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Book Recommendations For Maths To Astrophysics?
sexy_flying_yoda writes "I have just graduated from 3 years doing a BSc in Mathematics in the UK and will be beginning an MSc in Astrophysics and Astronomy in September. I have very limited knowledge in physics, and as my new course of study is basically physics, I'm currently searching for books that will enable me to get up to speed. What books would you recommend that would help a mathematics graduate convert to a physicist?"
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Try "The Feynman Lectures on Physics", Vol.s I - III. I've never encountered a better reasonably high-level introduction to the topic, and they're eminently readable. Here's a site devoted to them.
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I'm not sure about recommending the intro physics book I had, but as far as intro astrophysics, there's no better than Carroll and Ostlie
I second this. As far as a general intro to Physics these are by far the best set you can get. Here's the amazon link. There are audio copies of the lectures as well.
One caveat, many Physics & Astrophysics/Astronomy Departments are separated & have little overlap so take a careful look at your MSc course curriculum before leaping to the conclusion that you need to learn large amounts of general physics.
CJM
I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold for the classical mechanics side of things. I am not sure what to read for general relativity. The bit that I know I learned from "Semi-Riemannian Geometry" by Barret O'neil, but I don't feel that the book is a good place to learn general relativity unless you already have a very strong background in differential geometry. I hope this helps.
the Feynman lectures on physics.
Most astronomy degrees are basically physics degrees with the addition of astronomy classes and without the 400 level physics courses. If you wish to prepare yourself for astrophysics I recommend the following topics:
1) Classical Electrodynamics (you need to know Maxwell's equations backwards and forwards--this usually takes a year at the undergraduate junior physics level). You need to be able to solve line integrals and surface integrals without blinking an eye.
2) Mathematical physics. Unless you have an applied math degree or focus, your math education isn't going to be a great help here. Courses in this area would include complex analysis, partial differential equations (that's graduate level physics baby!), and a shitload of knowledge knowing how to work with Fourier transforms, Laplace transforms, and series solutions to ordinary and partial differential equations. Your BSc in mathematics should cover up the other odds and ends (a little group theory, eigenvectors, eigenfunctions, Hilbert spaces, etc.)
3) Mechanics at the junior level. You need to know mainly how Hamiltonians and Lagrangian operators work. This is not the same thing as introductory mechanics or a statics and dynamics class. The important things you care are about energy functions, potential functions, and conserved quantities.
4) Quantum mechanics. You will probably get a lot of help at the graduate level here as most schools don't expect astronomy majors to have a lot of knowledge in this topic. Just make sure you know what the postulates of quantum mechanics are and some of the basic concepts (like state vectors, the Schrödinger equation, and Dirac notation). If possible, learn how the Hamiltonian and Lagrangian operators work in quantum mechanics.
The minimum of all of this that you should learn is the mathematical physics and classical electrodynamics portions. This entire list assumes that you have the 'basic' physics prerequisites for these courses as well.
I've audited several of MIT's OpenCourseWare offerings in Physics. Some are ridiculously easy while others have thrashed my intellectual behind back and forth across the Internet. And the best part? They're free. http://ocw.mit.edu/OcwWeb/Physics/ [mit.edu]
No mod points, no meta-moderating/Firehose/all the other free work Slashdot wants me to do.
Physics to a degree will get you thinking like a physicist - it covers most undergraduate topics in physics with tutorial style questions and answers.
I found Introduction to Modern Astrophysics an interesting read after I graduated. It covered most of the stuff we did at Birmingham and did so very well.
Our introductory book was Introductory Astronomy and Astrophysics by Michael Zeilik, which was ok, and then Astrophysics: Stars Vol 1 by Richard Bowers and Terry Deeming, which was very good and Vol 2 similarly.
You don't mention what your course is going to cover or what its aim is - you are not going to cover the whole of astrophysics in 9 taught months. You also don't mention your interest in astrophysics - numerical simulation? So it is difficult to come up with any more specific recommendations.
Good luck anyhow. Post below with more info if you want any more detailed recommendations.
