding the lecturers' own pages for them: Linear Algebra, Analysis, Mechanics. Insofar as the courses are aimed at anyone they're aimed at students who have done the Irish Leaving Cert, so being familiar with Rudin, Strang etc beforehand is probably above and beyond the standard of preparation of nearly everyone who's gone into the course... *is envious

The special relativity course is just quite basic kinematics, don't worry about it in terms of being able to do well at it.

will the course ask more that the above books do of a student?

Definitely not. However the subject of theoretical physics itself will (there being a distinction between one's actual understanding and what one has to know to do well in a course...)

Fringe

I can upload all my notes if you want. I have pretty much all of them. One thing that'll be different this year is that Vlad is leaving which means you probably won't be studying the Gelfand book. I found it very hard to get into and I think the only reason he picked that one is because of his admiration for Gelfand. But really, my opinion is that you should just stop all this preparation because you've done enough. What you're preparing for is actually what you'll be learning so if you've already done it, college won't be as exciting and interesting going over something again.

EDIT: Oh and if I can remember, we had about two weeks before special relativity started so you're not instantly going into SR. You'll have done enough kinematics in Mechanics such that it'll be ok.

sponsoredwalk

Thanks for the offer for the notes, I might ask you later on in the year
if you don't mind, I've got a tight schedule for now though.

I've been through hell preparing this list, (think trial & error) but if you think
a plan like this is a good idea antiselfdual I might as well admit that it's not
enough, I have a lot more planned for myself so I'll show you what I'm
actually doing. I'd love to hear what you've done/have planned.
Before you judge remember I did pass math in school, hated it completely
but still passed the L.C. even though I couldn't tell the difference between
trigonometry & algebra! Kind of why I'm going over everything from
ground up!

A First Course in Calculus(I'm finishing this book tonight! Only took me 6 sessions! This book has so many novel & intuitive ways of looking at calculus compared to the Thomas Calculus book I suffered through )
Lang's Calculus of Several Variables
(Starting this on monday, looks great & uses a lot of linear algebra from
his book below, should finish it quick enough!)
Fundamental University Physics
(I'm doing the old 1967 version instead but this is the new version)
Basically, this 3-volume book isn't easy so my plan in physics is determined by
how well I get on with this book, the quicker/easier it is the sooner I'll crack into K&K etc...)


Discrete Mathematics Videos (Off the net to get an idea of the subject!)
Larson Geometry (I've never studied a proper geometry book but this is incredibly easy, gonna finish it over 12 days, chapter a day along with the videos!)


Number Theory Videos (Off the net to get an idea of the subject!)
Lang Geometry (Because this man is the best author ever! Just to get an intuitive feeling @ more advanced geometry)


An Interactive Introduction to Mathematical Analysis
(This book gives a proper introduction to proofs & techniques applied to Analysis without boring
through a whole discrete math book having no application to calculus, I got it the other day & it
looks perfect - plus there's solutions & I'm not confident enough to prove without proof's yet!)
Analysis With an Introduction to Proof
(Ditto, I wouldn't use either of these alone - together they're perfect!)
Introduction to Linear Algebra
(I've read a bit of this book & it's utterly amazing, so intuitive. I'm going to finish it after I read
his multivariable calculus book linked above. He goes over the L.A. in this book lightly in the
calc book so it's better to hold off on this one for now!)

Discrete Mathematics Book (I don't know what to use yet!)
Elementary Number Theory
(There's video lectures online using this book so it's a good idea to use it!)
Geometry Revisited This guy is really famous & he's written a more advanced Geometry book so I'll read this to get a feeling of his style, it's small!)



