Building a library of physics and math texts

[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?

 

[mathwonk]

as i look around at my own library whic keeps growing, it dwns on me it is more beneficial to just read a few of them than keep acquiring them. even one book like courant, well read, would change a man.

 

[Chris Hillman]

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

Manifolds:

William M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, 1986. Might look a bit unfriendly but actually very well written.

John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer, 2003. See also his other two books, which complement this one. Worthwhile for emphasis on level of structure alone!

Exterior calculus:

Flanders, Differential Forms with Applications to the Physical Sciences, Dover reprint. The most user friendly introduction, also very nice chapter on matrix Lie groups and the Maurer-Cartan form.

Spivak, Calculus on Manifolds is good for some things.

Differential geometry:

Too many books to mention. The five volume book by Spivak has wonderful stuff but I find the notation over-fussy and off-putting.

Chris J. Isham, Modern Differential Geometry for Physicists. A nice short book, not unsuitable as a supplementary text for math students.

Lie theory:

Bump, op cit.

The little book by Segal, Carter, and McDonald, LMS student text Vol. 32, is too sketchy to use as a textbook but is highly readable and very inspiring. (There is a mistake in the discussion of Penrose's description of the night sky via the Lorentz group.)

The books by Vadarajan, Humphreys, and Knapp are all excellent but maybe not the best first text. The book by Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications is notable for an unique mathematical symbol (a picture of banannas which appears as an argument), and has many convenient tables and is a bit more historical than some. The books by Hermann are idiosyncratic but intriguing, time permitting.

If you have any more questions, don't take it personally if I don't reply (lack of time, etc). Good luck!