For some reason I love books. Here I maintain a list of textbooks (under construction) and popular science books that I like with short comments on them. If you have recommendations of textbooks for me, just drop me an email. My goodreads site has some more non-science texts.
Highschool
- KVANT (Quantum). This is in fact not a textbook. It is a magazine originally published in the Soviet Union. When I was a highschool student, a friend gave me a copy of the translation (handwritten!) of the problems dicussed in different issues. I really learned a lot from that! (I am still looking for the author of the handwritten note.) The excellent part of it is that the problems discussed in there are not much about calculation or techniques for problem solving. They are better at training physical intuition than any other source I know of.
- Tuyển tập các bài thi học sinh giỏi Vật lý toàn Liên-Xô. This a collection of questions in the physics olympiad in the Soviet Union. The questions are short, lucid, with very little computation but force one to think carefully about the physics. They are somewhat simpler than problems dicussed in KVANT, but still very good.
- Đặng Mộng Lân, Câu chuyện các hằng số vật lý cơ bản, Nhà Xuất Bản Khoa Học Kỹ Thuật (Hà Nội, 1976). This is among the best semi-popular book telling stories around the fundamental constants I ever read. I wonder if it has been ever translated into English. I owned two copies, but eventually gave to my friends as gifts. In 2012, it was republished. But I learned about that too late and did not have chance to grap one.
- Khinchin, Các bài toán ngụy biện vui về Vật lý. This is a book translated from Russian. It contains a lot of very intersting questions to train physical intuition.
- I. Pereman, Vật lý vui. This a fun, little book explaining about the mechanical and thermal phenomena happening around us. It is popular in English too.
- Hà Huy Bằng và Nguyễn Văn Hướng, Ba trăm bài toán Vật lý sơ cấp, ĐHQG This is a collection of problems from Poland Physics Olympiad. Problems in there are rather hard, sometimes hard to formulate out, and sometimes even computationally hard. It is good to train solving problems.
- Irodov, Tuyển tập các bài tập Vật lý đại cương. This is in fact a problem book for physics in the university. It contains a lot of problems. In fact, they are not difficult, but it is good to learn canonical way of solving problem instead of using different clever tricks (which is often the case for other books to train highschool students.)
- Rumer, Thuyết tương đối, ĐHSP. This is a textbook teaching special relativity with a bit of general relativity too. It is for university students. Yet, I also find it very readable for highschool students who are curious about the theory of special relativity and bored with how popular books write about it.
- G. Polya, Giải một bài toán như thế nào?
- G. Polya, Sáng tạo toán học.
- G. Polya, Toán học và những suy luận có lý.
- Ian Steward, Các khái niệm của toán học hiện đại.
- Sawyer, Đường vào toán học hiện đại.
Mathematical background
Algebra
- Isawoa, Cơ sở của Toán học hiện đại. This is a good introductory text for basic understanding for the logical foundation of mathematics.
- Nguyễn Hữu Việt Hưng, Đại số tuyến tính, NXB ĐHQG Hà Nội. This is a very good textbook for linear algebra. It is somewhat difficult for first students to get used to university mathematics. Yet, if one gets over it, one can later get the spirit of university mathematics very well. The later part of the book on multilinear algebra, already touching universal properties. Admitedly, this was rather difficult for me to understand at the first year in the university.
- Hu, S. T., Mordern algebra. Hu’s books are always among my favorite (you find some more from him later.) It should be noted that he worked on homological algebra. It is therefore expectedly that his style is somewhat formal. But it is not dry. His writing is very clear, short and concise. The nice thing is that every proposition or lemma in his book shows very clearly why it is there. The logical structure allows one to see the big picture, and thus to know where one is heading too.
- Hus, S. T., Linear algebra and differential equations
- Adkins, W. and Weintraub, S., Algebra: an approach via module theory This is a beautiful book, somewhat forgotten. Here module theory is put at the central. As a result, algebra is presented in a rather unified way. One can get rather good intuition of the concepts of category theory, such as the notion of exact sequences, split, etc. The last chapter develope representation theory of finite group from module in a rather elementary way. Overall, it is a very good book (although I would like to have a bit more category theory); I actually do not know why the book is not that famous.