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You're going to be getting into grad-level physics books, like Goldstein (Mechanics), Jackson (Electrodynamics), and Sakurai (QM). They are not really the best places to start your physics education. As you have a math background, the math will not be so much of a problem. Rather, you lack familiarity with physics concepts. What you need is the equivalent of an undergraduate physics education. You can probably skim the Feynman Lectures for the rest of the summer and come out OK. Work through physics problems. Lots of them.
Popsci books are good too, for getting the big picture.
Newtonian Mechanics
Vibrations and Waves
Special Relativity
You might find "Quantum Mechanics for Mathematicians" useful. It's quite sophisticated, but if you've got a solid grasp of partial differential equations, you should be okay. Link: http://arxiv.org/abs/math-ph/0505059v1
I second the recommendation of Feynman's Lectures. They're a good overview, although I think you'll find that they're not sufficient to get you to a point where you can solve problems.
MIT's OpenCourseWare has many physics courses online, most including sample tests and exams. This will be useful to practice your skills.
Try that: http://en.wikipedia.org/wiki/Bioship I mean someone has to program the bio-organism main nerves center to calculate FTL jump properly right?
ok, joke aside, this is the list of book I built and that we give to new recruits around here.
Please discuss. I'd love to know what other people would add to that list.
To the original question I would answer: Did you ask your future teachers? They teach physics for a living they should be able to tell you what background you need to understand their courses. They should know what book they use in class better than the hippies like me who troll slashdot instead of working.
Otherwise why don't you go look at the MIT opencourseware and see how the curriculum are organized. (http://ocw.mit.edu/).
The suggestions from other posters about science books for the general public won't help you much. You need to learn the basic physics, such as mechanics, thermodynamics and electromagnetism. Thankfully there are good books that teach all of these areas at a basic level, and you'll be able to go through them quickly.
Although in a different way, I also changed from math to physics. One thing you should know is that physicists use math as a tool, and don't worry about convergences, approximations, etc. Prepare to be shocked with all the approximations made: Physicists keep expanding stuff in Taylor series and keeping only 1 or 2 terms, without worrying about what they left out, treat differentials basically as numbers, use distribution functions intuitively, without a proper theoretical support, say a differential equation is "solved" when they find one solution that matches what they need, etc.
I would recommend the introductory physics books by Paul A. Tipler, because they cover the whole physics you need to get up to speed, and are simple.
Another similar book is "Fundamentals of Physics" by Halliday and Resnick.
These two books / books series are simple, written for the beggining physics undergrad. I think they are what you need. However, if you are very good at math, and want grad student level physics books, the series "Course of Theoretical Physics" by Landau and Lifshitz is suberb. They are very advanced though.
After you master the books at the level of Tipler and/or Halliday and Resnick, you should move on to individual books about the various areas, such as mechanics, electromagnetism and thermodynamics.
"The Feynman lectures on physics" are a classic, and almost required reading for wanting to be a physicist, however they won't teach you much actual day to day physics. It was written to be a physics course, but to me it is more of an inspirational book than a manual, so you can always read these latter.
I wanted to recommend Feynman's lectures also, but it seems many others have done so already. Also Penrose's "Road to Reality", already mentioned.
What people haven't mentioned are Landau & Lifshitz's series of books, "Course on Theoretical Physics". This is stuff to read AFTER you have got through Feynman, and find his lectures too elementary. Landau is more demanding, but it will be a LONG while before you can finish reading his works.
Disagree. Sure there is some rehashing of material that mathematicians will be familiar with, but unless said mathematicians are familiar with applications in physics, the book will cover plenty of new material for them. Take complex analysis : the initial chapter on complex analysis will be a rehash, but later chapters on its applications in QM, QFT, GR will NOT be a rehash.
That it is very broad is a good thing: it looks like the reader WANTS an overview. For further detail, good use can be made of Penrose's excellent bibliography.
I've got a maths background, and found much of the maths in this book new: much of it is idiosyncratic to physics. The holes I had in my knowledge of physics I was able to fill in via Penrose's bibliography.
