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

 

[Kurdt]

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.

I like Hecht. It remains one of the most popular optics texts the world over. I will admit that the layout is not the best, but the content is second to none. Since this is a list of self study texts however you are probably best using something else and coming to Hecht when you are a lot more competent.

 

[Chris Hillman]

Molu/loom91, you haven't answered my question:

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.

You make it sound like an exclusive "gentleman's club". Any information would be appreciated, or failing that, any explanation for being coy.

(EDIT: Molu did say in another thread that he is a high school student in India, but this hardly resolves my mystification.)

 

[loom91]

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.)

You misunderstand my situation. I've not failed any exam, but I'm railing against ones I'm supposed to take soon. Let me give you an example. A frequently asked question in the State School-passing exam is "Why is KOH a stronger base than NaOH?"

Firstly, this question is not meaningful unless the solvent is specified (and inaccurate in the universal solvent because of water's strong levelling). But what's more, the answer expected of every student, the one you must either reproduce or be awarded zero, is the following: K is more electropositive than Na, therefore OH has a higher charge density in KOH than in NaOH, therefore KOH is a stronger base. WTF?

The exam is constructed so that if you have a minimum of true understanding of your subject, then you can not pass the exam unless you knowingly write such ridiculous answers like the above.

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.



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

Again you misunderstand me. I was not complaining that t'Hooft is not answering emails anymore. In fact, I was surprised that he was in the first place. It was merely an observation. Myfacility with English (my second language) is not very great, so my words may not always convey the intended subtexts.

As for teachers, what I mean is that I can read any book that has ever been written and distill from their collective a complete overview of the subject matter and various viewpoints for looking at it. But I can't pick and choose to study under the greatest teachers. I will never be able to study under Feynman, but I can always read his books. I do not disagree that a great teacher is more helpful than a great book, but a great teacher is much more difficult to find (and a lot of it is luck) than a great book.

Molu

 

[loom91]

Molu/loom91, you haven't answered my question:



You make it sound like an exclusive "gentleman's club". Any information would be appreciated, or failing that, any explanation for being coy.

(EDIT: Molu did say in another thread that he is a high school student in India, but this hardly resolves my mystification.)

Sorry, I overlooked it. It's a mixed bag mostly. Most are middle-aged men, some are curious high-school students like me. The men come from many different backgrounds originally: engineers (civil, mechanical etc), chemists, finances, literature. Even a couple of math graduates, but they have been doing clerical work for so long that they have forgotten most of what they had learned. Frankly, I don't believe many of these men will make it past the first few books, but some (including most of the students, all very gifted and inquisitive) probably have the thirst to actually do exercises. Anyway, I'm asked to give them a booklist and that's what I'm doing. Having such a thing at hand will benefit me too, both now and in my further studies.

Molu

 

[Johan de Vries]

Molu, it's 't Hooft, not t'Hooft :)

And he explains on his home page that he receives so many emails that he can't answer them all. I suspect that to be fair he ansers no emails at all except from his collegues.

 

[Chris Hillman]

Check, check... check

Hi, Molu,

Thanks for your responses!

My facility with English (my second language) is not very great, so my words may not always convey the intended subtexts.

Actually, I haven't noticed any particular difficulties in understanding your use of the English language (which doesn't seem noticeably inferior to that of most American high school students who post here!) and I don't think that was the reason for the communication problem.

I've not failed any exam, but I'm railing against ones I'm supposed to take soon. Let me give you an example. A frequently asked question in the State School-passing exam is "Why is KOH a stronger base than NaOH?"

Firstly, this question is not meaningful unless the solvent is specified (and inaccurate in the universal solvent because of water's strong levelling). But what's more, the answer expected of every student, the one you must either reproduce or be awarded zero, is the following: K is more electropositive than Na, therefore OH has a higher charge density in KOH than in NaOH, therefore KOH is a stronger base. WTF?

The exam is constructed so that if you have a minimum of true understanding of your subject, then you can not pass the exam unless you knowingly write such ridiculous answers like the above.

This is exactly the kind of information which would have been very helpful if you had included it in your first post in this thread. Indeed, the very first thing you should have said is that you are discussing (do I guess right?) a nation-wide exam given in India to (yes?) high school students which influences (determines ?) educational opportunities.