Spivak Calculus (Got scared away from this before That's why I got the above analysis books, to learn proofing so that I can conquer this behemoth - purely a personal quest!)
Apostol Calculus & Linear Algebra (II Volumes)
(Linked above, these 2 are great, I have the first one but it demands a lot & I need to be proof-wise before I can hack this one, also a personal quest but it is tipped as the physicists calculus book all over physicsforums.com!)
Lang Linear Algebra
Serious stuff


Boyce,DiPrima Elementary Differential Equations
Tenenbaum, Pollard Ordinary Differential Equations
Just to get more theoretical on differential equations than normal, already read some of
both of these books & was doing fine but this was when I was kind of skipping bits
here & there & couldn't manage a lot of basic calculus proofs. I can deal with them now so
I took a break!)


Apostol - Mathematical Analysis
Principles of Mathematical Analysis
Lang Undergraduate Analysis
When I get to here then I can claim success , I'll just say that yes I have
read bits and pieces of these three books & yes they are intelligible but I
have read a lot of parts where I have no clue what's going on, some
seemingly simple things pass by & I haven't a clue (e.g. months ago I'd
gotten stuck on a page only recently to re-read it & laugh - that kind of stuff!.
(The only answer book for these books is Lang but I hope to be confident
enough to not need it here!)


Lang Undergraduate Algebra
Obviously I'll make a new plan when I get to here

You can tell by the spaces between the above in what way I'm doing
them. It looks a bit daunting but over a whole year it's definitely doable,
I mean I bet most of you just read one book & soak it all in, I've learned
after much, much pain that having 2 or three books is the best way to
cope as you'll get a fresh perspective (and in the case of a Serge Lang book a better & more intuitive proof! )

myfatherrsson

Good aul Vlad! he will be missed!

ZorbaTehZ

Drop the number theory and discrete mathematics, they're not worth the time, especially the former.

Imo, you are doing too much too quickly, focus on the basics first, get a good grasp of linear algebra and analysis and then you can start dipping around. You sound like you are overburdening yourself with all these books, find 1/2 good books per area and stay with them.

sponsoredwalk

Tbh the discrete mathematics all depends on how well I get on with
the proofing in those first two analysis books, I'm not at all interested
in the computer applications of discrete mathematics but thought
they would give me a deeper knowledge of proofs so yeah that's
open to question (I haven't really bothered to find a book even...).

The number theory looks good though, it's not a burden to give that a go

Why do you say it's a burden?

Enkidu

sponsoredwalk wrote: »

I watched this lecture by Steven Weinberg & he was talking about how he
discovered some of his equations back in the 60's and, well, he basically
talks about how he discovered some weird Lagrangian equation through
use of Modern Algebra techniques & I as just floored :eek:

Yes, this stuff is part of the beauty of theoretical physics. If you are wondering Weinberg used group theory. The theories of the Weak and Strong Nuclear forces use groups to describe their symmetries.

By the way I am very impressed that somebody who has not yet started their degree has a goal to read Serge Lang's Linear Algebra book.

Number theory is a very interesting subject in its own right, but it tends not to have much application to physics. However, if you find yourself enjoying it, keep going.

Two possible suggestions:
1. As others have mentioned, you might enjoy Spivak. Anybody who can handle that book knows Calculus.
2. If you get through even half that list you will be really prepared.

Anonymo

sponsoredwalk, i'd recommend you give up this goal of reading every textbook set for these courses before you start. if you intend to do this you will burn yourself out after the year, be bored in your first year and most likely lose interest because you're not doing anything new. By the time second year comes along the other students will know as much as you and while in first year you were the guru you'll probably become a bit lost. By all means do a bit of light reading of these texts to get a general idea but an in depth study is too much. I'd recommend this light reading plus a read of some popular science books by respected authors. You'll get a good overview of the topics you'll learn which will add a lot more to your knowledge when you add the technical details later.

I'm a bit puzzled by your post. What year are you in? Why do you intend to do this?

