Building a library of physics and math texts

[loom91]

Hi,

A group of curious laymen have entrusted me with a curious project. I've been asked to build a small library of physics and math texts that intelligent students and adults may use to self-study the equivalent of a graduate course. This should include a mix of both introductory texts and more advanced comprehensive works. One member has expressed a desire that rigour, elegance and beauty of presentation be emphasised, though this of course has to be balanced by accessibility, since the goal is self-study rather than a formal academic setting. I've some knowledge about physics, so I've managed to compile the following list:

Classical Mechanics:
01)Kleppner and Kolenkow
02)Marion Thornton
03)Goldstein
04)Landau
05)Greiner-Point Particles and Relativity
06)Greiner-Systems of Particles and Hamiltonian Dynamics
07)VI Arnold
08)Sussman-Structure and Interpretation
09)Coulson-Wave Motion
Electrodynamics:
10)Griffiths
11)Greiner
12)Lorrain and Corson
13)Landau
14)Jackson
Fluid Mechanics:
15)Kundu, Cohen
16)Landau
17)Chorin, Marsden
Optics:
18)Guenther
19)Born, Wolf
20)Shen
GTR:
21)Misner, Thornee, Wheeler
22)Wald
23)Weinberg
QM:
24)Griffiths
25)Landau
26)Sakurai
27)Shankar
28)Cohen-Tannoudji
29)Greiner-QM Intro
30)Greiner-QM Symmetries
31)Greiner-Relativistic QM
Statistical Physics:
32)Chandler
33)Greiner
34)Huang
35)Reichl
36)Pathria
37)Landau Lif****z 1 & 2
38)Kardanoff-Statistical QM
QED:
39)Greiner
40)Cohen-Tannoudji
QFT:
41)Peskin, Shroeder
42)Weinberg 1, 2 & 3
43)Griffiths-Intro to Elementary Particles
44)Di Francesco-Conformal Field Theory
String:
45)Zwiebach
46)Polchinski
Solid State:
47)Kittel
48)Ashcroft, Mermin
General:
49)Feynman Lectures in Physics
50)Basdevant-Fundamentals in Nuclear Physics

Mathematics for Physics
01)Isham
02)James Nearing
03)J Lee
04)Nakahara
05)Nash, Sen
06)Szekeres
07)Reed, Simon 1 & 2

I'm sure there are gaps in this list, in the sense that some particular difficulty level in some particular topic is not covered, or a classic book has been omitted. I'll be grateful if you point these out to me. Also, what is the mathematical background required to appreciate Arnold?

As for mathematics, I don't even know which topics are covered in a standard course (and I suspect it's not as standardised as physics) so I'll like recommendations for a structured library like the one given above, such that one may sequentially proceed through it to get a comprehensive education. The goal is once again to strike a balance between intuitive, student-friendly texts and slick, rigorous classics of the sort that make mathematicians salivate.

A few obvious choices are Spivak's and Apostle's calculus, baby and big Rudin (what exactly are the differences between them?), Topology by Munkres, Manifold Calculus by same and Spivak etc. I'll like it if you gave recommendations where the different books complement each other, as I've attempted in the physics list. This is an ambitious project and I feel honoured to be given such a weighty duty. I'll be very grateful for your help.

Thanks a lot.

Molu

 

[neutrino]

Jenkins and White for Optics (intro)

Boas for Math-Methods

I see no SR at all... Spacetime Physics, Relativity(Rindler)

A book that I have not read but one that probably should make your list
Schutz for GR, and maybe even the one by Hartle for introduction.

 

[mgb_phys]

Hecht - modern optics
CRC - handbook physics and chemistry

 

[loom91]

Yes, I forgot Hecht. In SR, what is an adavanced text? I mean a text that explores the limits of SR eithout getting into much GTR or QFT.

 

[PhysiSmo]

Also, QM, a modern development by Ballentine and QFT by L. Ryder, a classic textbook for the field!

 

[mgb_phys]

You probably don't want to get into computer texts - but "Numerical Recipes In C/Fortran" is useful.
If you do lab classes squires - "practical physics", treatment of statistics, error analysis etc.

