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The Principles of Quantum Mechanics
"The standard work in the fundamental principles of quantum mechanics, indispensable both to the advanced student and to the mature research worker, who will always find it a fresh source of knowledge and stimulation." --Nature "This is the classic text on quantum mechanics. No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas
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First published January 1, 1958
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About the author
Paul A.M. Dirac
21 books145 followersPaul Adrien Maurice Dirac was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. He was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.
Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
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Displaying 1 - 25 of 25 reviews
January 10, 2009
I read Principles shortly after graduating from college. I hadn't attended any of the courses on quantum mechanics, but a friend told me that if I read this book I'd understand what I'd missed. Good advice!
Dirac's intuition is amazing. He messes around with the equations, doesn't obviously seem to be going anywhere, and then suddenly arrives at a conclusion about the real physical world. The piece de resistance comes at the end, where he deduces the existence of the positron more or less from first principles; they were indeed observed experimentally a few years later. He did this work when he was in his mid 20s, and received the Nobel Prize for it when he was only 31.
Lee Smolin, in The Trouble with Physics, bemoans the fact that it's now almost impossible for young scientists to get funding to pursue speculative ideas of their own. They usually have to work with other people's ideas until they are in their late 30s at least, by which time it's often too late. When you look at Dirac's great book, you appreciate just how wrong that is.
Dirac's intuition is amazing. He messes around with the equations, doesn't obviously seem to be going anywhere, and then suddenly arrives at a conclusion about the real physical world. The piece de resistance comes at the end, where he deduces the existence of the positron more or less from first principles; they were indeed observed experimentally a few years later. He did this work when he was in his mid 20s, and received the Nobel Prize for it when he was only 31.
Lee Smolin, in The Trouble with Physics, bemoans the fact that it's now almost impossible for young scientists to get funding to pursue speculative ideas of their own. They usually have to work with other people's ideas until they are in their late 30s at least, by which time it's often too late. When you look at Dirac's great book, you appreciate just how wrong that is.
October 16, 2015
قراءة اى شىء علمى مترجم مزعج جدااا!
عشان كده سيبت نسختى المترجمة وجيبت النسخة الأصلية من الكتاب ^^
الكتاب علمى اضاف ليا معلومات ليست بالقليلة وفادنى انى درست بالفعل كوانتم 1 و2
ومن اسمه هو بيعرض مبادئ او اساسيات وغير كافى كاى كتاب اخر لعلم ميكانيكا الكم
عشان كده سيبت نسختى المترجمة وجيبت النسخة الأصلية من الكتاب ^^
الكتاب علمى اضاف ليا معلومات ليست بالقليلة وفادنى انى درست بالفعل كوانتم 1 و2
ومن اسمه هو بيعرض مبادئ او اساسيات وغير كافى كاى كتاب اخر لعلم ميكانيكا الكم
June 25, 2020
كتاب رائع
August 29, 2017
Paul A M Dirac, the man, the myth, the legend, discusses Quantum Mechanics and its results from the first principles. Starting with the idea of a state, Dirac goes on to mention Eigenvalues and Eigenvectors and Eigenstates, continuing the discussion with some very advanced mathematics. This treatise builds on itself, deriving solutions from previous examples and ideas. The book is even a good length. My only real complaint is that the edition of this I found is from 1930 and I thought the paper would be damaged by my touching it. However, it seems that this notion of mine was unfounded, the thing I really needed to worry about was the binding.
In any case, this book was quite well done. My impasse came about at around a quarter of the way through the book, when it became necessary to have differential equations and Linear Algebra under your belt. I would like to find a book that explains this sort of thing in a manner that I can understand. Perhaps I shall reach out for that sort of thing.
In any case, this book was quite well done. My impasse came about at around a quarter of the way through the book, when it became necessary to have differential equations and Linear Algebra under your belt. I would like to find a book that explains this sort of thing in a manner that I can understand. Perhaps I shall reach out for that sort of thing.
