Mathematics is the part of physics where experiments are cheap." By clicking Post Your Answer, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct. A more rigorous counterpart to this material is the first hundred pages of Michors Natural Operations in Differential Geometry, this treatment is highly mathematical and very rigorous. MathJax reference. Update: It's very sad to hear Michael Spivak has passed away last year, thanks you ho-boon-suan for letting us know. Even better, a version of the book is available online at Paul Goldbart's webpage. Is there a grammatical term to describe this usage of "may be"? The cover of Spivaks Differential Geometry, Volume 1, second edition, has two yellow drawings of a pig. Arnold, Mathematical Methods of Classical Mechanics. Answers containing only a reference to a book or paper will be removed! In 1964 Spivak received a Ph.D. from Princeton University under the supervision of John Milnor. Learn more about Stack Overflow the company, and our products. It's nice because he clearly explains the difference between vectors and co-vectors ("up" and "down" indices) and relates it all to real life (ie. How does the number of CMB photons vary with time? http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322, tug.org/TUGboat/tb42-3/tb132beeton-spivak.html, CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows, "Methods of Theoretical Physics for Mathematicians". Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Complete your collection of children's books and save! Capture a web page as it appears now for use as a trusted citation in the future. Publication date of the book of Michael Spivak - Physics for Mathematicians II? So while we'll probably never get a second book, it can be positively assured that the same book that gave you, and others, joy has been made more accessible for future students. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics (based on Shankar's first online course, Fundamentals of Physics I) Shankar. For clarity, I've tried including the definitions and lemma that I believe may be relevant in regards to the result Spivak states. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. : Minimize is returning unevaluated for a simple positive integer domain problem. Some subjects off the top of my head that probably need covering: The last book I read on "background in math for physicists" was "Mathematics for Physics" by Stone and Goldbart, and I enjoyed it quite a bit. Try again. Springer, Texts and monographs in physics, 2nd edition, 2nd printing, (2002). $$\big\{ \big(A(b_1),\ldots ,A(b_K)\big) : A \text{ is an orientation preserving isometry of }\mathbb{R}^3\big\}.$$, Lemma: we have that $\langle v_i(0) - v_j(0), b_i - b_j\rangle = 0$, Proof: Follows by differentiating $(1)$ and evaluating at zero. How much of the power drawn by a chip turns into heat? It only takes a minute to sign up. Unable to add item to Wish List. Change of equilibrium constant with respect to temperature. This volume gives an overview over the main mathematical techniques used in quantum physics, in a way that you cannot find anywhere else. There are 0 reviews and 0 ratings from Australia, Your recently viewed items and featured recommendations. Why is it "Gaudeamus igitur, *iuvenes dum* sumus!" The premises of the book are great: to analyse, besides the advanced mathematical tools avaiable to theoretical Physics (tangent and cotangent bundles, sympletic geometry, etc), the common concepts of elementary Physics with minute details. What are the concerns with residents building lean-to's up against city fortifications? Munkres is indeed a great technical writer IMO. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. I'd suggest it as a nice first reading about groups it if weren't for its length. Can I also say: 'ich tut mir leid' instead of 'es tut mir leid'? In July 2022, did China have more nuclear weapons than Domino's Pizza locations? I believe that some portions really could be used for that. which is an excellent introduction to curved manifolds. What is Spivak trying to do in "Physics for Mathematicians"? The book should interest not only mathematicians, contrary to Spivak's opinion, but theoretical physicists as well, who want to have a well presented and connected account of the mathematical foundations of Mechanics. Is it possible for rockets to exist in a world that is only in the early stages of developing jet aircraft? }|>#c}J}g1&V~Cw}LkrNF63/Wwi+"SMr{>as1 |3250"UzPV^?E.DATUHDI/P@KTR'S6~>J 33"M0ixIm 6$^KUR$!xArH&JISypWTF{^t9q8Xzuq*Im+=pYfR^WkUej[DT1Hp. Publisher It is this last Theorem that Spivak states without proof, and I'm confused on two grounds: In what sense are the functions $\phi_{ij}$ linear? Although there was an amusing comment thread on Math Overflow by a mathematician whose dad (who is/was also a mathematician) could never get into topology because Munkres's book put him off. Bishop's Tensor Analysis on