Aoibheann

Fringe wrote: »

I can upload all my notes if you want. I have pretty much all of them. One thing that'll be different this year is that Vlad is leaving which means you probably won't be studying the Gelfand book. I found it very hard to get into and I think the only reason he picked that one is because of his admiration for Gelfand. But really, my opinion is that you should just stop all this preparation because you've done enough. What you're preparing for is actually what you'll be learning so if you've already done it, college won't be as exciting and interesting going over something again.

EDIT: Oh and if I can remember, we had about two weeks before special relativity started so you're not instantly going into SR. You'll have done enough kinematics in Mechanics such that it'll be ok.

myfatherrsson wrote: »

Good aul Vlad! he will be missed!

Doesn't seem to be leaving after all, guys. His course page on Linear Algebra is updated for this year (i.e. the 2010/2011 academic year), and I hear he's taking the SF Maths Number Theory course too (tempted to sit in on that!), so yay for that!

sponsoredwalk, like Fringe I'd be happy to give you any notes I have if you want the,. I've been scanning mine up and uploading them to my dropbox account anyway for some other people, so if you want an invite to the folder just drop me a PM!

That said though, I agree with Fringe in that I think you should just relax with all the preparation! I know you want to have a fair bit of knowledge going in, but half the fun of first year lies in those little moments when some concept in Linear Algebra suddenly clicks, whenever everything just starts to make sense. No point knowing it all before you go in!

SR is grand too actually. You'd expect it to be a lot worse, but the material covered isn't actually difficult and it's a fairly interesting course which makes it that little bit easier to follow.

I hope you enjoy the course too. We tend to be small class groups (and dwindling fast too!), which is great because you get to know everyone pretty quickly and they're all lovely (even the above two, I suppose! :pac:).

myfatherrsson

Aoibheann wrote: »

Doesn't seem to be leaving after all, guys. His course page on Linear Algebra is updated for this year (i.e. the 2010/2011 academic year), and I hear he's taking the SF Maths Number Theory course too (tempted to sit in on that!), so yay for that!

sponsoredwalk, like Fringe I'd be happy to give you any notes I have if you want the,. I've been scanning mine up and uploading them to my dropbox account anyway for some other people, so if you want an invite to the folder just drop me a PM!

That said though, I agree with Fringe in that I think you should just relax with all the preparation! I know you want to have a fair bit of knowledge going in, but half the fun of first year lies in those little moments when some concept in Linear Algebra suddenly clicks, whenever everything just starts to make sense. No point knowing it all before you go in!

SR is grand too actually. You'd expect it to be a lot worse, but the material covered isn't actually difficult and it's a fairly interesting course which makes it that little bit easier to follow.

I hope you enjoy the course too. We tend to be small class groups (and dwindling fast too!), which is great because you get to know everyone pretty quickly and they're all lovely (even the above two, I suppose! :pac:).

You're here as WELL!! Ah cmere!

Ms.Forbes

sponsoredwalk wrote: »

Hi I've been browsing the course contents periodically over the past few
months as I've been getting better & better @ math & physics & I think
it's time I asked some of you who know the course well some specifics
on what you actually go through in the course.
Btw, I'm not starting in September but am hoping to start the following
year so will study as often as I can over the following year while I do
other things...

I'll stick with first year for now;

Mathematics:

Michaelmas term

• MA1111 Linear algebra I
• MA1121 Concepts of analysis
• MA1131 Advanced calculus
• MA1241 Mechanics I (PDF description of MA1241)

Hilary term

• MA061 Practical computing I]0 credits[/I
• MA1212 Linear algebra II
• MA1122 Analysis on the real line
• MA1242 Mechanics II

Alright, the Linear Algebra class does not give a recommended text but I'll
assume this linear algebra course is going to be more theoretical than say
a Gilbert Strang book? I find those books that skip the motivation
more challenging.
I'm currently reading Serge Lang's "Introduction to Linear Algebra" to
prepare for his more theoretical "Linear Algebra"., this book just
gives you the secrets behind L.A. that other books I've read just ignore!
Would that book be enough to withstand first year L.A. in TCD?
I have a lot to read but if I finish these books fast enough I would crack
into Axler's Linear Algebra Done Right as well, what do you think?