July 9, 2012
Dirac was one of the most original thinkers of the last century and you really get a sense of that in this book. Probably one of the most abstract presentations of the subject, but to my mind at least, the most insightful.
Want to read
October 18, 2025Rovelli in his book Helgoland says that this book of Dirac is still the best book on Quantum Mechanics.
May 24, 2022
P.A.M. Dirac’s The Principles of Quantum Mechanics merits study as an historical document which was influential in the early development of the field. For perhaps one could say that Dirac’s contribution is to realize that quantum physics could admit of a sweeping derivation from first principles on a par with what has already been done for its predecessor theory, the classical mechanics of Lagrange, Laplace, Hamilton and Jacobi. Thus, his perspective is entirely different from that of, say, Arnold Sommerfeld or Max Born, who are eager to show how the novel ideas explain phenomena on the atomic level and plunge into the details without attending so much to the formal development of the underlying concepts. Dirac’s strong point is to formulate these in express mathematical terms. Nevertheless, as he remarks in the preface,
All the same mathematics is only a tool and one should learn to hold the physical ideas in one’s mind without reference to the mathematical form. [p. viii]
Dirac systematically follows a symbolic method of presentation, i.e. denotes a vector in Hilbert space with a letter instead of writing out a concrete function. In order to motivate his formal construction of Hilbert space, he presumes the photon concept and discusses how photons behave when passing through a beam splitter or through a polarizer. From this empirical basis he proceeds inductively to the principle of linear superposition and the probabilistic interpretation. At this point, one may ask what really justifies the principle of superposition? On the statistical interpretation, the logical point is that there is more than one possibility for how to prepare the system [p. 12]. For, as Dirac remarks in excluding Schrödinger’s view and in making Born’s more precise,
What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place….each photon then interferes only with itself. Interference between two different photons never occurs. [p. 9]
The whole of the first two chapters [pp. 14-45 ] is almost exclusively mathematical (linear algebra in function spaces), no physics at all. To be sure though, a theoretical physicist’s view of mathematics. For instance, Dirac equates the dual with scalar product [p. 19]! In other words, he silently presupposes the Riesz representation theorem. But linear functionals makes sense in Banach spaces, not just in Hilbert space: which raises the question as to what fundamentally a linear functional is and what role they play in physics? Thus, what Dirac does in the present work is to be viewed as sufficient for his purposes of producing an heuristic framework in which perform calculations, but not strictly speaking an exacting construction of a mathematical model of quantum physics (such as Kant provides with respect to Newtonian physics in the Metaphysische Anfangsgründe der Naturwissenschaft).
A signal feature of Dirac’s alternative approach to quantum physics is his discovery of the connection between the classical Poisson bracket and the quantum commutator. For this is what justifies the introduction of q-numbers on analogy with c-numbers in a way that renders comprehensible, if not visualizable, the passage from classical to quantum. Heisenberg and Schrödinger, in contrast, portray their versions of quantum mechanics as self-standing edifices which go over into the classical limit according to the correspondence principle, thereby presuming atomic physics itself to be uninterpretable in classical terms. Yet, one may wonder whether Dirac is too optimistic. For, at the time of writing, neither van Hove’s nor Haag’s theorem was known. The former radically circumscribes the scope of what Dirac wants to do, in that it excludes the possibility of assigning a q-number to every c-number in a consistent way (sc., such that Poisson brackets of c-numbers pass over to commutators of the corresponding q-numbers). The crux here is the qualifier every. As Dirac shows, at least for the commonest pairs of conjugate variables, such as position and momentum, the desired correspondence exists, just that it cannot be extended into a Lie algebra homomorphism. As for the latter, Haag’s theorem shows that in systems comprising infinitely many degrees of freedom, there is no canonical way in which to represent the Poisson bracket but that, instead, there may exist inequivalent representations (reflecting different boundary conditions). Another question begged by Dirac’s procedure is to ask what is the fundamental meaning of the Poisson bracket in classical mechanics? Formally, it corresponds to the operation of passing from a function in phase space to its Hamiltonian vector field, taking the Lie bracket and then passing back to Hamiltonian generator of the vector field so obtained; thus, it invokes two concepts: Lie bracket of vector fields, and the correspondence in symplectic geometry between phase space functions and their Hamiltonian vector fields – the latter being a natural concept, if one view phase space functions as themselves generators of canonical transformations. Then, isn’t the significance of the Poisson bracket/commutator analogy not the canonical commutation relations for conjugate variables per se but that it assigns an interpretable meaning to the commutator of two operators? One wishes our author, Dirac had troubled himself to spell out at greater length his understanding of these things – which perhaps he regards as obvious. For the relevant issues become non-trivial when considering constrained systems, a subject to which Dirac himself made major original contributions [see his Lectures on Quantum Mechanics]. None of all this in the present work, however! A nice feature of Dirac’s standpoint, not usually encountered, is his demonstration that < q(t) | q(0) > = exp iS = quantum analogue of action function to which it tends in the limit as Planck’s constant goes to zero [pp. 127-128].
