
Archived: 07 Aug 2014, 09:32

Author 
Message 
ignace
Joined: 12 Dec 2009, 18:56 Posts: 5

Road to the road
Hy there,
First of all, i'm not a native english speaker, i'll do my best.
When you see the book, having done a fair amount of high school and even some univ maths quite some time ago, what is really the studyroad before even trying to tackle the book.
I can't live with the idea of reading the road without having a proper math background to understand what is in there.
Browsing through the contents tells me there is a lot of advanced maths involved.
So, what is a proper preparation ?
Calculus in the reals and the complex ? single and/or multivariable ? Is this ok or do we need real and complex analysis. Differential geometry ? But this has analysis as a prerequisite. Where do riemann manifolds fit in ? Does it all require proving skills or mechanical skills.
In one word, when it requires mathematics for theoretical physics type of skills,then this takes years. And so on.
I'm trying to find the road to the road, let alone the road to reality.
Thanks for any suggestions, although I suppose this topic has been discussed in some other way, somewhere else.
Ignace Belgium

12 Dec 2009, 19:08 


vasco
Supporter
Joined: 07 Jun 2008, 08:21 Posts: 235

Re: Road to the road
Hi Your English seems fine to me! As for the maths skills required to do the exercises in RTR then probably all the ones you've mentioned. However, I wouldn't start studying all these branches of maths before starting the book. I would suggest: 1. Read a chapter and try and understand the main points without worrying too much about the maths 2. Read chapter again and try the maths this time. If the maths is too hard for you then find a book/internet and study what is needed. 3. try the exercises marked very straightforward 4. maybe try some marked needs a bit of thought 5. and so on as you gain confidence
Don't feel that you need to do every exercise before progressing to the next chapter  you can always go back later! Also ask for help on this forum in the exercise discussion part.
A lot of the answers can be found here  especially for the earlier chapters. Good luck! Vasco

16 Dec 2009, 20:09 


ignace
Joined: 12 Dec 2009, 18:56 Posts: 5

Re: Road to the road
Thanks for the support. I'll give it a try and see from there on...
Ignace

18 Dec 2009, 21:58 


thatguy
Joined: 31 Jan 2010, 11:14 Posts: 2

Re: Road to the road
Thanks for posting this question Ignace, I was going to be posting something similar myself (stuck on complex numbers in c4).

31 Jan 2010, 11:31 


ignace
Joined: 12 Dec 2009, 18:56 Posts: 5

Re: Road to the road
Yes, it is hard. I still think you need first to walk the road to the road before seeing the light on the road. I am still considering studying books in my native language dutch (especially real, complex analysis, group theory and differential geometry). The hard way is the only way I think. My studytempo cannot be high, so it will take very long. Be it the way monks walk every day before achieving lightness, or something like that. I found a text of over 2000 pages that should deal with most elementary and advanced aspects in theoretical physics. But again, even this can be too dense and rapid as an approach. It is however a marvelous project under still being worked on today. It might help some of you. Under Projects : http://www.its.caltech.edu/~sean/Kind regards, Ignace

06 Feb 2010, 09:24 


eskimo
Joined: 28 Apr 2011, 10:53 Posts: 1

Re: Road to the road
I've had exactly the same question for a long time: What is the road to the Road, from having no maths at all to having to all the math required to understand it? Does anyone have suggestions for books to read and understand before embarking on the Road? An annotated bibliography would be invaluable. I appreciate the suggestions to "read a chapter" in the Road without doing the exercises, then rereading it doing the exercises etc etc but it's really very little help to absolute beginners who nevertheless are hungry to learn about how the universe works.

28 Apr 2011, 10:57 


markvyt
Joined: 17 May 2012, 02:07 Posts: 1

Re: Road to the road
I have lurked a little on this forum and have now registered and am posting because I like this question and the reply by vasco. It goes to what I love about RTR.
I have undergraduate calculus and little more math and an undergraduate course in Quantum Mechanics, but was not a physics or math major. After the first couple of chapters, I was in way over my head. I have more or less done what vasco suggested because it seemed that was the only way to get what I wanted out of the book. It is very hard, but it is good! I am in Ch 18 and the binding on my hardcover copy is broken and some pages are falling out.
I have at least written down some rambling thoughts about all of the exercises so far. Some I have solved to my satisfaction. In a few cases, I found a solution to an earlier exercise only when a later, harder one made me look back to the earlier chapter.
I have avoided looking at the solutions here for the most part because I want to discover them myself, but I am glad that they are here.
I do not know what possessed Penrose to write this book which is too hard for almost everyone outside the field and too brief to really teach the material; but I am glad he did. I do not know how he got it published when it seemingly has such a small niche; but I am glad he did.
I have had to look at other materials, mostly on the internet, to try to understand some of the topics. On the other hand, I would not want to read whole books or take whole undergraduate or graduate courses before tackling RTR.
It may be a hard road, but the road is one I want to follow.

17 May 2012, 03:34 


ignace
Joined: 12 Dec 2009, 18:56 Posts: 5

Re: Road to the road
There is a contradiction in what you say. First you and vasco say, begin, try the exercises,... and so on. At the end you say, what did Penrose had in mind, too hard for beginners outside the field, and no good for teaching. So, we do need to study upfront, and do maths first. You cannot attack surface integrals and Riemann Manifolds before having done a whole year or 2 in the undergraduate department maths.
I think it is useless for me, except, and that is possible but very hard to, do the 2 volumes on Calculus by Apostol. Incredible what these volumes cover, far beyond calculus, even differential geometry, vector spaces... But again, is it worth all the work, to do the RtR.
I still think we are better off with a GĂ¶del Escher Bach, not easy at all, or something different.
Apostol is the only solution for me.

07 Mar 2014, 22:40 