I'll finally say that "Dancing Wu Li", "Tao of Physics", etc, are all pop physics that are easy to get through, but useless to learn anything. The danger with these books is that you can walk away with a completely wrong understanding of what they're on about, and you wouldn't be able to tell. They are simply too vague and "new agey", too many slippery concepts that can't be taught properly without mathematics, and dangerous without the appropriate background.
I've got a degree in physics, and the two most important physics books there are, baring quantum mechanics, are:
Classical Mechanics - Goldstein
Classical Electrodynamics - Jackson
If you want something a little easier, I would recommend their 'little brothers' of sorts:
An Introduction To Mechanics - Kleppner and Kolenkow
Electricity and Magnetism - Purcell
The Feynman lectures are good, and are pretty good at getting you to think about the physics, but are aimed at first year undergrads. I've just completed a BA in maths and I find them interesting, but a little easy.
I'd suggest just googling for course notes for the relevant topics. I'm assuming your vector calculus is already good. Other than that you need to know:
Basic QM
Probably some fluid dynamics
Special and general relativity
Statistical physics / thermodynamics
Some programming experience might also help, Fortran is still in quite common use in physics and is easy to learn.
If you really do want to buy dead trees, I recommend:
Quantum Mechanics by Alastair IM Rae (IOP publishing)
Gravity by James Hartle (Addison-Wesley)
Any of the Landau & Lifshitz books (Butterworth-Heinemann)
They should cover the relevant physics whilst not insulting your intelligence.
One of the best, and most consistently relied upon, physics texts is Fundamentals of Physics, by Halliday and Resnick. The link leads to the 2007 edition - prior editions are still available for lower cost.
I used this book in high school, and then had the opportunity to use it again during several courses in college. The text is now in its 8th edition, and has been regularly updated and improved. Depending on where most of your colleagues went to school, its likely some or many have been exposed to H&R.
H&R does not spoon-feed; some of the exercises are difficult. Working through the text is assuredly not going to be a random walk in the park.
A number of the other comment threads discuss Feynman's lectures, which are also excellent.
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As a physicist I should tell you that the Feyman Lectures on Physics are not really en vogue anymore. The style is often very nice and entertaining and they contain a few brilliant chapters. But they severely lack mathematics: hence inappropriate for a mathematician. They also lack a structure that allows you open the book at a random topic and teach yourself about just that.
I would recommend you to get a general Physics book like the Tipler,Mosca "Physics for Scientists and Engineers" which you can probably buy as a used book for cheap. Just so you have something to read before going to bed and get a general Idea about a myriad of physics topics.
And then you really want to learn analytical mechanics. Maybe the Landau, Lifshitz "Course of theoretical physics: Mechanics" isn't so bad... it might be a bit of an overkill, but the other ones that I like have not been translated yet.
After that it really depends what you want to specialize in:
If your goal is very mathematical like relativistic magneto-hydrodynamics you would need very different books from something like spectral lines or kinectic gases.
For a solid mathematical background (and a price that won't force your bank account to violate the second law of thermodynamics), try Fundamentals of Physics by Halliday, Resnick, and Walker. Excellent mathematical descriptions, but short on the kind of insight you can find in Feynman's work. A used, earlier edition costs very little and would be good reference for a person with a degree in mathematics.
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Having gone through a physics undergrad, an astrophysics-slanted grad and currently teaching undergrad physics, I am always on the lookout for good texts. Here are my suggestions...
Firstly, if you have never taken undergrad physics or are looking for a reference, you will want a good intro text. Feynman is good for conceptual understanding but is a bit short on worked examples and problems for you to try. There are several good intro texts out there, my personal favorite is Physics for Scientists and Engineers by Serway & Jewett. Used copies of older editions are the way to go price-wise.
As for advanced undergrad texts, here are my suggestions.
