What are you reading now? (STEM only)

[MidgetDwarf]

Still reading Contemporary Abstract Algebra by Gallian. Probably my second favorite book on Algebra, besides Artin.

I tried reading a few books on graph theory (own 4), but the subject bores me. I think I will put off learning it, until I need it for something. I find it a bit annoying that most graph theory books I have seen, have the problems at the end of chapter (like physics books), instead of at the end of each section.

Glad that I know that Graph Theory is something I am not interested at all. Since a professor, who publishes a lot, approached me a few times about doing research together. Im sure the research experience would have been very enlightening, but I do not want to waste someones time.

Started reading Alfhors book on Complex Analysis, but switched to Lang's book. Much prefer Lang. But will work through Alfhors at some point. Not a bad book by any means, but I have seen better presentations of the material. Love the concise nature of it.

 

[malawi_glenn]

Glad that I know that Graph Theory is something I am not interested at all

Same, I skip all chapters in books that deals with this topic.

I am so glad that the national school board in sweden decided to get rid of graph theory in the highest level compulusory course last year :D They replaced it with proof techniques which I think was a pretty good choice

Started reading Alfhors book on Complex Analysis, but switched to Lang's book. Much prefer Lang

Isn't Alfhors complex analysis book considered very difficult/advanced?

 

[ohwilleke]

Related but not precisely on point:

I find that in STEM, my reading is perhaps 90% articles and pre-prints (although some do run to hundreds of pages including supplemental materials), 5% reference books and textbooks that I am using like reference books, and 5% actual new (to me) books (lightly used dead tree books are A LOT cheaper and in many subjects, hot off the presses publication dates don't matter much) that I am reading cover to cover more or less in order.

My STEM reading is also maybe 93% in digital formats rather than in dead tree form.

 

[malawi_glenn]

dead tree form

And you also don't eat meat and only buy used clothes...

Reading on computer screens can't be good to ones eyes.

 

[Hyperfine]

Three books covering the historical development of modern physical cosmology:

Malcolm S. Longair, "The Cosmic Century: A History of Astrophysics and Cosmology", Cambridge University Press, 2006.

P. J. E. Peebles, "Cosmology's Century: An Inside History of Our Modern Understanding of the Universe", Princeton University Press, 2022.

Helge Kragh and Malcolm S. Longair (Eds.), "The Oxford Handbook of the History of Modern Cosmology", Oxford University Press, 2019.

 

[MidgetDwarf]

Same, I skip all chapters in books that deals with this topic.

I am so glad that the national school board in sweden decided to get rid of graph theory in the highest level compulusory course last year :D They replaced it with proof techniques which I think was a pretty good choiceIsn't Alfhors complex analysis book considered very difficult/advanced?

Thats a great thing what Sweden is doing! The proof techniques will be more beneficial for students. I feel that they should make this, and one proof based course mandatory for all undergrads. In order for them to further their tool kit and analyze the conditions of theorems they use in the science.

Yes, Alfhors is more advanced and difficult, but I feel that the difficulty lies in lack of examples and the brevity of the writing. Rudins undergrad book comes to mind. I would have hated Alfhors being my first exposure, but since I am familiar with the subject, I can feel in the blanks and add examples as needed.
I find Lang and even the book by Ullrich to offer more insights.

 

[malawi_glenn]

I feel that they should make this, and one proof based course mandatory for all undergrads

Remember I teach high school :D
So it is basically 2 weeks of teaching, 4-5 lessons.
Direct proofs, contrapositive proofs, proofs by contradiction and proof by induction.
Also we will put more emphasis on proofs related to congruences.

You know I am on a quest revisting my university math, since it was so long time ago since I did formal real analysis, complex analysis and complex analysis, etc... I do have Lang's book on my "to read" list when I come to complex analysis. Currently (still) reading Axler's analysis and linear algebra books. Things slowed down since I got my first kid and written a physics book for advanced high school students (in swedish). Oh well, it's the journey that matters

Three books covering the historical development of modern physical cosmology:

Malcolm S. Longair, "The Cosmic Century: A History of Astrophysics and Cosmology", Cambridge University Press, 2006.