As an indication of the peculiarity of Dirac’s approach, he doesn’t get down to any applications until chapter six [p. 136ff]! Characteristically, he introduces spin angular momentum in the abstract without reference to any experiment or Pauli-type reasoning [p. 143]. The derivation of harmonic oscillator stationary states [pp. 136-139] and properties of angular momentum [pp. 144-146] will appear familiar but slightly non-standard. In pp. 159-165, a streamlined proof of selection rules (Dirac obviously became an expert at manipulating the relevant operators). In pp. 185-188, a smooth explanation of collision problems to set the groundwork for scattering theory. This illustrates the mature stage of development of the theory; one can see here the reason for the popularity of this textbook among the succeeding generation of physicists.
The latter chapters (ten through twelve) take up the problem of treating the radiation field as a dynamical entity in itself – what is normally avoided in introductory expositions of quantum mechanics, but a topic on which Dirac, along with Jordan, happens to be an original contributor. Thus, we get a nice derivation of Kramers’ dispersion formula from a coupled atom + quantized radiation field [p. 248]. P. 255ff rehearses reasoning leading to the Dirac equation: one sees how his operatorial q-number point of view facilitated the discovery (he already knew about Pauli matrices and guessed his form rather than proceed from a classification of spinor representations as does Wigner – and as we would go these days – the other way around but see pp. 260-261 where Dirac gives a physical interpretation showing the transformed field represents the same thing). Then pp. 263-267 interpret the Dirac equation to yield electron spin, maybe Itzykson-Zuber would be easier to follow? The same goes for pp. 269-272 on fine structure.
Chapter 12 covers quantum electrodynamics in second quantization with constraints to eliminate the longitudinal mode. Observe how Dirac is applying a formalism already worked out, which he understands well, not inventing it for the first time. Seemingly there is no general procedure, one merely lucks out that the interaction term is simple enough to respect Lorentz symmetry in canonical constrained quantization. Lastly, he punts on calculating the Lamb shift and the anomalous magnetic moment of the electron (pp. 310-312; he will do so in his lectures on quantum field theory, published elsewhere). Nonetheless, in the last paragraph on p. 311 Dirac does declare his stance re. renormalization: the Schrödinger picture is unsuited to quantum electrodynamics as unphysical vacuum fluctuations play such a dominant role there (which can be ignored in the Heisenberg picture). Therefore, physicists who invoke renormalization are guilty of a blatant faux pas in working blindly with formulae known to be inconsistent in themselves and in justifying the procedure solely on pragmatic grounds. Dirac feels himself bound to higher intellectual standards as a mathematical physicist!