Introduction to Electrodynamics by Griffiths (a real standard)
An introduction to Thermal Physics by Schroeder (has astrophysics examples)
Principles of Quantum Mechanics by Shankar
Classical Dynamics of Particles & Systems by Marion & Thornton (Classical Mechanics)
Gravity: An introduction to Einstein's General Relativity by Hartle
I think the important thing to realize in your situation is that whatever you _need_ to know to do your masters your classes and your professor will point you to the right books. As such, what you really need to do is go back and fill all the wholes that were left from a non-physics undergraduate degree. Most of these textbooks that I will list are the standard for MIT, and Harvard and the like. So let's begin.
Classical Mechanics:
Kleppner and Kolenkow
If you have time: Goldstein
Electricity and Magnetism:
This one is a little tricky, I'll give you the 1st undergrad, the Junior level undergrad and then the two Grad texts. You can probably just read the Junior level text.
Purcell
Griffiths
Jackson and Schwinger
Statistical Mechanics and Thermodynamics:
There are really no agreed upon texts here (sorry), I used Baierlein at MIT but that seems to switch every year.
Same goes for graduate texts, BUT the MIT profesor who has been teaching grad stat mech just put out his own books which I hear are quite good. We'll call them Kardar 1 and Karadar 2
Quantum Physics:
What you really need is an introduction to two fundamental ideas, the wave-function formalism and the linear-algebra formalism.
Wave-function: French and Taylor
Linear Algebra: Griffiths - Best Book in this list in my opinion.
Special Relativity and General Relativity:
Special: French
General: Carroll
That should fill in everything that you missed. What we are skipping is every other specialty in physics, but, it seems like you've already chosen one, so no big loss.
As an aspiring astronomer your profile will strongly resemble that of a theoretical physicist. And you'll certainly need to know about just about everything he lists on that page: from classical mechanics, optics, special and general relativity, quantum mechanics, statistical mechanics, thermodynamics, plasma physics, plain old electromagnetism, to electronics. 't Hooft lists freely downloadable high-quality reading material on just about every topic!
And although you didn't ask, don't forget the computational side of things! Most astronomers I know are heavy computer users and very good programmers.
So make sure you know about Fortran and the libraries that are written in it (e.g. have a look at http://www.netlib.org/liblist.html and acquaint yourself with Lapack, Sparsepack, fftpack, cephes etc). Many of those routines can also be found in Matlab, Octave, Scilab, etc., but if you need full control and a standalone executable on a big supermini you might have to go back to Fortran and C++), And make sure (well ... I hardly need tell a mathematics undergraduate but I can't omit it) that you know about Maple and/or Mathematica.
But ... if I may be so bold ... whilst reading and self-study are an indispensable element of learning physics they are rarely sufficient. You'll also need to learn a special way of thinking that sometimes comes hard to people with a background in mathematics. Which is to know when and where to cut corners and use approximations, and sometimes even go beyond the mathematics you know.
Think of Paul Dirac (of the Dirac Delta function). His "function" isn't a function at all, it's a distribution, and trying to think of it as a function will lead you to contradictions. But Dirac set up a formalism using it (and got the properties right !) without knowing about distributions (they were invented later partly to put what he had done on a firm mathematical basis). He simply let mathematical firmness go hang at the appropriate moment. Now I'm not comparing you to Dirac (and I'm certainly not encouraging you to take liberties with mathematics), but Dirac was a physicist first and a mathematician second. That's what I mean. Someone suggested the Feynman Lectures ... they're great (if sometimes a tough read) exactly because Feynman makes this very point.
You see ... in Physics, the physics comes first and the mathematics second; meaning that in thinking about physics problems you'll have to think in terms of physics (of course greatly helped by the mathematical formalisms in which physical laws are couched) but if you'll need to be able to think through a physical line argument without necessarily working through all the maths. Physicists do this as a second nature, and you'll need to learn how.
I'll second the Landau Mechanics book which is very concise and goes right into lagrangian formalism which takes other books hundreds of pages. CAUTION: there are a *lot* of crappy copies of this book. Try your best to get one of the original hard covers, I think it was first printed around 1961.