Manifolds is a great introduction to the subject, and published by Dover, is very cheap (less than $10 on amazon). Thanks for contributing an answer to Physics Stack Exchange! Lacks the systematic theorem based approach of the two books above, but boasts great explanations and nice pictures. Reviewed in the United States on 7 May 2011. It is full of comments and explanations that a mathematician needs and are usually not in the physics books. I have not read his book but he was mathematically precise and rigorous, and physically astute, went to the physical issue, and wrote well (maybe a little concise, but that's the math). The following is from the fifth Chapter Rigid Bodies of Spivak's Physics for Mathematicians. , Hardcover Uploaded by . asked for physics from the. How to deal with "online" status competition at work? Spivak's most recent book, Physics for Mathematicians: Mechanics I, which contains the material that these lectures stemmed from and more, was published on December 6, 2010. Spivak: Physics for Mathematicians: Mechanics I, $90.00, 1302 Waugh Drive PMB 377 Houston, TX, 77019, US. There's an amazon preview here: You mention, in specific, GenRel. The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. The main difference between mathematicians and physicists is that the former define their terms, and the latter do not. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. To learn more, see our tips on writing great answers. *If the above URL doesn't work; try this one: http://goldbart.gatech.edu/PG_MS_MfP.htm *. WebI took a class on C* algebras and was told they gave a useful formulation of quantum mechanics and even that many of the questions people originally considered were only motivated by quantum mechanics. $$m=\big( A(b_1), \ldots ,A(b_K)\big)\in \mathcal{M}_b$$ Or else the original papers by Einstein and Hilbert. What one-octave set of notes is most comfortable for an SATB choir to sing in unison/octaves? If you've always been frustrated by the lack of rigor and cohesion in Physics courses but are interested in the content this is the book for you. Would sending audio fragments over a phone call be considered a form of cryptology? He not only did Sachs and Wolfe but was one of the 3 people who laid out a mathematically coherent and invariant theory of gravitational waves (it's easy when linear, not so in full GR). Web15 You want the book by V.I. Spivak has lectured on elementary physics. Of course, the theorem follows immediately from the preceding discussion in the text (particularly the lemma you quote). I would like to, but I cannot bring myself to do it. Code works in Python IDE but not in QGIS Python editor. In Germany, does an academic position after PhD have an age limit? What happens if a manifested instant gets blinked? In this movie I see a strange cable for terminal connection, what kind of connection is this? How to deal with "online" status competition at work? WebClassical Mechanics 1 Lecture 1. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. I am not pleased with Arnol'd, Marsden, Sternberg, et hoc genus omne. I mean, the mathematicians. And, as usual in Spivak's books, a lot of historical notes illustrate how the subject evolved. Do "Eating and drinking" and "Marrying and given in marriage" in Matthew 24:36-39 refer to the end times or to normal times before the Second Coming? I mean, for example, that I don't understand this lever. Collection. This large book has the same spirit of the author's book A Compreensive Introduction to Differential Geometry. The book by Lee, Introduction to Smooth Manifolds is very good and tackles the subject in a leisurely and motivated manner. I personally don't know of particular books dedicated to the subject covering all areas of physics (maybe " Mathematical Methods for Physics and B. Blackadar, Operator algebras. &:=\langle (\mu v_i+w_i)-(\mu v_j+w_j), b_i-b_j\rangle\\ The best answers are voted up and rise to the top, Not the answer you're looking for? E. Zeidler, Quantum Field theory I Basics in Mathematics and Physics, Springer 2006. http://www.mis.mpg.de/zeidler/qft.html. Only a comment because I have only read about this book sofar: Talagrand, M. (2022). He taught my E&M class when I was a graduate student at Berkeley in the early 1990s. I bought the book "Physics for Mathematicians I" by Michael Spivak (http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322), have worked through quite some chapters and love it. In addition to the above books, for a more complete list of general references on $C^*$-algebras and operator algebras as well as for an easy reading for beginners see my lecture notes on $C^*$-algebras here. Is there any evidence suggesting or refuting that Russian officials knowingly lied that Russia was not going to attack Ukraine? I knew immediately that I would buy this book when I saw that in the first few pages it addresses the "proof" of the law of lever as presented in