Always recall: "it's a great big wide world out there". (Usually I need to remind my fellow Americans of this, not people from Asia!) You should always ask yourself before posting whether your question/comments will make sense without further explanation to people with different backgrounds or from different parts of the world.

Hope it is clear that at the risk of getting OT I am trying to convey a lesson on how to post better in future!

Again you misunderstand me. I was not complaining that t'Hooft is not answering emails anymore. In fact, I was surprised that he was in the first place.

OK.

As for teachers, what I mean is that I can read any book that has ever been written and distill from their collective a complete overview of the subject matter and various viewpoints for looking at it. But I can't pick and choose to study under the greatest teachers. I will never be able to study under Feynman, but I can always read his books. I do not disagree that a great teacher is more helpful than a great book, but a great teacher is much more difficult to find (and a lot of it is luck) than a great book.

OK, hard to argue with that

Sorry, I overlooked [my question about the reading club]. It's a mixed bag mostly. Most are middle-aged men, some are curious high-school students like me. The men come from many different backgrounds originally: engineers (civil, mechanical etc), chemists, finances, literature. Even a couple of math graduates, but they have been doing clerical work for so long that they have forgotten most of what they had learned. Frankly, I don't believe many of these men will make it past the first few books, but some (including most of the students, all very gifted and inquisitive) probably have the thirst to actually do exercises. Anyway, I'm asked to give them a booklist and that's what I'm doing. Having such a thing at hand will benefit me too, both now and in my further studies.

True, true. And yes, it is impressive that you (a high school student?) were asked to compile the reading list--- someone must think highly of you!

 

[loom91]

This is exactly the kind of information which would have been very helpful if you had included it in your first post in this thread. Indeed, the very first thing you should have said is that you are discussing (do I guess right?) a nation-wide exam given in India to (yes?) high school students which influences (determines ?) educational opportunities.

It's not nation-wide, it's a state-wide exam (though the state, West Bengal, is larger and far more populous than the average European nation). The nation-wide ones are in a slightly better condition (though they are also a whole lot easier), except the IIT-JEE, which is of course in a class of its own. That's one exam that rewards intelligence and skill. The entrance exam for the IIS is also not bad. These centralised exams will make or break your future.

Molu

 

[Chris Hillman]

Some OT queries (sorry!)

It's not nation-wide, it's a state-wide exam (though the state, West Bengal, is larger and far more populous than the average European nation). The nation-wide ones are in a slightly better condition (though they are also a whole lot easier), except the IIT-JEE, which is of course in a class of its own. That's one exam that rewards intelligence and skill. The entrance exam for the IIS is also not bad. These centralised exams will make or break your future.

It's always interesting to learn a bit more about how higher education is organized in other countries, since there seems to be quite a bit of variation. Here in the U.S. allegations of bias in our own nationwide entrance exam, the SAT (characteristically, this is actually prepared/proctored/graded by a private company which makes enormous profits!), are a perennial topic for "letters to the editor". However, in my experience, the SAT is only one component of admissions decisions by American universities.

except the IIT-JEE, which is of course in a class of its own.

Of course! Err, what is the IIT-JEE? (Indian Institute of Technology?) What is the IIS?

Another somewhat off-topic (OT) question: do you know whether it is true, as I have seen some Indians allege, that Indian universities have a particularly severe problem with rampant plagiarism and other gross misconduct? And is the story of Balwant Singh Rajput well known among Indian students as (I trust) an example of someone who made very bad choices and who consequently came to a very bad end?
http://www.geocities.com/physics_plagiarism/
http://www.hinduonnet.com/thehindu/2003/02/07/stories/2003020705470103.htm
http://www.hinduonnet.com/fline/fl1922/stories/20021108003508400.htm
http://www.indianexpress.com/full_story.php?content_id=17786
http://chronicle.com/weekly/v49/i09/09a04401.htm
Just curious...