Group theory
- Armstrong, M. A., Groups and Symmetry, (Springer), This is a beautiful undergraduate text for group theory. It starts with the basis and goes all through to rather advanced topics. The plus point of it is that it makes me understand classification of crystal by their symmetry. I surely read this many times in physical textbooks, but never really get the exact statement of the classification.
Representation theory
- Serre, J. P, Representation theory of finite groups (Spinger) This is a very readable book for the basic concepts of the representation theory of finite groups (the first three chapters.) I did not manage to read the later chapters as a student, though 🙂
- Etingof, P. and his students, Introduction to Representation theory. (AMS) The book is the lecture note given by Etingof to his students. Etingof is an expert in tensor category theory, and clearly his lecture is developed in a general abstract manner In fact he chooses to use the representatio theory of algebra as a framework. Indeed, this clearly shows the unified feature of representation theory. (I did not understand why he did not use representation of rings, though; I would expect this to allow for the use of module theory as a unified framework.) The last chapters touch the concept of tensor category and homological algebras. The book is really good, very concise. It is however probably not the best for the first read of the topic (I read it when being a bit familiar with the basic concepts.)
- Hall, B. C., Lie groups, Lie algebras and representations: an elementary introduction (Springer). The book does excellently what it promises: an elementary introduction to the topic. It emphasizes on matrix groups as a way to understand the representation theory of Lie algebras and Lie groups. In that way, the theory is very intuitive and concrete. The back side is of course one may find lacking a bit of abstract taste from the differential geometry approach; but this can be complemented very well by another text such as Lee’s books (below).
- Barut, A. O. and Raczka, R. “Theory of group representations and applications,” World Scientific (1986). The interesting part of this book for me is that it develops the representation theory of the Pointcare’ group by means of Mackey’s theory of induced representation. Other textbooks, particularly physics text, used most often the Lie algebra approach. While of course Mackey’s theory is somewhat more complicated at the beginning, I find it necessary to understand some feature of the physics of the representation theory of the Pointcare’ group.
- Kim, Y. S. and Noz, M. E.. Theory and applications of the Poincare group, D. Reidel Publishing Compamy (1986)
Category theory
- Awodey, S., Category theory, Oxford Logic Guides (2010). This book is very concise. Everywhere and there it gives very good intuition to understand the construction in category theory. Although, I would not consider it to be an easy book to read, I would think it is very good additional reference source to be used in conjunction with other text even in first encounter of the topic.
Algebraic geometry
- Watkins, J. J. Topics in commutative ring theory, Princeton University Press (2007) This is a beautiful book for commutative rings. It is very readable for ones who have very little background on abstract algebras.
Functional analysis and operator algebras
- Pedersen, G. K., Analysis now, Springer (1988). This is a very good book. It can serve as a course in advanced analysis too. The good part is that it has the modern style of using abstract notions, and goes very directly into functional spaces. It gives a very good big picture, and does not go too much in the details, which fits me very well.
- Sakai, S., C*-algbras and W*-algebras, Springer; Sakai, S., Operator algebras and dynamical systems. The good part of Sakai’s books is that they used the notion of abstract W*-algebra instead of concerete operator algebras of a Hilbert space (I think this was discovered by Sakai, in fact.)
- Ringrose, J. R. and Kadison, R, Fundamentals of the theory of operator algebras I, II, III (AMS) This is somewhat standard references of the field. Three volumes are however too thick for me. They are good as references in parts, but sometimes a bit tedious, I find. From time to time I get lost, but this can be only because of my little background in operator algebras.
- Connes, A.,Noncommutative geometry (1993). This is a big and thick book. It contains many topics in operator algebras with orientation for noncommutative geometry. Topics are well motivated, and logically developed. It does not contain proofs, if you are interested in those (me not much). But it shows the logical picture very well. Overall, it is good to have it as a reference. It can be hard to read as a first book on the topic, unless one really has a very good background.