P. J. E. Peebles, "Cosmology's Century: An Inside History of Our Modern Understanding of the Universe", Princeton University Press, 2022.

Helge Kragh and Malcolm S. Longair (Eds.), "The Oxford Handbook of the History of Modern Cosmology", Oxford University Press, 2019.

Have you read Narlinkar's Facts and Speculations in Cosmology?

 

[Hyperfine]

Have you read Narlinkar's Facts and Speculations in Cosmology?

No. But I assume I should.

 

[vanhees71]

Thats a great thing what Sweden is doing! The proof techniques will be more beneficial for students. I feel that they should make this, and one proof based course mandatory for all undergrads. In order for them to further their tool kit and analyze the conditions of theorems they use in the science.

Yes, Alfhors is more advanced and difficult, but I feel that the difficulty lies in lack of examples and the brevity of the writing. Rudins undergrad book comes to mind. I would have hated Alfhors being my first exposure, but since I am familiar with the subject, I can feel in the blanks and add examples as needed.
I find Lang and even the book by Ullrich to offer more insights.

During studying physics I attended a lot of lectures for (pure) mathematicians. First the analysis course (4 semesters, including analysis of one and multiple variables, vector analysis, ordinary differential equations, complex function theory) and linear algebra (2 semesters) were mandatory also for physics students and then simply, because I was interested. All these lectures were strictly about proving everything. How to use this abstract math, you never learnt from the mathematicians but in the physics lectures ;-). So I'm a bit puzzled about this statement: Aren't all math lectures about proving all theorems and lemmas?

 

[Hyperfine]

Other books I neglected to mention previously:

Two short, yet rewarding books on physical cosmology:

Lyman Page, "The Little Book of Cosmology", Princeton University Press, 2020.

Will Kinney, "An Infinity of Worlds: Cosmic Inflation and the Beginning of the Universe", The MIT Press, 2022.

Then there is P. J. E. Peebles, "Principles of Physical Cosmology". Princeton University Press, 1993 that sits on my desk as I attempt to summon the courage to pursue it.

And finally, Manjit Kumar, "Quantum: Einstein, Bohr, and the Great Debate About the Nature of Reality", W. W. Norton which I have just gotten today from the library.

All links are to Amazon.

 

[Demystifier]

How to use this abstract math, you never learnt from the mathematicians but in the physics lectures

I guess engineers have a similar complaint about physics: How to use this abstract physics, you never learnt from physicists but in the engineering lectures. Similar things chemists can say about physics, biologists about chemistry, medics about biology, all scientists about statistics, and politicians about everything else. The hierarchy in different kinds of human knowledge is a blessing and a curse.

 

[MidgetDwarf]

During studying physics I attended a lot of lectures for (pure) mathematicians. First the analysis course (4 semesters, including analysis of one and multiple variables, vector analysis, ordinary differential equations, complex function theory) and linear algebra (2 semesters) were mandatory also for physics students and then simply, because I was interested. All these lectures were strictly about proving everything. How to use this abstract math, you never learnt from the mathematicians but in the physics lectures ;-). So I'm a bit puzzled about this statement: Aren't all math lectures about proving all theorems and lemmas?

Hope I am more clear.
What I meant was, in the US, one can earn a STEM degree without having to take a pure math course. Ofcourse, non math majors do not need the abstraction for their coursework. But it is beneficial for one to at least learn the rudiments of how to read and prove mathematical statements. ie., employment purposes, expanding tool kit, gaining insights ( can be non rigorous such as geometric insight) of the tools they currently know, and what the short comings of said tools are.