(I should perhaps add that I can, unfortunately, name citizens of many other countries who have been plausibly accused of this kind of misconduct, so no-one is claiming this is unique to India or any country--- this just happened to be a particularly well publicized case. Nonetheless, some articles in India newspapers do quote whistleblowers who claim, in particular, that plagiarism is an "endemic and almost universally accepted practice" in Indian medical schools. More generally, my Indian friends acknowlege that corruption in India is often blatant, while in the U.S. it tends to be discreet--- I am not sure which is worse!)

 

[francescopadormo]

Don't forget to double up (at least!) on the books! After the unveiling, everyone will say "OK, I think I'll start at the beginning, where's the *intro physics text*? Hmm, it's gone..."

 

[Chris Hillman]

Possibly useful book list

Hi, Molu,

I just remembered this book list from a leading Indian statistician and information theorist: J. N. Kapur, Some aspects of school mathematics, New Delhi: Arya Book Depot, 1967. There's also a book of biographical essays on Indian mathematicians edited by Kapur, but I haven't read that. These might be useful if anyone in your club expressed a particular interest in books by leading Indian mathematicians (in recent days I have mentioned Chandrasekhar and Harish-Chandra, and I can point you at some expository articles published in journals [i.e. not suitable for your booklist] by SC, whose "serious" works tend to be daunting even for the most serious student--- I've been working my way through his seven volume collected works and its worth the struggle, but this definitely isn't bed time reading--- you need to read very "actively", e.g. keeping notes on notation, performing computations, and so on).

 

[loom91]

It's always interesting to learn a bit more about how higher education is organized in other countries, since there seems to be quite a bit of variation. Here in the U.S. allegations of bias in our own nationwide entrance exam, the SAT (characteristically, this is actually prepared/proctored/graded by a private company which makes enormous profits!), are a perennial topic for "letters to the editor". However, in my experience, the SAT is only one component of admissions decisions by American universities.

Privetisation of education is a highly charged political issue here.

Of course! Err, what is the IIT-JEE? (Indian Institute of Technology?) What is the IIS?

The IIT are, as you say, the Indian Institutes of Technology, the premier educational institutions in the country. Their entrance examination was known for its supreme difficulty (often called the most difficult examination in the world). In the golden days, every question set in the IIT-JEE set the benchmark for several decades to come. There are IIT problems, and then there are everything else. They often require tying together many different fields of physics, and innovating complex avenues of attack on the spot. The greatest of IIT problems require several conceptual and technical breakthroughs to solve completely. In recent years, the standard has fallen somewhat as the IIT-JEE has shifted towards more conventional easier multiple-choice questions. While they remain the most difficult and prestigious examination in the country, that X-factor is gone. In 1997 the physics questions in the screening were so difficult that the cutoff was set to 7 out of 100! Remember that the greatest brains in India attempt this examination. One of the questions involved refraction through an inhomogenous optical media (we are not supposed to know Fermat's principle).

The IIS are the Indian Institutes of Statistics, another group of highly exclusive institutions teaching math and statistics. Their examination is also very difficult, though not as famous due to the niche appeal.

Another somewhat off-topic (OT) question: do you know whether it is true, as I have seen some Indians allege, that Indian universities have a particularly severe problem with rampant plagiarism and other gross misconduct? And is the story of Balwant Singh Rajput well known among Indian students as (I trust) an example of someone who made very bad choices and who consequently came to a very bad end?
http://www.geocities.com/physics_plagiarism/
http://www.hinduonnet.com/thehindu/2003/02/07/stories/2003020705470103.htm
http://www.hinduonnet.com/fline/fl1922/stories/20021108003508400.htm
http://www.indianexpress.com/full_story.php?content_id=17786
http://chronicle.com/weekly/v49/i09/09a04401.htm
Just curious...

(I should perhaps add that I can, unfortunately, name citizens of many other countries who have been plausibly accused of this kind of misconduct, so no-one is claiming this is unique to India or any country--- this just happened to be a particularly well publicized case. Nonetheless, some articles in India newspapers do quote whistleblowers who claim, in particular, that plagiarism is an "endemic and almost universally accepted practice" in Indian medical schools. More generally, my Indian friends acknowlege that corruption in India is often blatant, while in the U.S. it tends to be discreet--- I am not sure which is worse!)