Conclusion: Dirac definitely does not think after the pattern of Planck, Einstein, Bohr, Sommerfeld, Schwarzschild, Heisenberg, Schrödinger, Born et al. His pseudo-justifications are not what motivated the former authors to erect the theory of quantum mechanics in the first place, but evidently more retrospective than prospective in character. John von Neumann’s very different formalization appears to respect more the thought processes of the founders (see our immediately preceding review here). How shall we characterize the present work, then? Dirac represents a passage from fundamental theorizing to building machinery with which to flesh out calculations, i.e. from Kuhnian revolutionary science to the ensuing normal phase which however necessary seems like something of a loss to one romantically inclined. Yet, the perception of Dirac among the generation of physicists to follow was quite positive, for, free of the baggage carried along by the other founders, he shows them how facilely to grasp the terms of the new theory and thereby enables them to forward their own investigations, which were eventually to be met with stunning successes and thus to fulfill the promise of the quantum revolution.
All the same mathematics is only a tool and one should learn to hold the physical ideas in one’s mind without reference to the mathematical form. [p. viii]
Dirac systematically follows a symbolic method of presentation, i.e. denotes a vector in Hilbert space with a letter instead of writing out a concrete function. In order to motivate his formal construction of Hilbert space, he presumes the photon concept and discusses how photons behave when passing through a beam splitter or through a polarizer. From this empirical basis he proceeds inductively to the principle of linear superposition and the probabilistic interpretation. At this point, one may ask what really justifies the principle of superposition? On the statistical interpretation, the logical point is that there is more than one possibility for how to prepare the system [p. 12]. For, as Dirac remarks in excluding Schrödinger’s view and in making Born’s more precise,
What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place….each photon then interferes only with itself. Interference between two different photons never occurs. [p. 9]
The whole of the first two chapters [pp. 14-45 ] is almost exclusively mathematical (linear algebra in function spaces), no physics at all. To be sure though, a theoretical physicist’s view of mathematics. For instance, Dirac equates the dual with scalar product [p. 19]! In other words, he silently presupposes the Riesz representation theorem. But linear functionals makes sense in Banach spaces, not just in Hilbert space: which raises the question as to what fundamentally a linear functional is and what role they play in physics? Thus, what Dirac does in the present work is to be viewed as sufficient for his purposes of producing an heuristic framework in which perform calculations, but not strictly speaking an exacting construction of a mathematical model of quantum physics (such as Kant provides with respect to Newtonian physics in the Metaphysische Anfangsgründe der Naturwissenschaft).
A signal feature of Dirac’s alternative approach to quantum physics is his discovery of the connection between the classical Poisson bracket and the quantum commutator. For this is what justifies the introduction of q-numbers on analogy with c-numbers in a way that renders comprehensible, if not visualizable, the passage from classical to quantum. Heisenberg and Schrödinger, in contrast, portray their versions of quantum mechanics as self-standing edifices which go over into the classical limit according to the correspondence principle, thereby presuming atomic physics itself to be uninterpretable in classical terms. Yet, one may wonder whether Dirac is too optimistic. For, at the time of writing, neither van Hove’s nor Haag’s theorem was known. The former radically circumscribes the scope of what Dirac wants to do, in that it excludes the possibility of assigning a q-number to every c-number in a consistent way (sc., such that Poisson brackets of c-numbers pass over to commutators of the corresponding q-numbers). The crux here is the qualifier every. As Dirac shows, at least for the commonest pairs of conjugate variables, such as position and momentum, the desired correspondence exists, just that it cannot be extended into a Lie algebra homomorphism. As for the latter, Haag’s theorem shows that in systems comprising infinitely many degrees of freedom, there is no canonical way in which to represent the Poisson bracket but that, instead, there may exist inequivalent representations (reflecting different boundary conditions). Another question begged by Dirac’s procedure is to ask what is the fundamental meaning of the Poisson bracket in classical mechanics? Formally, it corresponds to the operation of passing from a function in phase space to its Hamiltonian vector field, taking the Lie bracket and then passing back to Hamiltonian generator of the vector field so obtained; thus, it invokes two concepts: Lie bracket of vector fields, and the correspondence in symplectic geometry between phase space functions and their Hamiltonian vector fields – the latter being a natural concept, if one view phase space functions as themselves generators of canonical transformations. Then, isn’t the significance of the Poisson bracket/commutator analogy not the canonical commutation relations for conjugate variables per se but that it assigns an interpretable meaning to the commutator of two operators? One wishes our author, Dirac had troubled himself to spell out at greater length his understanding of these things – which perhaps he regards as obvious. For the relevant issues become non-trivial when considering constrained systems, a subject to which Dirac himself made major original contributions [see his Lectures on Quantum Mechanics]. None of all this in the present work, however! A nice feature of Dirac’s standpoint, not usually encountered, is his demonstration that < q(t) | q(0) > = exp iS = quantum analogue of action function to which it tends in the limit as Planck’s constant goes to zero [pp. 127-128].