 

[vanhees71]

I couldn't agree more. Some formal math is important to also have a better insight on what's behind the mathematical methods used in the natural sciences. E.g., in teaching QT I learnt that many textbooks go over some important details in a pretty superficial way. E.g., there are only very few textbooks, which really explain, why there are no half-integer representations of orbital angular momentum. The answer is that the corresponding angular-momentum eigenstates lead out of the proper domain for the angular-momentum operators to be essentially self-adjoint. The usual sloppy argument that wave functions must be unique under rotations about an angle of $2 \pi$ can be made rigorous by demanding that the angular-momentum operators are the generators of rotations acting in the usual way on wave functions. Half-integer angular momenta can thus only be realized in the sense of spin and are therefore indeed a generic quantum feature without real analogue in classical physics.

 

[andresB]

I couldn't agree more. Some formal math is important to also have a better insight on what's behind the mathematical methods used in the natural sciences. E.g., in teaching QT I learnt that many textbooks go over some important details in a pretty superficial way. E.g., there are only very few textbooks, which really explain, why there are no half-integer representations of orbital angular momentum. The answer is that the corresponding angular-momentum eigenstates lead out of the proper domain for the angular-momentum operators to be essentially self-adjoint. The usual sloppy argument that wave functions must be unique under rotations about an angle of $2 \pi$ can be made rigorous by demanding that the angular-momentum operators are the generators of rotations acting in the usual way on wave functions. Half-integer angular momenta can thus only be realized in the sense of spin and are therefore indeed a generic quantum feature without real analogue in classical physics.

What textbook do you recommend for that topic?

 

[vanhees71]

I think in this respect the best textbook is

L. Ballentine, Quantum Mechanics - A modern development, Addison-Wesley

It's also constructing non-relativistic QM from a detailed analysis of the Galilei group.

 

[andresB]

I think in this respect the best textbook is

L. Ballentine, Quantum Mechanics - A modern development, Addison-Wesley

It's also constructing non-relativistic QM from a detailed analysis of the Galilei group.

Ok, I checked Ballentine. He gives the quantum canonical transformation to Harmonic oscillator proof. I knew about that proof from an exercise in Griffiths. I think the original is from Schwinger, but I'm not sure.

 

[gentzen]

Well Greenspan's biography of Born is very revealing concerning the behavior of Heisenberg!

I am currently reading "Max Born - Baumeister der Quantenwelt. Eine Biographie" by Nancy Thorndike Greenspan, i.e. Anita Ehlers translation of the English original "The End of The Certain World. The Life and Science of Max Born. The Nobel Physicist Who Ignited the Quantum Revolution" from 2005.

So far I read the chapters 3. - 13. completely, but not in sequential order. So far, my impression is that Greenspan made no specific efforts to reveal unpleasant behavior of Heisenberg. At least she contrasts Born's (both Max and Hedwig) positive and forgiving attitude towards Heisenberg with the much more negative assessment of their friends (already before the war). And she reports many positive acts of Heisenberg (like explicitly mentioning Born's real contributions in some of his lectures all by himself, letters to Born where he expresses his regrets that Born's contribution get neglected, ...) to make this positive attitude more understandable.

I very much doubt that the remaining chapters will change this overall impression. But I fear that this says more about the positive attitude of Greenspan towards Born and Heisenberg, than about the actual behavior of Heisenberg. To be honest, if you think that this book talks negatively about Heisenberg, then you were already heavily biased against him before. There are many negative things to be said about him, but you will find only very few of those in this book.

 

[vanhees71]

It may well be that I read a bit too much in Born's complaints about a radio feature given by Oppenheimer, where is contribution (particularly his probabilistic interpretation of the quantum state) was neglected. I've the English original version of Greenspan's book. There this episode with a quote of a letter Born wrote to Oppenheimer after his radio talk is in the very beginning (at the end of the Prologue). It's, however, true that Born didn't blame Heisenberg directly for having been neglected in the recognition of his part in the development of matrix mechanics and the statistical interpretation.

I also admit that I'm not so much a fan of Heisenberg's and Bohr's writings on the foundations of quantum theory, because I don't like there overemphasis of philosophy. I like more the writings of Bohr, Jordan, Pauli and, particularly, Dirac with there more mathematical and scientific emphasis sparing out too many nebulous reflections on philosophy.