As for Analysis, well before I begin the year I am going to have completed
Walter Rudin's Principle's of Mathematical Analysis
(I'm doing the pre-requisites now to get ready for this book & will be using
Apostol's Mathematical Analysis along with it as backup).
There is no recommended text on the page but I would guess that being
able to cope with Rudin would be enough for the whole year, right?

As for Advanced Calculus well that's just multivariable calculus &
by the beginning of term I'll have read Serge Lang's Multivariable Calculus
and both volume's of Apostol's Calculus 1 & 2 so I think that will be
enough. If not, let me know!

As for Mechanics, well I have given up University Physics by
Young/Freedman & gone back to the first edition of Alonso & Finn's
Fundamental University Physics because they actually use calculus in
this book properly (according to physicsforums.com anyway!) so that I'll be able to
read Kleppner/Kolenkow along with the Berkeley physics course properly.
I think having read these books will be enough for the course.

I'll asume practical computing would be Ordinary Differential Equations,
would that be correct? Well I can kind of fake my way through some of
those already but I've got two Diff Eq. books that I'm going to focus
on later in the coming months to get a grip with these babies...

Physics:

I'm pretty confused by the page here because
they've made it out as though they jump straight into special relativity.
I don't think that's a good idea at all, I mean at all!
Anyway, whatever way the course is layed out I'll have read Alonso & Finn,
Kleppner/Kolenkow, The Mechanics & E&M Berkeley physics books &
if I can fit them in I'll do the old Taylor/Wheeler Special Relativity book &
Gregory's Classical Mechanics (It flirts with Lagrangians!!!).



Some of this may be over-preparation but they way I have things
constructed I'll need to be over-prepared so I would like some
input on whether or not I'll need to do more, i.e. will the course ask more
that the above books do of a student?

Thanks, I await your replies

My advice don't do physics

it's rubbish

we did it for 4 weeks in transition year

what a load of crap

i thought it sounded good until we started learning about mirror reflections

Aoibheann

myfatherrsson wrote: »

You're here as WELL!! Ah cmere!

I have all the "cool" forums (here/maths/tcd) subbed. Yeah, I'm not a loser.. >_>

Ms.Forbes wrote: »

My advice don't do physics

it's rubbish

we did it for 4 weeks in transition year

what a load of crap

i thought it sounded good until we started learning about mirror reflections

It does get somewhat more interesting at a college level - things like special relativity especially. That said, there's a lot of boring physics early on anyway. It has its moments though.

ZorbaTehZ

Ms.Forbes wrote: »

My advice don't do physics

it's rubbish

we did it for 4 weeks in transition year

what a load of crap

i thought it sounded good until we started learning about mirror reflections

So physics is crap because you didn't like mirror reflections - what a useful contribution to the thread. :rolleyes:

sponsoredwalk

Ms.Forbes wrote: »

My advice don't do physics

it's rubbish

we did it for 4 weeks in transition year

what a load of crap

i thought it sounded good until we started learning about mirror reflections

You're damn right, what a shame. I have the leaving cert physics book & I
am so glad I didn't do it for leaving cert all those years ago, you'll learn
nothing deep about physics memorizing formula's, definitions etc...

My brother is starting 5th year & he didn't even pick it, I'm getting him to
focus on learning his math so that by 6th year he'll be able to rederive all
of the things in the leaving cert physics class with a bit of calculus &
do it as an added subject (assuming he actually works! ).

If I had chosen physics back then I would have quit in disgust...
As I keep telling people though, if you want to know what physics
is really like you should watch all 52 half-hour lectures on physics
that are in the show The Mechanical Universe. Here is the first one,
just a flavour of things to come

Fringe

Did you get in?

sponsoredwalk

Me? I didn't apply this year, I'm not going to be going until next year