As an indication of the peculiarity of Dirac’s approach, he doesn’t get down to any applications until chapter six [p. 136ff]! Characteristically, he introduces spin angular momentum in the abstract without reference to any experiment or Pauli-type reasoning [p. 143]. The derivation of harmonic oscillator stationary states [pp. 136-139] and properties of angular momentum [pp. 144-146] will appear familiar but slightly non-standard. In pp. 159-165, a streamlined proof of selection rules (Dirac obviously became an expert at manipulating the relevant operators). In pp. 185-188, a smooth explanation of collision problems to set the groundwork for scattering theory. This illustrates the mature stage of development of the theory; one can see here the reason for the popularity of this textbook among the succeeding generation of physicists.
The latter chapters (ten through twelve) take up the problem of treating the radiation field as a dynamical entity in itself – what is normally avoided in introductory expositions of quantum mechanics, but a topic on which Dirac, along with Jordan, happens to be an original contributor. Thus, we get a nice derivation of Kramers’ dispersion formula from a coupled atom + quantized radiation field [p. 248]. P. 255ff rehearses reasoning leading to the Dirac equation: one sees how his operatorial q-number point of view facilitated the discovery (he already knew about Pauli matrices and guessed his form rather than proceed from a classification of spinor representations as does Wigner – and as we would go these days – the other way around but see pp. 260-261 where Dirac gives a physical interpretation showing the transformed field represents the same thing). Then pp. 263-267 interpret the Dirac equation to yield electron spin, maybe Itzykson-Zuber would be easier to follow? The same goes for pp. 269-272 on fine structure.
Chapter 12 covers quantum electrodynamics in second quantization with constraints to eliminate the longitudinal mode. Observe how Dirac is applying a formalism already worked out, which he understands well, not inventing it for the first time. Seemingly there is no general procedure, one merely lucks out that the interaction term is simple enough to respect Lorentz symmetry in canonical constrained quantization. Lastly, he punts on calculating the Lamb shift and the anomalous magnetic moment of the electron (pp. 310-312; he will do so in his lectures on quantum field theory, published elsewhere). Nonetheless, in the last paragraph on p. 311 Dirac does declare his stance re. renormalization: the Schrödinger picture is unsuited to quantum electrodynamics as unphysical vacuum fluctuations play such a dominant role there (which can be ignored in the Heisenberg picture). Therefore, physicists who invoke renormalization are guilty of a blatant faux pas in working blindly with formulae known to be inconsistent in themselves and in justifying the procedure solely on pragmatic grounds. Dirac feels himself bound to higher intellectual standards as a mathematical physicist!
Conclusion: Dirac definitely does not think after the pattern of Planck, Einstein, Bohr, Sommerfeld, Schwarzschild, Heisenberg, Schrödinger, Born et al. His pseudo-justifications are not what motivated the former authors to erect the theory of quantum mechanics in the first place, but evidently more retrospective than prospective in character. John von Neumann’s very different formalization appears to respect more the thought processes of the founders (see our immediately preceding review here). How shall we characterize the present work, then? Dirac represents a passage from fundamental theorizing to building machinery with which to flesh out calculations, i.e. from Kuhnian revolutionary science to the ensuing normal phase which however necessary seems like something of a loss to one romantically inclined. Yet, the perception of Dirac among the generation of physicists to follow was quite positive, for, free of the baggage carried along by the other founders, he shows them how facilely to grasp the terms of the new theory and thereby enables them to forward their own investigations, which were eventually to be met with stunning successes and thus to fulfill the promise of the quantum revolution.