 

[gentzen]

So, I now finished chapter 14, and read all the preambles, prolog, epilog & co.

The trouble (for me) with Heisenberg is that it seems "pretty fashionable" to claim that "the behavior of Heisenberg" was problematic, or that "Heisenberg was a pretty horrible person". And of course, since Heisenberg was no angle (like most of us), there is some truth to such statements. But even with a complete and explicit (and reasonable) justification, it can still be troublesome. Take for example:
https://scottaaronson.blog/?p=6576#comment-1941742

Heisenberg was a pretty horrible person. It is true that he was not a nazi. But he was a hard line German nationalist. It is true that he didn’t like Hitler. But he did support Hitler’s war and simply believed that the nazis would be replaced by quality people after the war. He believed that the nazis could be tamed in about 50 years. Good luck with that. It is true that he was not particularly anti Jewish. But he believed that revolutions were inherently messy and the harm done to the Jewish population was an acceptable side effect of a political movement that would put Germany in it’s rightful place on the world stage. It is True that Heisenberg steered Germany away from the Bomb. But it was his honest assessment that the massive resources needed to develop the bomb would distract from the war effort and was very unlikely to produce results before the end of the war. He was probably correct.

Watch this:
[link to a video which is is “probably indefensible, once one starts to dig into details”]

The text is well argued, and the used information seems to be true, based on all that I have read about Heisenberg. But it ends with a link to a video that claims much more, and paints a very sinister picture of Heisenberg. And this time, the information often seems surprising, and contradict what I believed to know. So I start checking, and after one or two clear refutations, I conclude that its claims are “probably indefensible, once one starts to dig into details”:
https://scottaaronson.blog/?p=6576#comment-1941826

But in fact, things are even more complicated than that. Both Samuel Goudsmit (in 1947) and Leslie Groves (in 1962) tried to suggest that Heisenberg was too stupid to build an atomic bomb, and believed the critical mass to be in the order of tons. They claimed that the secret Farm Hall protocols would contain statements by Heisenberg that proved that. But when the protocols were released in the 90s, they painted a very different picture. ... But they also contained the moment were von Weizsäcker sort of invented "their defense," which strongly hint to me that "We can safely assume that Heisenberg’s and von Weizsäcker’s version from 1957 of what happened in Copenhagen is completetly fabricated." So all involved parties including Goudsmit, Groves, Heisenberg & co. lied to smaller or bigger extents, and all had their own sorts of agendas.Given all this conundrum, it would have been interesting of having a completely independent demonstration of problematic behavior by Heisenberg, especially in connection with Born. Greenspan's book is nice in this that it at least reports relevant rumors around Heisenberg's behavior, and also the results of Greenspan's own attempts to verify or refute those rumors. At least I learned that Heisenberg already got attacked (by rumors) much earlier than the war and the atomic bomb project. Perhaps the best theory why is that he really was actually horrible. At least my other theories cannot really handle that early opposition. There are definitively many strange things about him, for example, it seems like he never published together with Niels Bohr (despite claiming that their philosophy and viewpoints would closely match), and he didn't care when Bohr warned him not to publish something. And he piles the highest praise on Bohr, but at the same time describes in nasty detail how Bohr mercilessly tried to convince Schrödinger that he was wrong, continuing even after Schrödinger felt ill. And he also describes with glee other weaknesses of Bohr, like that his lectures were often bad and hard to understand.

 

[gentzen]

I also admit that I'm not so much a fan of Heisenberg's and Bohr's writings on the foundations of quantum theory, because I don't like there overemphasis of philosophy.