 

[robphy]

Some others to consider:

EM: Purcell
SR: Taylor&Wheeler(1966), T.A.Moore, Woodhouse http://www2.maths.ox.ac.uk/~nwoodh/ (he also has books published by Springer), Naber, Ellis&Williams
GR: Ludvigsen (elegant modern SR presentation), Ohanian, Lightman(problem book), D'Inverno, Sachs&Wu, Hawking&Ellis
MathPhysics: Boas, Lea, Strang, Geroch, Frankel, Isham, Bamberg-Sternberg, Abraham & Marsden & Ratiu, Choquet-Bruhat & Dewitt-Morette, Guillemin & Sternberg, Morse-Feshbach, Courant-Hilbert
Overviews ("big pictures"): E.G.Harris, W.Thirring, G.G.Emch
Classics: Lorentz-Einstein-Minkowski, Weyl, Pauli, Dirac(QM), Synge(SR&GR), Lanczos(Variational Principles)

You might want sections on Astrophysics, Cosmology, and Computational Physics.

This may be useful... and thanks to the wayback machine, it is still available
http://web.archive.org/web/20061205215309/http://math.berkeley.edu/~ajt/physics_textbooks.html

 

[loom91]

Math suggestions? I'm looking more for these. I want to concentrate more on areas like Topology, Algebra and Analysis rather than Number Theory.

Some of the books I've listed are

Friedberg-Linear Algebra
Spivak-Calculus
Apostle-Calculus
Tenenbaum-ODE
Munkres-Topology
Rudin-Principles of Mathematical Analysis
Rudin-Real and Complex Analysis
Brown-Complex Variables and Applications
Munkres-Calculus on Manifolds
Spivak-Calculus on Manifolds
Farlow-PDE
Feller-Probability Theory
Chung-Probability Theory

As you can see, the current list is heavily dominated by analysis because that's my personal favourite. Please tell me what books I need to fill in the gaps. Thanks.

Molu

 

[loom91]

Some others to consider:

EM: Purcell
SR: Taylor&Wheeler(1966), T.A.Moore, Woodhouse http://www2.maths.ox.ac.uk/~nwoodh/ (he also has books published by Springer), Naber, Ellis&Williams
GR: Ludvigsen (elegant modern SR presentation), Ohanian, Lightman(problem book), D'Inverno, Sachs&Wu, Hawking&Ellis
MathPhysics: Boas, Lea, Strang, Geroch, Frankel, Isham, Bamberg-Sternberg, Abraham & Marsden & Ratiu, Choquet-Bruhat & Dewitt-Morette, Guillemin & Sternberg, Morse-Feshbach, Courant-Hilbert
Overviews ("big pictures"): E.G.Harris, W.Thirring, G.G.Emch
Classics: Lorentz-Einstein-Minkowski, Weyl, Pauli, Dirac(QM), Synge(SR&GR), Lanczos(Variational Principles)

You might want sections on Astrophysics, Cosmology, and Computational Physics.

This may be useful... and thanks to the wayback machine, it is still available
http://web.archive.org/web/20061205215309/http://math.berkeley.edu/~ajt/physics_textbooks.html

I'm already pushing the boundaries of our budget, I don't think I can include that many. I didn't find the need for a Purcell-level bridge between Halliday-Resnick and Griffiths. Also, since there's going to be a separate math library, I don't want to include many of those mathematical technique cookbooks. It's better to learn the math from math textbooks and the physics from the physics textbooks. Math methods books are usually neither here nor there. Of course, books like Arnold, Isham etc are not really math methods books.

Thanks for the link.

Molu

 

[J77]

It's a broad range to say you want a library for a graduate course -- for example, a lot of great math books come from the Springer Applied Mathematical Sciences series: http://www.springer.com/east/home/math?SGWID=5-10042-69-173621535-0

 

[loom91]

I'm adding these to the physics list:

Mechanics:
Taylor*
Calkin
ED:
Landau-Classical Fields*
Elasticity:
Sadd
GTR:
Schutz-A First Course in General Relativity*
d'Inverno-Introducing Einstein's Relativity*
Dirac
QM:
Ballentine
Feynman-Path Integrals
QFT:
Greiner-Field Quantization
Zee-QFT in a Nutshell
Optics:
Hecht*
String:
Witten et al*

I hope that's a physics library to satisfy anyone. Perhaps the QED/QFT department is slightly lacking. Tell me, what is the standard order of presentation of the subjects QED, QCD and QFT. Will the QFT books listed above cover QCD and Electroweak theory?