I haven't heard any of this before. Corruption is indeed widespread, though I can't compare with other countries. Plagarism is also common. Recently the doctorate of a researcher was revoked because his thesis was found to contain a large amount of content copied verbatim from a textbook, including errors.

Molu

 

[loom91]

So, any suggestions about those math books?

Molu

 

[Chris Hillman]

Random booklist

Privetisation of education is a highly charged political issue here.

As here, where a fairly new phenomenon is privatised primary education. That is, in cases where particular "school districts" (city government level (dis?)-organizations which run local public schools) have done particularly badly on standardized nationwide reading/math exams, the local schools are now sometimes taken over by private companies. The question of how well this works is a political "hot potato" in the U.S.

Remember that the greatest brains in India attempt this examination. One of the questions involved refraction through an inhomogenous optical media (we are not supposed to know Fermat's principle).

So its a cross between an entrance exam and a national talent exam? (In the U.S., at the high school level there are entrance exams for elite "magnet schools", and at the undergraduate level in mathematics there is a talent search, the Putnam exam.)

I haven't heard any of this before. Corruption is indeed widespread, though I can't compare with other countries. Plagarism is also common. Recently the doctorate of a researcher was revoked because his thesis was found to contain a large amount of content copied verbatim from a textbook, including errors.

Interesting. Do you happen to have a link to a newspaper article in English or something like that?

Check out http://arxiv.org/new/withdrawals.aug.07.html for a huge scandal at the arXiv, in which two distinct plagiarism rings (both operating in Turkey, as it happens) were recently uncovered when a facutly member at one of the institutions became suspicious about the output of 40 papers over two years by two graduate students

So, any suggestions about those math books?

Didn't you say your budget has already been exhausted? FWIW, the suggestions I saw above seemed pretty good ones. I'd probably give greater weight to books which discuss great ideas but which I think have a better chance of being useful to someone who dips into or skims rather than studying very carefully over many months, and the greatest weight of all to books which should reward all three styles of reading. And I'd limit my suggestions to textbooks discussing the very best of modern mathematics. On this basis, some books which happened to pop into my mind are:

Some Great Books notable for their charming style as well as their delightful content:

E. Atlee Jacson, Perspectives of Nonlinear Dynamics, two volumes, University of Cambridge Press, 1991.

Bela Bollobas, Modern Graph Theory, Springer, 1998.

Tristan Needham, Visual Complex Analysis, University of Cambridge Press, 1998.

Hilbert and Cohn-Vossen, Geometry and the Imagination, Chelsea, 1990 (translation of 1932 classic).

Rademacher and Toeplitz, The Enjoyment of Mathematics, Princeton University Press, 1957.

Ulam and Kac, Mathematics and Logic, Praeger, 1968.

Cox, Little, and O'Shea, Ideals, Varieties, and Algorithms, Springer, 1992.

Hardy and Wright, An Introduction to the Theory of Numbers, 5th edition, Oxford University Press, 1979.

Arnold, Ordinary Differential Equations, Springer, 1992.

Halmos, Finite Dimensional Vector Spaces, Van Nostrand, 1958.

Kac, Statistical independence in probability, analysis and number theory, Wiley, 1959.

Some Really Good Math Books of Which I Happen to Be Particularly Fond:

Harris, Algebraic Geometry, Springer, 1992.

Gibson, Elementary Geometry of Algebraic Curves, Cambridge University Press, 1998.

Michael Artin, Algebra, Prentice Hall, 1991.

Khinchin, Continued Fractions, Dover 1994 (reprint of translation of 1949 original)

Cover and Thomas, Elements of Information Theory, Wiley, 1981.

Kapur and Kesevan, Entropy Optimization Principles with Applications, Academic Press, 1992.

Lawvere and Schanuel, Conceptual Mathematics, Cambridge University Press, 1991.

Flanders, Differential Forms with Applications to the Physical Sciences, Dover, 1989 (reprint of 1963 original).

Guenther and Lee, Partial Differential Equations of Mathematical Physics and Integral Equations, Dover, 1996 (reprint of of 1988 original)

Olver, Applications of Lie Groups to Differential Equations, 2nd edition, Springer, 2000.