Heisenberg certainly was well educated in philosophical matters, some of his students (like Grete Hermann, or Carl Friedrich von Weizsäcker) later became philosophers, and his genuine philosophical contributions were not so different from later contributions by "real philosophers", see for example
http://philsci-archive.pitt.edu/1614/ ("Open or Closed? Dirac, Heisenberg, and the Relation between Classical and Quantum Mechanics" by Alisa Bokulich, 2004)

I like more the writings of Bohr, Jordan, Pauli and, particularly, Dirac with there more mathematical and scientific emphasis sparing out too many nebulous reflections on philosophy.

I guess you mean "Born," not "Bohr". But have you actually read their "reflections on philosophy" like
http://gymarkiv.sdu.dk/MFM/kdvs/mfm 30-39/mfm-30-2.pdf ("Continuity, Determinism, and Reality" by Max Born, 1955)

I've the English original version of Greenspan's book.

I have no idea whether German or English is easier for you when it comes to non-scientific writting. But in case reading such stuff in English is enjoyable to you, I really recommend to completely read this book (if you have not done so already). It contains many unbelievable and interesting stories, and Greenspan's handling of the unavoidable historic uncertainties is very well done.

 

[vanhees71]

Heisenberg certainly was well educated in philosophical matters, some of his students (like Grete Hermann, or Carl Friedrich von Weizsäcker) later became philosophers, and his genuine philosophical contributions were not so different from later contributions by "real philosophers", see for example
http://philsci-archive.pitt.edu/1614/ ("Open or Closed? Dirac, Heisenberg, and the Relation between Classical and Quantum Mechanics" by Alisa Bokulich, 2004)

Grete Hermann was a student of Emmy Noether's and a Postdoc with Heisenberg. I know her excellent paper about von Neumann's no-hidden-variables proof, which is very good.

I better keep silent about what I think about CFvW ;-)).

I guess you mean "Born," not "Bohr". But have you actually read their "reflections on philosophy" like
http://gymarkiv.sdu.dk/MFM/kdvs/mfm 30-39/mfm-30-2.pdf ("Continuity, Determinism, and Reality" by Max Born, 1955)

Of course, I meant Born. Of course, he also wrote philosophical essays. That seems to be a disease of retired theoretical physicists ;-)).

I have no idea whether German or English is easier for you when it comes to non-scientific writting. But in case reading such stuff in English is enjoyable to you, I really recommend to completely read this book (if you have not done so already). It contains many unbelievable and interesting stories, and Greenspan's handling of the unavoidable historic uncertainties is very well done.

Yes, I've read this book completely. It's excellent!

At the moment I'm reading a biography about Pauli, which is great too:

Charles P. Enz, No time to be brief

 

[gentzen]

Grete Hermann was a student of Emmy Noether's and a Postdoc with Heisenberg. I know her excellent paper about von Neumann's no-hidden-variables proof, which is very good.

You are right. And she was already a real philosopher before she joined Heisenberg.
And including postdocs in the people a teacher influenced would be problematic, in certain ways. For example, Shin'ichirō Tomonaga was also a postdoc with Heisenberg, but his work and interest in quantum electrodynamic had already started earlier. What Heisenberg brought in additionally was only his interest in nuclear physics.

I better keep silent about what I think about CFvW ;-)).

Yeah, CFvW is ... maybe easiest dealt with by keeping silent. Whenever new historical records emerge, and you study them in the hope to find something more definite concerning Heisenberg, you always have that risk of instead finding something definitely unfavorable concerning CFvW. And you know that Heisenberg must have known, and covered up for it. (It seems much easier to me to reproach Heisenberg that he accepted those structures in Germany that CFvW was part of and collaborated with them, then to reproach him that he would have been a Nazi or would have collaborated with them.) And CFvW's style as a philosopher is overly wordy, even so his positions seem generally fine, as far as I can tell. His physical contributions too seem fine to me, probably nothing revolutionary, but nothing to be ashamed of either.

 

[haider]

Started Div, Grad, Curl And All That by H.M. Schey because I really need to (re)learn vector calculus before next semester's Griffiths based electrodynamics course. Really liking it so far.