Axiomatic geometry
Topology
- Amstrong,Basic topology, Springer.
Differential geometry
- M J Lee
Physics
Classical mechanics of particles
- Landau
- Goldstein, H., “Classical Mechanics”
Classical mechanics of fields
- Jackson, “Classical electrodynamics”
- Scheck, F., “Classical field theory”
- Baez, J. and Munian, J. P., “Gauge fields, Knots and Gravity”
Quantum mechanics of particles
- Sakurai, J. J., Modern quantum mechanics.
- Balentine, J. J.,
- Schiffs
Quantum mechanics of fields
Traditional textbooks of quantum field theory often start with quantum field theory in flat spacetime and quantum field theory in curved space time is often thought of as a trickery advanced subject. I tend to think in the other way around. I would prefer to start the subject with the quantum field theory in curved spacetime, probably not in its full techincal details, but at least in its general settings. It is then easy to see that while the relativistic description of fields tends to merge time with space, the quantum description really comes about when one is able to separate time from space (Fulling 1989). One also sees that quantum field theory does not requires symmetries as built-in properties, rather, as useful assumptions based on the `principle of maximal simplicity’. As a matter of fact, it becomes clear that the concept of particle is deeply related to the symmetry of spacetime, that is, Wigner’s classification of elementary particles based on spacetime symmetry is set on a new basis. The best elementary textbook that expresses this point of view is that of Fulling:
- Stephen A. Fulling, “Apects of quantum field theory in curved spacetime”, Cambridge University Press (Cambridge, 1989)
- Mukhanov and Winitzki, “Introduction to quantum effects in gravity”, Cambridge University Press (Cambridge, 2007)
- J. J. Sakurai, “Advanced quantum mechanics”, Cambridge University Press (Cambridge, 2007)
However, the mathematical arguments in the book can obscure some physical intuition of beginer. It is best supplied with a more calculational text, of which the best one around seems to be Mukanov and Winitzki: One then can easilly goes with more traditional texts, of which I prefer Sakurai’s: This book is not as old as it sounds. I think the basic ideas of pratical QED remains like that until now. The only drawback of the text is that it uses imaginery time coordinates to express spacetime symmetry, which does not meet more modern standards of differential geometry (using lower and upper indices, or no indices). Other than that, the ideas are clear, pedagogical and calculations are detailed when needed. This would serve very well as a basis to emback on more modern topics such as QCD and supersymmetry.
- Florian Scheck, “Quantenfeldtheorie”, Springer
- Michele, M., “A modern introduction to quantum field theory”, Oxford University Press (2006)
Foundation of quantum mechanics
- Schumacher
General relativity and quantum gravity: theory of spacetime
- Semiriemann geometry
- Weinberg
- Fleshbach
- Leonard Susskind and James Lindesay, “An introduction to black holes, information and the string theory evolution”, World Scientific (2006)
- Mann
- Roveli
Statistical mechanics and thermodynamics*
- Pipard
- Bazarov
- Kerson Huang
- Landau
- Lubensky
- Reich
- Kardan
- Godenfeld
Condensed matter physics
- Altland and Simon
Quantum information and quantum computation
- Nilsen Chuang
- Mermin
- Witten Notes
Other (more specialised) topics
Probability, stochastic processes and information theory
Mesoscopic physics
Quantun phase transitions
- Chajrabarti, B. K., Dutta, A. and Sen, P., Quantum Ising phases and transitions in transverse Ising models, Springer 1996.
Topological insulators
Condensation and superconductivity
- Annett, J. F.,
Conformal field theory
- Blumenhagen, R. and Pauschinn, E., Introduction to conformal field theory, Springer (2009)
- Musardo
Supersymmetry
- Aitchison, I., Supersymmetry in particle physics: an elementary introduction, Cambridge (2007)