Thanks

 

[loom91]

It's a broad range to say you want a library for a graduate course -- for example, a lot of great math books come from the Springer Applied Mathematical Sciences series: http://www.springer.com/east/home/math?SGWID=5-10042-69-173621535-0

I know it's a broad range, but in physics I found I could reasonably cover it with 50-60 texts. Note that it's for undergraduate+basic graduate. Also, there's no emphasis on applied maths, there are some pure math geeks in the group I mentioned who enjoy spending their leisure hours proving wonderfully abstract propositions.

Molu

 

[J77]

OK -- from the link I gave, for the level you want; ie. something a bit above UG, for bifurcation analysis, I'd suggest:

Elements of Applied Bifurcation Theory
Kuznetsov, Y.A., Vol. 112, ISBN 978-0-387-21906-6, 2004, Hardcover

and

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of...
Guckenheimer, J., Holmes, P., Vol. 42, ISBN 978-0-387-90819-9, 2002, Hardcover

These have been the two core texts for a long time now...

 

[loom91]

OK -- from the link I gave, for the level you want; ie. something a bit above UG, for bifurcation analysis, I'd suggest:

Elements of Applied Bifurcation Theory
Kuznetsov, Y.A., Vol. 112, ISBN 978-0-387-21906-6, 2004, Hardcover

and

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of...
Guckenheimer, J., Holmes, P., Vol. 42, ISBN 978-0-387-90819-9, 2002, Hardcover

These have been the two core texts for a long time now...

Check out http://chaosbook.org/. It seemed very comprehensive to me.

Molu

 

[J77]

Check out http://chaosbook.org/. It seemed very comprehensive to me.

Oww... That's a bit strong saying a web resource is comprehensive

Check out the Guckenheimer book I gave above to see how a small fraction of "chaos theory" is done in a comprehensive way -- and then another to see how say, symbolic dynamics are done in a comprehensive way -- and so on...

If you want a list of books to read slightly above UG level, you wouldn't go for something called "University Physics" would you?

 

[eGuevara]

Math suggestions? I'm looking more for these. I want to concentrate more on areas like Topology, Algebra and Analysis rather than Number Theory.

Some of the books I've listed are

Friedberg-Linear Algebra
Spivak-Calculus
Apostle-Calculus
Tenenbaum-ODE
Munkres-Topology
Rudin-Principles of Mathematical Analysis
Rudin-Real and Complex Analysis
Brown-Complex Variables and Applications
Munkres-Calculus on Manifolds
Spivak-Calculus on Manifolds
Farlow-PDE
Feller-Probability Theory
Chung-Probability Theory

As you can see, the current list is heavily dominated by analysis because that's my personal favourite. Please tell me what books I need to fill in the gaps. Thanks.

Molu

Since you seem to have analysis covered...

Linear Algebra Done Right - Axler
Topics in Algebra - Herstein
Introduction to Topology - Gamelin (Dover, cheap!)
Algebraic Topology - Hatcher (Free online)

 

[Stingray]

Yes, I forgot Hecht. In SR, what is an adavanced text? I mean a text that explores the limits of SR eithout getting into much GTR or QFT.

Dixon's "Special Relativity" is far more advanced and interesting than its title makes it sound (if that's what you want). It's out of print, though.

 

[neutrino]

One more link...
http://www.ocf.berkeley.edu/~abhishek/chicphys.htm

 

[J77]

One more link...
http://www.ocf.berkeley.edu/~abhishek/chicphys.htm

Nice link

I like this on Arfken:

I suppose it's probably quite a learning experience to go through and work all the problems, but this is more likely to leave you with a head full of formulae than a good understanding of how to apply math to physics problems.

Sums up a lot of textbooks for me.

 

[robphy]

Dixon's "Special Relativity" is far more advanced and interesting than its title makes it sound (if that's what you want). It's out of print, though.

Dixon's book is probably too specialized for his list... but, I agree, it is interesting. I've been browsing through it [mainly on the Newtonian limit] on and off for the past year.

 

[Chris Hillman]

Curious indeed

A group of curious laymen have entrusted me with a curious project. I've been asked to build a small library of physics and math texts that intelligent students and adults may use to self-study the equivalent of a graduate course.

In principle a laudable goal, but after years of experience of interacting with persons trying to teach themselves advanced math/science, I feel that someone should try bring this down to Earth. While experts (in this case, self-appointed experts!) can help you gather an excellent library full of wonderful things, unfortunately, it doesn't follow that your "curious group" will benefit as much as we/they would hope.

My experience suggests that "natural-born scholars" seem to stumble around until they hit gold, reading wise, and then to absolutely get the most out of that source. Today's society--- at least, in the developed world--- offers many opportunities for such gifted young students to wander into challenging programs at good universities where they can truly master some area of scholarship, including topics in advanced math/science.