Boas, A Primer of Real Functions, Wiley, 1960.

Bartle, Elements of Real Analysis, Wiley, 1964.

Neumann, Stoy, and Thomspon, Groups and Geometry, Oxford University Press, 1999.

Lee, Introduction to Smooth Manifolds, Springer, 2003.

Hatcher, Algebraic Topology, Cambridge University Press, 2002.

I would also suggest some volumes from the "LMS student text series", e.g. 5, 32, 35, 40, 45, 50, 53, 58. Also, the Chauvenet Prize papers (two volumes) from the American Mathematical Association.

Alright, I could add more, that's enough.

I stress that I didn't try to cover topics, just to name some books which I think might have a wide appeal and might reward more than one type of reader or style of reading. The kicker is that this library would have "prerequisite gaps" to which I haven't paid any heed but which your reading club would have to deal with.

 

[leon1127]

The entire series of Lang and Boubaki should fill half of your library

 

[loom91]

As here, where a fairly new phenomenon is privatised primary education. That is, in cases where particular "school districts" (city government level (dis?)-organizations which run local public schools) have done particularly badly on standardized nationwide reading/math exams, the local schools are now sometimes taken over by private companies. The question of how well this works is a political "hot potato" in the U.S.

So its a cross between an entrance exam and a national talent exam? (In the U.S., at the high school level there are entrance exams for elite "magnet schools", and at the undergraduate level in mathematics there is a talent search, the Putnam exam.)

It's not a talent search exam, it's purely an entrance test for undergraduate study in select institutions.

Interesting. Do you happen to have a link to a newspaper article in English or something like that?

No, it was sometime ago.

Check out http://arxiv.org/new/withdrawals.aug.07.html for a huge scandal at the arXiv, in which two distinct plagiarism rings (both operating in Turkey, as it happens) were recently uncovered when a facutly member at one of the institutions became suspicious about the output of 40 papers over two years by two graduate students

A mathematician friend of my dad once complained that there were some such plagarism groups, with connections among journal referees, who survived on others papers. I think Perelman also made the allegation of rampant plagarism.

Didn't you say your budget has already been exhausted?

That was the physics budget.

Thanks for your suggestions. What topics (and in what order) do a standard European undergraduate course in mathematics cover?

Molu

 

[loom91]

The entire series of Lang and Boubaki should fill half of your library

Hardly the ideal books for self-study!

Molu

 

[siddharth]

Molu,

Have you and your group thought about obtaining access to the library of a local university/institution? If that's possible, it might be cheaper, and you'd have access to a vast number of books.

Also, what is the mathematical background required to appreciate Arnold?

You mean his book, "Mathematical Methods of Classical Mechanics"? I've partially used that book as a reference for my current UG classical mechanics course, and I liked the parts on Lagrangian and Hamiltonian mechanics. However, I lack sufficient knowledge on topology and differential geometry to understand the sub-chapters on symplectic manifolds and lie algebras in Hamiltonian Dynamics.

 

[Chris Hillman]

I should have thought of that

Have you and your group thought about obtaining access to the library of a local university/institution? If that's possible, it might be cheaper, and you'd have access to a vast number of books.

Good point!

You mean [Arnold's] book, "Mathematical Methods of Classical Mechanics"?

No, I mentioned his Ordinary Differential Equations, which has fewer prerequisites.

I've partially used that book as a reference for my current UG classical mechanics course, and I liked the parts on Lagrangian and Hamiltonian mechanics. However, I lack sufficient knowledge on topology and differential geometry to understand the sub-chapters on symplectic manifolds and lie algebras in Hamiltonian Dynamics.

Every educated person really should know manifold theory and Lie theory.

 

[leon1127]

Hardly the ideal books for self-study!

Molu

If anyone does all the exercise in Lang's book, I am certain you can pretty much write a book in that particular subject... You would understand what i mean when you have used lang's book in any of your classes.

 

[siddharth]

Every educated person really should know manifold theory and Lie theory.

I have time, and am working on it. Could you recommend introductory texts in the aforementioned subjects at the advanced undergrad/beginning graduate level?