I would strongly suggest getting the basics under your belt first - mechanics and E&M before going onto quantum mechanics. As far QM, I think Morrisons Understanding Quantum Phyics A User Guide is by far the best intro/mid-level QM book and will get you through many of the trickier points. In E&M I've heard a few good things about Franklins Classical Electromagnetism but haven't used it myself. Once you are all past that you may need some nuclear under your belt - the two tomes by Feshbach and Shalit are classics and still relevant though Wong is probably the way to go for a quick spin.
I imagine that if he's going into astrophysics, he's probably already familiar with the typical pop-sci material or at least the content.
No, you will need more technical know-how and fundamentals if you wish to compete in a graduate level program. Here's a list of textbooks that would cover the basics at a bachelor's level. I imagine all of these would be at your University library, and are certainly available on amazon. And IAAP.
Quantum mechanics: R. Shankar, "Principals of Quantum Mechanics" (the first few chapters should give you a basic foundation of the theory).
Electricity and Magnetism: D. Griffiths, "Introduction to Electrodynamics"
Thermo/statmech: C. Kittel & H. Kroemer, "Thermal Physics"
Particle Physics: D. Griffiths, "Introduction to Elementary Particles" (this covers a little bit of quantum field theory too)
Statistics: G. Cowan, "Statistical Data Analysis" (as a mathematics major, you might already know the content, but the formalism as used in physics is important to learn).
Classical Mechanics: S. Thornton & J. Marion, "Classical Dynamics of Particles and Systems".
Different people mean different things when they say "astrophysics", but if you're doing this with heavy emphasis on Astronomy, then you would be better off focusing more on the classical mechanics and statmech than on quantum mechanics and particle physics.
The vast majority of the recommendations here are top notch. A lot of which book to use really is personal preference and background. Here are my personal choices after having been in 3 separate Physics departments. Also, you should consider looking at ANY of the Landau-Lifshitz texts. These Soviet scientists wrote comprehensive texts that might be right up your alley as someone with a math background. I only wish I could understand them more, their physics is really beautiful.
First off, a general reference book. I recommend the Halliday and Resnick series. Buy this used. It is basically an encyclopedia of physics that is presented at the intro undergraduate level. I use it frequently when working through problems outside my specific area of expertise.
Electricity and Magnetism: Three books. Griffiths, Purcell, and Jackson. The first is a classic undergrad text, the second is a more advanced undergrad text, and the last is the standard graduate text in E&M.
Quantum Mechanics: Griffiths' undergrad text is a must, though it is not very mathematically rigorous. I recommend Shankar as a supplement- Shankar is used as both a grad and undergrad text. I'm an experimentalist who stopped learning formal quantum mechanics after 1 year of graduate study, so Shankar may not be enough for you depending on your interests. Check out other's recommendations. Griffiths and Shankar are very good intro and reference books.
Statistical Mechanics- I used Kittel and Kroemer as an undergrad, and it's OK, a little dated. Huang was my grad text, and it is also OK. I don't have strong feelings here. Landau and Lifshitz may be better for you
Classical Mechanics- Marion and Thorton was my undergrad text. Personally, I don't think the CM text really matters. They are all equally bad. The basics they teach you are what a Langrangian is, and unfortunately always underemphasized what a Hamiltonian is (used REPEATEDLY in QM).
Finally, make sure to get a good Mathematical Methods book, even if you really understand math well (I am sure you do). I recommend Arfken as a reference tome, and the Schaum's outline as a handy desktop reference for solving various partial differential equations. Past that, you should be able to pick up texts cheap used from fellow students, or on eBay. Good luck!
Yup, it is. The only bachelor degrees Cambridge award are BAs, and the degree certificate doesn't even state the subject or class, that's all in some other document called a results transcript.
Anywhere else would have done the sensible thing and changed the title of all the science degrees, but here the attitude seems to be "well no one's complained too much in the last 800 years..."
In my undergrad, a physics professor told me, "There's no particularly good book on QM".