On the other hand, while being intensely curious is certainly a prerequisite for scholarship, very few have the luck/ability/discipline to really master some area of modern mathematics/science without a good deal of expert guidance in formal academic settings. Indeed, even among lucky, talented, disciplined, and hardworking individuals who have attained prominence in math or science, it is striking how often Nobel Prize or Fields Medal recipients mention one or more mentors who they feel played a crucial role in their intellectual development.

Context would help--- for example, is your curious group composed of retirees who have previously mastered some other discipline? If so, extensive previous experience of independent thinking and of acting as "self-starters" might increase the chances of success.

I might caution those offering books in this thread that I have had several experiences of being berated by angry would-be autodidacts who complained "I bought all the books you recommended and didn't learn any math!"

This said, let me offer my best wishes to any curious individuals seeking mathematical/scientific knowledge. I didn't say it's impossible to attain, just not as easy as having a bunch of good books at hand!

 

[loom91]

In principle a laudable goal, but after years of experience of interacting with persons trying to teach themselves advanced math/science, I feel that someone should try bring this down to Earth. While experts (in this case, self-appointed experts!) can help you gather an excellent library full of wonderful things, unfortunately, it doesn't follow that your "curious group" will benefit as much as we/they would hope.

My experience suggests that "natural-born scholars" seem to stumble around until they hit gold, reading wise, and then to absolutely get the most out of that source. Today's society--- at least, in the developed world--- offers many opportunities for such gifted young students to wander into challenging programs at good universities where they can truly master some area of scholarship, including topics in advanced math/science.

On the other hand, while being intensely curious is certainly a prerequisite for scholarship, very few have the luck/ability/discipline to really master some area of modern mathematics/science without a good deal of expert guidance in formal academic settings. Indeed, even among lucky, talented, disciplined, and hardworking individuals who have attained prominence in math or science, it is striking how often Nobel Prize or Fields Medal recipients mention one or more mentors who they feel played a crucial role in their intellectual development.

Context would help--- for example, is your curious group composed of retirees who have previously mastered some other discipline? If so, extensive previous experience of independent thinking and of acting as "self-starters" might increase the chances of success.

I might caution those offering books in this thread that I have had several experiences of being berated by angry would-be autodidacts who complained "I bought all the books you recommended and didn't learn any math!"

This said, let me offer my best wishes to any curious individuals seeking mathematical/scientific knowledge. I didn't say it's impossible to attain, just not as easy as having a bunch of good books at hand!

Thanks for your helpful words!

Well, where I live, all the interest in physics will not get me into a good university unless I learn to master the process of taking exams, which has little to do with the process of learning. Almost all exams are based either on memorization of definitions and 'explanations' that are utterly and ridiculously in contradiction to modern science or developing a type of robotic problem solving skill where you look at a problem, mentally sift through thousands of problems you have previously practiced until they fit into one of the patterns, and then plug in the numbers in the formula to get the answer. Most exam toppers are never heard of again. Only rarely does someone come along who has both real skill and the ability to crack exams.

Another thing about depending on good teachers is that it's a matter of luck. I may or may not get a teacher whose style suits me, but I can always find a book that suits me. I believe that really great textbooks remove a lot of the necessity of a teacher. Also, with the advent of Internet and forums like this, if I get stuck I can always ask for help, or even email Nobel-laureate teachers like Gerard t'Hooft (though he seems to have given up on answering his emails). No teacher has ever excited me like a good book. In fact, the books I truly like to learn from are the ones where I can feel someone speaking to me, someone guiding my hand as if he was standing right over my shoulder.

Right now, I'm very excited by Arnold's Mathematical Methods in Classical Mechanics. It's a very dense book, and I find myself constantly rereading paragraphs and brushing up my math to gain a full understanding, but it's also very rewarding. The rigorous construction of Galilean spacetime was simply breathtaking. It gave me the feeling that something I had found something I had been looking for a long time, without really knowing what I was looking for. Can a good teacher produce a better feeling? The book is the teacher. When I'm reading QED, it's Feynman I'm hearing, not some stupid book.

In addition, if I feel the need for verbal explanations, I can always turn to the MIT or Berkley video lectures (which will surely expand fast).

Molu

 

[mathwonk]

we've answered this question many times before and the answers should be findable from a quick search of this site, e.g. my thread above on who wants to be a mathemarician.