June 11, 2019
A brilliant introductory treatise of the subject with amazing mathematical and physical insight, rigor and clarity.
Paul Adrien Maurice Dirac is well known not only as one of the founders of Quantum Theory, but also as one of the most clear when it came to his writing and it shows.
This is the ideal textbook for undergraduate freshmen in their first quantum mechanics course and can very well be used for their entire undergraduate quantum mechanics curriculum.
Paul Adrien Maurice Dirac is well known not only as one of the founders of Quantum Theory, but also as one of the most clear when it came to his writing and it shows.
This is the ideal textbook for undergraduate freshmen in their first quantum mechanics course and can very well be used for their entire undergraduate quantum mechanics curriculum.
March 8, 2010
Quantum mechanics from the mouth of one of the founders. Everything about his approach I found odd, yet novel. Recommended as a supplement, not a primary text.
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May 18, 2010Diracs formulation of Quantum Mechanics.
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January 6, 2008Dirac's view of Quantum Mechanics, very concise and to the point. Not a lot of giberish.
March 21, 2021
I recently read the wonderful biography of Dirac "The Strangest Man" by Graham Farmelo, so decided I would read Dirac's classic Quantum Mechanics book. This is not an easy book - there is not a single figure or diagram anywhere in it, and it is intensely mathematical. Nevertheless, it is very logically put together and gives a good picture of Dirac's well-organized thinking on a subject that he helped to invent and led to his Nobel Prize.
November 23, 2018
A very good book. The best I've read on quantum mechanics. A lot of plain explanation of what is happening behind the formulas. Recommend to improve understanding of physical principals behind quantum physics monstrous mathematics!
March 26, 2019
الكتاب حلو لو كان بالانجليزي فقط النسخة العربية سيئة نوعا ما، مع تقديري للمترجمين وجهودهم.
بالنسبة للنسخة الانجليرية تستاهل ٥ نجوم وكيف يتقيم اقل والكتاب حرفيا من اهم العلماء في هذا الجزء من العلوم يستاهل القراءة لاي شخص يهتم بفهم عالم الكم.
بالنسبة للنسخة الانجليرية تستاهل ٥ نجوم وكيف يتقيم اقل والكتاب حرفيا من اهم العلماء في هذا الجزء من العلوم يستاهل القراءة لاي شخص يهتم بفهم عالم الكم.
December 16, 2021
A fascinating read about our future, and AI's, with their Incredible Methods of Operation, Binary State BITS, How & and Why it Operates and too it's Master's Bidding and SOP. Leaving nothing safe, I mean Really Safe in our Digital Lives where "No Case" of/for Any Security.
May 23, 2018
¿Que clase de biblia es esta?
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August 12, 2021just read parts of , this is great textbook but it's all mathematics
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February 4, 2021An essential primer on QM
April 8, 2012
Beautiful science. Elegant and perfect mathematical physics, in a lovely binding and typeface from OUP.
Not a popular work. (You do need to know your physics and your mathematics!)
Belongs on shelves with G H Hardy's mathematics texts and Chandrasekhar's physics work.
Not a popular work. (You do need to know your physics and your mathematics!)
Belongs on shelves with G H Hardy's mathematics texts and Chandrasekhar's physics work.
November 30, 2021
This book changed the face of Physics for good.
"God is dead and Dirac is his prophet", W. Pauli.
P. A. Dirac was a genius of the highest caliber, and a very gentle and down to earth man, known for not talking a lot. We have lots to learn from him. Thank you professor Dirac...
"God is dead and Dirac is his prophet", W. Pauli.
P. A. Dirac was a genius of the highest caliber, and a very gentle and down to earth man, known for not talking a lot. We have lots to learn from him. Thank you professor Dirac...
December 30, 2013
One of the best book ever written about QA
December 27, 2014
superb, thanks paul!
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December 26, 2016The English background most people have in science makes it difficult to catch up with the information.
Displaying 1 - 25 of 25 reviews