I've heard the same thing, and used to think so too, but one book I discovered which I really like is Modern Quantum Mechanics by Sakurai. It is a modern, and reasonably complete treatment which I like.
I second the vote for Jackson's Classical Electrodynamics. I used it in my last undergrad year, and it is very good. In order to do the problems, you really need a solid background in solving PDEs, but with a math undergrad degree, you've likely already had a course in that subject.
For Classical Mechanics the book I used as an undergrad was Goldstein. Many of the problems are tedious and difficult, but there is a wealth of useful information in the text.
I also second the recommendation of Kittel & Kroemer for an introduction to Stat. Mech. The problems are all very doable making this a great book for self study. That might not be so true of Jackson or Goldstein, but others have already recommended some less difficult texts.
Also, if you're going into astrophysics, you'll need some background on relativity. For special relativity, Taylor & Wheeler is a good introduction, and Schutz is a good intro. to general relativity.
If I can be modded down for being a troll, can I be modded up for being an orc, or a balrog?
Oh, I forgot - I wanted to comment on the rest of those books and add a couple.
Re: Griffiths books - they are both really good as intros to these topics (both are amongst my favorite "pleasure" reading physics books), but in the field they are often considered too elementary to be "serious," for better or worse. It's not that they are wrong, just that they are a little too user-friendly, which to me is a good thing.
If you can manage to wade through the extreme density that is that Shankar book, that should rectify things for QM - I have to say, though, I did not particularly enjoy that book, which surprised me since I adored his "Basic Training in Mathematics" book (likely too basic for a math major, I'd guess) and found him to be a fascinating lecturer (I never took one of his classes, but I occasionally slipped in and watched while between other classes). I think it's just too difficult to be so brutally thorough and remain interesting throughout an entire tome like that.
Jackson's E+M book is really the gold standard for classical E+M, though I'd really recommend hitting the literature if you're into stuff like self-action and all that.
Actually, I just noticed that the Griffith's recommendation was for his particles book, not QM, so scratch my QM comments - though if you find Shankar's book too weighty, pick up Griffith's QM book as a start, like most of his books it's very digestible (should take just a couple days to get through). If you find Griffith's particles book too light, which you hopefully will after a couple reads, you'll want some real field theory. The "standard" here is the Peskin/Schroeder book. That can be a little tough if you don't already know something about it; as a slightly more basic step in that direction, check out Zee's Quantum Field Theory in a Nutshell, which I was very pleasantly surprised with.
You'd also be remiss not to pick up something that Feynman has written on field theory, as I don't know that anyone else has understood it in as straightforward a manner as he has - there's always his various QED papers, which you MUST read all of, but as an astrophysicist, your thoughts will likely turn to gravity, in which case the often overlooked Feynman Lectures on Gravitation are definitely worth your time. Take the later chapters with a grain of salt, as some of the claims about stars are wrong; that said, his approach is quite interesting, and his approach to the Einstein equations is freaking amazing (he starts with a "bare" spin-2 theory, figures out how it's "wrong," and "fixes it up" until it "works," and lo and behold, Einstein's equations pop out of nowhere; those quotation marks hide all of the hard work required to get there, of course!).
Er, and also, I kind of hate to dump another 1000+ page monster of a book on your list, but as an astrophysicist you probably ought to read Misner/Thorne/Wheeler's Gravitation. It's great, though I can't promise it's just a few days work. The Wheeler stuff at the end is too speculative and flowery for my tastes, but the rest is pretty useful, and it's definitely worth keeping in your bookcase to intimidate anyone that might enter!
Robert Wald also has a great General Relativity book that might be less threatening; IMO, you should definitely own Wald and MTW. I'd suggest you avoid anything written by either Einstein or Dirac on the subject like the f***ing plague.
Also, check out http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html for Joh
I would go for an older edition (e.g. the 4th edition) of H&R's Physics, rather than the watered down Fundamentals of Physics.
I would recommend any of the books by A. P. French in the MIT Physics series. These are all beautifully done and very readable.
Also, the Berkeley Physics series is good.
And the Feynman Lectures are essential.