A good way to work through Hassani's Mathematical Physics

[Geofleur]

I have learned a lot from reading Sadri Hassani's book "Mathematical Physics", and have also had many frustrations with it. On the one hand, it covers both the classical and the modern methods of mathematical physics, a huge amount of material and at a good level. On the other, it sometimes lacks examples and discussion that would put major results in context; moreover, it periodically says things that are misleading or even false. So if one wants to be able to use Hassani's book as a learning resource and reference, what is the best way to proceed?

An approach that I have found useful is to treat Hassani's book as a workbook that one converts into a reference. The book has huge margins, and many blank pages. So I read from many sources about whatever topic interests me and, as homework, go through the relevant chapter in Hassani, correcting mistakes, adding contextual discussions, and extending the textbook results with my own. This way, each chapter becomes useful as a review and reference after I've "filled it in".

I thought that perhaps other people might find it interesting or useful to hear about this way of reading Hassani's (or any other) book; hence this post. Any comments?

 

[ShayanJ]

it periodically says things that are misleading or even false.

So, why should anyone want to use this book in the first place?

 

[dextercioby]

Can you give some examples of erroneous or misleading statements ?

 

[Geofleur]

Can you give some examples of erroneous or misleading statements ?

As an example of something misleading see: https://www.physicsforums.com/threads/minimal-left-ideals-in-hassani.863334/#post-5418929

An example of an error: On pg. 715, the matrix action should be defined as gx = (ax+b)/(cx+d) and not gx = (ax+c)/(bx+d). The latter does not produce an action with matrix multiplication as the law of multiplication. Most examples of erroneous statements, at least in the 2nd edition, involve mild things like this, or like not specifying that a set needs to be nonempty, like in the definition of groups/subgroups in Chapter 23.

The first edition has some more serious errors in it; unfortunately, I don't have that edition anymore so I can't go leafing through it to find the errors I had spotted.

So, why should anyone want to use this book in the first place?

Because most of what it says is true. Like I said above, I have learned a lot of things from studying this book. Further, it has some things that I have not seen in any other book (such as the multidimensional treatment of Green functions). Finally, there is a lot of appeal in having most of the mathematics that one needs in one place.

 

[vanhees71]

So, why should anyone want to use this book in the first place?

Well, tell me to write a typo free textbook! ;-)))

 

[ShayanJ]

Well, tell me to write a typo free textbook! ;-)))

Typos are acceptable, but Geofleur was talking about scientific inaccuracies or errors.

 

[MathematicalPhysicist]

Because most of what it says is true. Like I said above, I have learned a lot of things from studying this book. Further, it has some things that I have not seen in any other book (such as the multidimensional treatment of Green functions). Finally, there is a lot of appeal in having most of the mathematics that one needs in one place.

I read the table of contents, it seems it covers classical and modern mathematical physics methods.

I find that for classical mathematical physics you can't get wrong with using Morse and Feshbach Courant and Hilbert and Simon and Reed's books (more than 2000 pages to read :-D );

for modern mathematical physics which is basically algebraic topology and geometry and differential geometry there are many books.

I find it difficult to think that Hassani has succeeded to shrink this vast literature to one big book of 1000-1500 pages.
For me using only the mathematical methods without understanding the proofs of the theorems is a bit like being a robot not understanding why he does what he does.

 

[Geofleur]

I find it difficult to think that Hassani has succeeded to shrink this vast literature to one big book of 1000-1500 pages. For me using only the mathematical methods without understanding the proofs of the theorems is a bit like being a robot not understanding why he does what he does.

I agree, which is why I keep adding results, proofs, and references in Hassani's book from other sources. There is not "one book to rule them all" but I'm basically trying to make it be the closest reasonable approximation to that by writing in it a lot. And I mean a lot. The exercise seems worth it - I'm just doing my self-imposed homework and, when I'm done, I have a gigantic review article in the form of a book, with all the details spilling out on the margins.

 

[Geofleur]

I would also like to mention that, over the years whenever I have asked "What do I need to know?", I always have 500 books recommended to me that I could certainly never get around to finishing. As a solution, I have been trying to construct for myself what seems a sensible core of material, using Hassani's book along with Analysis, Manifolds, and Physics by Choquet-Bruhat et al. as a basis.

 

[S.G. Janssens]

I think what you, the OP, have done is very good. It is my experience that when reading one often learns the most from understanding errors and resolving inconsistencies. (That is why physics books are so instructive.) Unfortunately, I do not like to write in my own books (just thinking about it gives me the shivers) but I sometimes create a separate set of notes to go with them. Usually these are limited to a few chapters, because it does not happen too often that I read a book front to back.

Maybe you could contact the author to discuss your notes? If I were him, I would find this extremely useful.

 

[S.G. Janssens]

for modern mathematical physics which is basically algebraic topology and geometry and differential geometry there are many books.

I sure hope (and think) that there is more to modern mathematical physics than this, which of course makes your next point

I find it difficult to think that Hassani has succeeded to shrink this vast literature to one big book of 1000-1500 pages.

even more relevant.

 

[MathematicalPhysicist]

I sure hope (and think) that there is more to modern mathematical physics than this, which of course makes your next point

even more relevant.

Well I could have said all of math is used in mathematical physics; but then how would you differentiate between the two? :-)

 

[EE18]

I have learned a lot from reading Sadri Hassani's book "Mathematical Physics", and have also had many frustrations with it. On the one hand, it covers both the classical and the modern methods of mathematical physics, a huge amount of material and at a good level. On the other, it sometimes lacks examples and discussion that would put major results in context; moreover, it periodically says things that are misleading or even false. So if one wants to be able to use Hassani's book as a learning resource and reference, what is the best way to proceed?

An approach that I have found useful is to treat Hassani's book as a workbook that one converts into a reference. The book has huge margins, and many blank pages. So I read from many sources about whatever topic interests me and, as homework, go through the relevant chapter in Hassani, correcting mistakes, adding contextual discussions, and extending the textbook results with my own. This way, each chapter becomes useful as a review and reference after I've "filled it in".

I thought that perhaps other people might find it interesting or useful to hear about this way of reading Hassani's (or any other) book; hence this post. Any comments?

Hi there,

I am just starting read Hassani now and have found two major errors (not typos) within the first 25 pages. Would you happen to have typed up a list of the errors you found? I am generally enjoying the book but want to be sure I'm not missing anything.

Thank you!

 

[vanhees71]

Interesting! Which errors are that?

 

[dextercioby]

Yes, please report errors here, or post the link to the publisher's website (in case there's an "official" list).

 

[EE18]

Interesting! Which errors are that?

I'll link my Math SE question for one of them (top page 24 in Hassani).

I have also since found that the definition of a direct sum (Def 2.1.14) is incorrect (it asserts that pairwise intersections containing the zero vector is sufficient). As well, the discussion of tensor products on page 29 is incomplete (not every element of $U \otimes V$ can be written as $u \otimes v$ and Hassani does not make clear how things generalize).

If you've read the book, is it worthwhile to continue? I am worried that once I get into material I don't already know then I will miss things like this.