 

[haider]

Then there is P. J. E. Peebles, "Principles of Physical Cosmology". Princeton University Press, 1993 that sits on my desk as I attempt to summon the courage to pursue it.

Same here but home directory instead of desk :)

 

[LittleSchwinger]

I also admit that I'm not so much a fan of Heisenberg's and Bohr's writings on the foundations of quantum theory, because I don't like there overemphasis of philosophy. I like more the writings of Bohr, Jordan, Pauli and, particularly, Dirac with there more mathematical and scientific emphasis sparing out too many nebulous reflections on philosophy.

Wow, you've a very different experience to me. Pauli wrote essays about Jungian psychology and so on and Born wrote long essays on the meaning of science and society in general.
Bohr however always seemed flat and sober to me. Aside from the Como essay which was a bit confused, most of his writing is short and not particularly philosophical I would have said. Maybe it's different ideas of what's "philosophy".

 

[haushofer]

Wow, you've a very different experience to me. Pauli wrote essays about Jungian psychology and so on and Born wrote long essays on the meaning of science and society in general.
Bohr however always seemed flat and sober to me. Aside from the Como essay which was a bit confused, most of his writing is short and not particularly philosophical I would have said. Maybe it's different ideas of what's "philosophy".

Yes, that could be the case. It's an ongoing discussion, especially in topics on quantum mechanics. Somehow, a lot of physicists nowadays see "ontology" as "mere philosophy", while for many physicists and especially founding fathers of quantum mechanics it was just part of the physics. Maybe it's part of the increased level of abstraction of modern physics that physicists nowadays make this distinction between "philosophy" and "physics", but in my opinion such a cut is as artificial as the one by Heisenberg in quantum mechanics :P

 

[vanhees71]

I know that Pauli was also inclined to the "paranormal" and some Jungian psychology. Fortunately he kept this part of his thinking separate from his physics, which he as always presented in the no-nonsense mathematical style, which is clarifying and "demystifying" things rather than introduce obscure notions like "complementarity" like Bohr and Heisenberg. For me Bohr's writings are usually pretty obscure. Particularly his answer to the EPR paper is even more confusing than the EPR paper itself. To get Einstein's true thoughts one should rather read the Dialectica article of 1948:

A. Einstein, Dialectica 2, 320 (1948)

I'm sure that there must be somewhere an English translation of this brillant article.

Concerning philsophy and quantum theory I'm also thinking that the philosophers usually mess up the subject severely and unnecessarily. It's indeed true that to talk about quantum theory adequately you have to use pretty abstract descriptions of "physical reality", i.e., Hilbert-space vectors and operators and also, if you want to understand it from a fundamental level, Lie group and algebra-representation theory.

 

[LittleSchwinger]

Pauli's Handbuch der Physik article is very good. I guess for me Heisenberg is pretty much the same, his Chicago lectures are excellent, mathematical and concise and the more general musings are in other essays.
Bohr and Complementarity always seemed pretty clear to me as well since he constantly talks about experiments, it's just the physical fact corresponding to the mathematical fact of operators not commuting. I never found him obscure I have to say. In fact Complementarity is a common enough word in quantum information. Perhaps a difference between fields?

Currently I'm reading the 2nd Edition of Gottfried's textbook with Yan as co-author as preparation for teaching.

 

[vanhees71]

Pauli's "Handbuchartikel" is indeed a masterpiece, particularly such little gems like the argument, why time must be a parameter and not an observable. Gottfried and Yan is a very good textbook too.

 

[LittleSchwinger]

I should have said Complementarity is usually mathematical stated in modern QI as two operators $A$ and $B$ whose associated eigenstates obey $(a_{i},b_{j}) = const, \forall i,j$. That's the mathematical encoding of what Bohr spoke about.

Pauli's "Handbuchartikel" is indeed a masterpiece, particularly such little gems like the argument, why time must be a parameter and not an observable. Gottfried and Yan is a very good textbook too.

One of the best reasons for a non-Teutophone physicist to learn German is the price difference between the English translation of Pauli's article and the original!