 

[loom91]

we've answered this question many times before and the answers should be findable from a quick search of this site, e.g. my thread above on who wants to be a mathemarician.

Which question are you talking about?

Molu

 

[ice109]

Hecht - modern optics
CRC - handbook physics and chemistry

you can't be serious. in my opinion this is one of the worst textbooks ever written. even if it's a substantive book the style in which it is written is deplorable. the text constantly refers back to figures and formulae in other sections, in both directions. The layout is also terrible in that figures in the same section will be referenced on pages other than those on which they are. not to mention none of multipart figures have captions. i sincerely regret that my professor chose this book and i took this class.

 

[cristo]

On the other hand, while being intensely curious is certainly a prerequisite for scholarship, very few have the luck/ability/discipline to really master some area of modern mathematics/science without a good deal of expert guidance in formal academic settings.

This is a very good point. In fact it's only in the first few weeks of starting my graduate studies that I've realized how true this is. Finding a specific book that will be completely useful for what you want to study and totally self contained is pretty much impossible (since we all study slightly different areas in a field). so, having someone (or many people) there who's academically experienced enough to point one towards specific books and other available sources of knowledge is invaluable. Instead of advising you to read a certain book, they will be able to say things like "this book is good for x" or "read this book but be careful of y"-- advice that one cannot get from a booklist!

That said, there are already booklists out there on the internet (I think there's one on John Baez's webpage, but that may no longer be there) if you wish to search.

 

[cristo]

Also, with the advent of Internet and forums like this, if I get stuck I can always ask for help, or even email Nobel-laureate teachers like Gerard t'Hooft (though he seems to have given up on answering his emails).

I think there's probably a reason for that; imagine how many emails a well known professor gets each day, either from students, or from people with "new" theories-- it would be impossible to reply to them! Your first port of call for such issues should be either someone you know, or someone in your university. You're more likely to receive a reply if you email from a local address!

No teacher has ever excited me like a good book. In fact, the books I truly like to learn from are the ones where I can feel someone speaking to me, someone guiding my hand as if he was standing right over my shoulder.

I imagine the time will come-- I've had a few lecturers who are fascinating to listen to, simply because they know so so much and are stood in front of me teaching me anything I desire to know!

 

[Chris Hillman]

I demur

Well, where I live, all the interest in physics will not get me into a good university unless I learn to master the process of taking exams, which has little to do with the process of learning. Almost all exams are based either on memorization of definitions and 'explanations' that are utterly and ridiculously in contradiction to modern science or developing a type of robotic problem solving skill where you look at a problem, mentally sift through thousands of problems you have previously practiced until they fit into one of the patterns, and then plug in the numbers in the formula to get the answer. Most exam toppers are never heard of again. Only rarely does someone come along who has both real skill and the ability to crack exams.

I am not sure I agree with your premise. From mathematical "entrance exams" I have seen, it seems clear that exams in France are traditionally more challenging than exams in the U.K., which are traditionally more challenging than exams in the U.S., but nonetheless if one has really mastered the subject, one should perform very well. I suggest that rather than regarding the possibility of studying for retaking whatever exam has upset your plans as a painful prospect, you should regard this as an opportunity to mentally organize your knowledge. You should find that this kind of studying is far more efficient, far more enjoyable, and leads to genuine mastery.

By the way, what exam in what area of the world were you railing against?

(EDIT: just noticed that in another recent thread, Molu said he is a high school student in India. I know little about exams in that country, but I presume they are vaguely Tripos-inspired.)

Another thing about depending on good teachers is that it's a matter of luck. I may or may not get a teacher whose style suits me, but I can always find a book that suits me. I believe that really great textbooks remove a lot of the necessity of a teacher.

Well, as I trust you already realize from what I have said in my previous post in this thread, I profoundly disagree. You are correct that faculty have very different styles and that a mismatch can hurt you, but everyone else is in the same boat there. And I don't agree that one can neccessarily find a book on every topic to suit every style.

Also, with the advent of Internet and forums like this, if I get stuck I can always ask for help, or even email Nobel-laureate teachers like Gerard t'Hooft (though he seems to have given up on answering his emails).

I am not surprised, if you think he and other Nobel Laureates are at your beck and call!

 

[Chris Hillman]

Yes, this really is a FAQ, as a search will quickly reveal

Which question are you talking about?

"What are the great books in mathematics?" Obviously.

 

[Johan de Vries]

The best book on Quantum Mechanics that has ever been written