Mach's "The Science of Mechanics" and also when Cohen and Whitman's new translation of the Principia is a prominent reference. Elegant way to write a system of ODEs with a Matrix, Change of equilibrium constant with respect to temperature. How to say They came, they saw, they conquered in Latin? If so, how would you rate it? Thanks. Archived post. Reviewed in the United States on 18 September 2013. One admirable feature of the book is that the exercises are just that exercises, that is they teach how to comprehend the material. But people are different so one has to try fro himself. I personally don't know of particular books dedicated to the subject covering all areas of physics (maybe "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence isn't quite what you're looking for), but if you happen to come across the subject of Quantum Field Theory then I suggest you have a look at "Quantum Field Theory for Mathematicians" by Ticciati. Webspivak's physics for mathematicians volume i mechanics. However, the Internet Archive has scanned the book and made it freely, publicly accessible. There's also an unusual primer at the end on the measurement theory and technology of gravitational wave detection. Samelson, Notes on Lie Algebras written in a Definition, Theorem, Proof style, so it's little hard to grasp (I recommend mutliple rereading) but gives a good overview of the structure, classification (root systems and Dynkin diagrams) and representations (highest weight theory) of Lie algebras. Why do front gears become harder when the cassette becomes larger but opposite for the rear ones? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Spivak is also the designer of the MathTime Professional 2 fonts which are widely used in academic publishing. This does not include reasons for choosing those books and a short overview about their content and is hence. &=\mu\langle v_i-v_j,b_i-b_j\rangle + \langle w_i-w_j,b_i-b_j\rangle \\ I don't know much about either differential geometry or algebraic topology, but having studied groups a little, I think I can provide some references for Lie groups. Frankel: The Geometry of Physics, An Introduction, Cambridge U.P. @Mathemagician1234: Could you please quote an interesting stuff from "Physics for Mathematicians I" by Michael Spivak to convince me why I must read it? I do have a high opinion of Thirring's series, but I don't know why. Feynman is not what you want either. Academic press, Inc. (1994). Spivak's book, Physics for Mathematicians: Mechanics I (published December 6, 2010), contains the material that these lectures MathJax reference. =%N{#&`[VKsbxc#ma6n s["~:&q5*;?I qH1JlaC *f>/hK*}\EUUkUE!7X4A;>~fvM9 >-v Cg''f^\|@4gvCW~{+D9*?4j *+Z These and similar matters confused me in the way I was taught physics, and it's great to find that a mathematician of Spivak's stature was similarly perplexed and see how he has sought to clear up that perplexity. -- V.I. O. Bratteli, D. W. Robinson, Operator algebras and quantum statistical mechanics 1, $C^*$- and $W^*$-algebras, symmetry groups, decomposition of states. You want the book by V.I. How and from where does a mathematician learn physics from a mathematical stand point? I am a physicist, and his book on mechanics was by far one of the best I have read. Learn more about Stack Overflow the company, and our products. I consult Greiner's volumes quite often, but you had better avoid them. Please try again. Unfortunately, as shown in the link by ho boon saun in the comments, there probably will never be a "Physics for Mathematicians II" by Michael Spivak since he passed away before it got published/fully written - unless someone who personally knew him, and had access to his belongings, could publish his unfinished drafts, which seems unlikely at this point. Is there any evidence suggesting or refuting that Russian officials knowingly lied that Russia was not going to attack Ukraine? This &=\mu\phi_{ij}(v) + \phi_{ij}(w), What does it mean, "Vine strike's still loose"? @Schutz's "Geometrical methods " is what I turned to when Lie derivatives were causing me great headaches. E. Zeidler, Quantum Field theory I Basics in Mathematics and Physics, Springer 2006. http://www.mis.mpg.de/zeidler/qft.html is a book I highly rec Differential Geometry explained as computer algorithms. (Since then I've tended to hit the pure math books, but that's a different story). Spivak coined Spivak pronouns, a set of English gender-neutral pronouns. And, as that one, is pretty uncommon. Learn more. First story of aliens pretending to be humans especially a "human" family (like Coneheads) that is trying to fit in, maybe for a long time? It is the first volume of a sequence, of which not all volumes have been published yet. $$\square$$, Theorem: if we define the linear functions $\phi_{ij}$ on $(\mathbb{R}^3)^K$ by Still, it's amazingly readable, and I never found one single mistake in the entire book. Is there any philosophical theory behind the concept of object in computer science? It may or may not have anything to do with Reality. , ISBN-13 WebWhat is Spivak trying to do in "Physics for Mathematicians"? This particular edition is in a Hardcover format. : Would sending audio fragments over a phone call be considered a form of cryptology? Sad news: Michael Spivak passed away on October 1, 2020 at the age of 80. The theoretical physicist perhaps never took the pains to do that, but the process should work in some way or another for the whole structure to be consistent. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Spivak: Calculus, 4th edition, $110.00, But besides this the book provides an in-depth look at lots of concrete representations (e.g. 1: Classical dynamical systems. Definitely recommended. . An introduction", Theodore Frankel. Sachs is the one known to relativists and cosmologists for the Sachs-Wolfe effect. How to correctly use LazySubsets from Wolfram's Lazy package? : Can I infer that Schrdinger's cat is dead without opening the box, if I wait a thousand years? I would recommend giving them a miss. He says that the configuration space of the point. This book has a very specific audience: those with a pure Mathematics foundation who are interested in Physics. Language. $$\mathcal{M}_b\subseteq \bigcap_{i,j}\ker \phi_{ij}.\tag{2}$$. The post consists of a statement Spivak makes -with no proof- that I do not understand. http://www.amazon.com/Course-Modern-Mathematical-Physics-Differential/dp/0521829607, Distributions (Fourier transforms, Green's functions). Full content visible, double tap to read brief content. on July 10, 2021, There are no reviews yet. How does a government that uses undead labor avoid perverse incentives? Like the author, I'm a mathematician who had difficulties with the way that physics is often presented in a manner that makes it look like mathematics (or at least the Platonic ideal of mathematics), with conclusions deduced from axioms by inexorable logic, but when one examines the arguments more closely there are often all sorts of unstated assumptions that creep in. Vol 1, $60.00 / Vol 2, $50.00 / Vol 3, $50.00 / Vol 4, $55.00 / Vol 5 , $60.00 Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics (based on Shankar's first online course, Fundamentals of Physics II) Bueche and Hecht. The best pedagogical explanation of diff. How is $(2)$ derived? As for the subject, it covers essentially the whole subject of Classical Mechanics, from elementary portions to Lagrange's and Hamilton's equations. You'll need other books obviously but if you are looking for one book for a solid review of the basics, this book is excellent. Humphreys, Introduction to Lie Algebras and Representation Theory less theorem-heavy and more talkative than Samelson and contains huge number of great exercises. I am reading the book by Spivak Elementary Mechanics from a mathematicians view point. Spivak Physics for Mathematicians - Help understanding the derivative of a one-parameter family of linear transformations. Arnold (. It's a course in differential geometry, actually, but one oriented towards physics, with succinct but comprehensive enough developments of physical theories (mechanics, electromagnetism, thermodynamics, Yang-Mills ). There is also O'Neill's book "Semi-Riemannian geometry: With applications to Relativity", though more focused on the mathematics of the subject. opensource. Office Hours: MWF 3:15-4:15, 6125 Etcheverry Hall . If you're into general relativity, you could try General Relativity for Mathematicians, by Sachs and Wu. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Spivak is the author of the five-volume A Comprehensive Introduction to Differential Geometry. Those without rigorous training may find they prefer other resources. The first couple of pages of Lecture 1 of the book summarizes what I intend by physics from a mathematical stand point. Even better, a version of the book is available online at Paul Goldbart's webpage. How can an accidental cat scratch break skin but not damage clothes? It is not just local-patriotism, but because I really think this book series should be very accessible to Mathematicians: Walter Thirring, Michael Spivak is the author of Calculus and the 5 volume work Comprehensive Introduction to Differential Geometry. Hope I'm wrong. Spivak's most recent book, Physics for Mathematicians: Mechanics I, which contains the material that these lectures stemmed from and more, was published on It takes a very rigorous, axiomatic approach to Lagrangian and Hamiltonian mechanics, and it should be accessible to, and enjoyable by, a broad spectrum of mathematicians. It is an old book, but essential if you want to understand Jackson's Classical Electrodynamics or Messiah's Quantum Mechanics. then The same author wrote the best introduction to calculus there has ever been. Extremization of functions on manifolds is developed really well and the authors give insightful information on how to approach the analytical topics presented in the book numerically. I am currently reviewing Classical Mechanics now and want to move on to General Relativity some time later. I am really looking towards the sequel(s) and wonder how far the author, secretive as usual, has gotten with them. Concepts and principles of classical mechanics. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. WebStart by following Michael Spivak. Reviewed in the United States on 27 February 2011. Before answering, please see our policy on resource recommendation questions. Whenever I would tell people that, they would say, Oh good, you're going to explain quantum mechanics, or string theory, or something like that. It's extremely clear and conveys deep understanding on the first reading. Elementary Mechanics from a mathematicians view point, pauli.uni-muenster.de/~munsteg/arnold.html, Jerrold E. Marsden & Tudor S. Ratiu, "Introduction to Mechanics and Symmetry", Springer, 1994, http://www.amazon.com/Quantum-Theory-Mathematical-Surveys-Monographs/dp/0821847058, CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows, Physics.SE remains a site by humans, for humans, Prereqs for The Geometry of Physics by Frankel, Mathematician learning theoretical physics, Book on Representations and Group Theory in Particle Physics for Mathematicians. rev2023.6.2.43474. Anyway, for someone who already understands Mechanics, is a pleasant fountain of knowledge of the Queen of physical Sciences, Classical Mechanics. This book is extremely approachable, requiring only multivariable calculus and linear algebra to completely understand it. The same author wrote the best introduction to calculus there has ever been. Springer, Encyclopaedia of Mathematical Sciences, vol. WebME 170: Engineering Mechanics III . There was an error retrieving your Wish Lists. , Publish or Perish; First Edition (6 December 2010), Language Spivak: A Comprehensive Introduction to Differential Geometry, 3rd edition, Making statements based on opinion; back them up with references or personal experience. I'm not clear on just what his purpose was in writing Semantics of the `:` (colon) function in Bash when used in a pipe? Arnold's book. , ISBN-10 Springer, Lecture notes in mathematics, vol. 2}Wo).hf-.?u?F? Please try your request again later. For mechanics at the next level (or perhaps skipping a level), you could try Jerrold E. Marsden & Tudor S. Ratiu, "Introduction to Mechanics and Symmetry", Springer, 1994. So here are the books I found useful. It depends on what physics domain one wants to work in. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. 'Modern Mathematical Physics' by Peter Szekeres is the best book I've found for the foundations of mathematical physics. geom. In July 2022, did China have more nuclear weapons than Domino's Pizza locations? Learn more about Stack Overflow the company, and our products. This answer contains some additional resources that may be useful. Weberger $$\phi_{ij}(v_1,\ldots ,v_K) = \langle v_i - v_j, b_i - b_j\rangle$$ Can I trust my bikes frame after I was hit by a car if there's no visible cracking? The citations in those publications will also point to towards a lot of good material and there's more goodies if you dig around in the source code. Please try again. Why does bunched up aluminum foil become so extremely hard to compress? My review will be mostly comparing the book to Spivak's lecture notes. A Comprehensive Introduction to Differential Geometry, Vol. It doesn't as far as I recall tie this in to physics in a natural way. He is still around doing math biology. For more details see this review by Ian Sneddon, which also covers Walter Thirring's A course in mathematical physics, vol. WebMichael Spivak Publish or Perish, 2010 - Mechanics - 733 pages 0 Reviews Reviews aren't verified, but Google checks for and removes fake content when it's identified What @TH@i=,iXBd1j Mathematics is a language in which physicist express their ideas. After viewing product detail pages, look here to find an easy way to navigate back to pages you are interested in. Is there a reason beyond protection from potential corruption to restrict a minister's ability to personally relieve and appoint civil servants? Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. English. The following is from the fifth Chapter Rigid Bodies of Spivak's Physics for Mathematicians. For more details see this review by Ian Sneddon, which also covers V.I. Lie groups, Lie algebras and their representation theory. You want the book by V.I. Arnold, Mathematical Methods of Classical Mechanics . It takes a very rigorous, axiomatic approach to Lagrangian and Ham Also he clearly says which parts a rigorous, from a mathematics point of view, and which are not. Scalars, vectors, and tensors. Wasn't my experience - I quite like his topology book, especially as a reference, but it's not a first reader for sure.