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Book Recommendations For Maths To Astrophysics?
Posted by
kdawson
on Sun Jul 13, 2008 04:20 AM
from the take-a-left-at-newton dept.
from the take-a-left-at-newton dept.
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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News: Ivy League Computer Science Curricula Exposed 312 comments
Doug Treadwell writes "Many people have wondered what the difference is between the Computer Science education given in the average public university versus one given in an Ivy League university (or a top level public university). There have also been discussions here on Slashdot about whether any Computer Science curriculum gives students the knowledge they need for the working world. As a computer science student both questions are very important to me, so I decided to answer them for myself and build a website to share what I found. I was able to find the required reading for hundreds of courses at Stanford, Princeton, Carnegie Mellon, and Berkeley; along with some other institutions. This should also help answer some of those 'What should I read?' questions."
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Pop-Sci but well worth it... (Score:5, Interesting)
I can heartily recommend "The road to reality" by Roger Penrose, there'll be a lot of stuff that's old-news to a math major, but it's essentially an undergraduate course in mathematical-physics for the lay-reader (of course this normally means scientist from another discipline :-)
Best of luck!
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Re:Pop-Sci but well worth it... (Score:5, Informative)
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.
Parent
Re:Pop-Sci but well worth it... (Score:5, Interesting)
Quantum mechanics: R. Shankar, "Principals of Quantum Mechanics" (the first few chapters should give you a basic foundation of the theory).
In my undergrad, a physics professor told me, "There's no particularly good book on QM". I thought he was being pedantic, but years later I found out he was actually correct. Every book has some serious deficiency (serious if that's the only book you learned it from). I've read only the first few chapters of Shankar, and they're quite decent - I liked them. I tried reading some of the stuff later in the book and didn't feel he did justice to them (either too brief on the topic or hand-waving). Another problem with Shankar is that it doesn't really challenge the reader.
I can't exactly recommend a QM book, as I learned it from my professor's lecture notes - which were awesome. But from memory, he consulted a bunch when he wrote them. They included the books by Messiah, Davydov, Landau & Lifshitz, Baym.
At the undergrad level (in case you did not learn it during your BSc), two common books are the ones by Griffith and Liboff. Again, both have weaknesses but they do complement one another well.
Electricity and Magnetism: D. Griffiths, "Introduction to Electrodynamics"
Best undergrad book on the topic ever. Well worth reading for its insights even if you think you know E&M very well.
In the US, at the grad level the standard is the book by Jackson. I hear in some countries they sometimes use that in the final year of undergrad. It's a standard and a must if your program requires you to know EM.
In general, people speak very highly of the series by Landau & Lifshitz. Might want to keep them as references and read them at some point.
Parent
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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
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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
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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 Penr
Potential jobs, Space Pirate? (Score:4, Funny)
Feynman Lectures (Score:5, Informative)
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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 [amazon.co.uk]. There are audio copies [amazon.co.uk] 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
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came here to say the exact same thing. :( )
(yes, i am a physicist... just not have completed my studies yet
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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 a
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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..."
Re: Landau (Score:3, Informative)
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 b
Intro Astrophysics (Score:3, Informative)
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Thirded. A lot of people are recommending pop-physics books which are fine for an odd read, but are useless for actually gaining an in-depth knowledge of physics. Carroll and Ostlie is the standard catch-all general reference textbook all the Astrophysics lecturers at my (English) University tend to recommend. I find it very good as a reference text for odd topics I have little knowledge of, but it shouldn't assume too much prior knowledge you don't have - the maths is the important thing to have covered se
Try the classics (Score:2)
The Tao of Physics [amazon.com]
The Dancing Wu Li Masters [amazon.com]
To get you thinking the right way, then, for a new classic, try:
The Road to Reality [amazon.com]
For some seriously heavy slogging.
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Guh. I know I'll engender flamage but I found these two books to be little more than dreck. It's been a long while since I read them but at my recollection, there was essentially zero useful science in them. It was a lot of "oh, isn't that coincidence MEANINGFUL...?"
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Tao taught me that where there was nothing (literally no thing), there could suddenly be a few particles which would almost instantaneously annihilate themselves, to leave "no thing" behind. The notion of the quantum
Roger Penrose - The road to reality (Score:2)
http://books.slashdot.org/article.pl?sid=05/05/09/2145236 [slashdot.org]
Coincidentally, I started reading it last night, so a review will have to wait weeks/months(/years?)
Physics for Dummies? (Score:2, Funny)
For the classical mechanics side of things.... (Score:3, Informative)
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.
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I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold
Seconded, but make sure you have another textbook in mechanics handy for the inevitability that you get confused by Arnold's presentation. Goldstein is probably a good choice.
Oh Boy, Math to Astro-Physics? (Score:5, Funny)
Get a Financial Life [amazon.com]
Dating For Dummies [amazon.com]
Paint the Sky with Stars: The Best of Enya [amazon.com]
Getting Things Done: The Art of Stress-Free Productivity [amazon.com]
the classic Feynman (Score:3, Informative)
Recommended topics (Score:4, Informative)
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.
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Always Best To Go To The Source ... (Score:5, Informative)
From an Astrophysicist (Score:5, Informative)
Physics to a degree [amazon.co.uk] 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 [amazon.co.uk] 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.
3rd Time (Score:2)
"What I tell you three times is true." I'm saying it once but two others already have.
Feynman's "Lectures" + "Tips"
If you want an expert's opinion, ask the chancellor of John Moore's University in Liverpool. He's an astrophysicist, as well as a member of the Luxuriant Flowing Hair Club For Scientists, which counts for naught save as an indicator of a sense of humor and thus probably approachability. And he's a bit of a musician so I hear. He has a web site with a contact link: http://brianmay.com/main.html# [brianmay.com]
Read textbooks, work problems (Score:3, Informative)
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.
Anthony French's books (easy to understand) (Score:2, Informative)
Newtonian Mechanics [amazon.com]
Vibrations and Waves [amazon.com]
Special Relativity [amazon.com]
Galactic Astronomy (Score:2)
General intro to physics books (Score:4, Informative)
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.
Landau & Lifshitz (Score:2, Informative)
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.
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Another book worth mentioning is Sakurai's "Modern Quantum Mechanics".
Start with Newton (Score:2)
a good maths text book (Score:2)
obligatory xkcd comic (Score:3, Funny)
There's one for every Slashdot discussion !
http://www.xkcd.com/435/ [xkcd.com]
One of the best (Score:4, Informative)
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.
Best Textbooks (Score:5, Informative)
Classical Mechanics:
Kleppner and Kolenkow [amazon.com]
If you have time: Goldstein [amazon.com]
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 [amazon.com]
Griffiths [amazon.com]
Jackson [amazon.com] and Schwinger [amazon.com]
Statistical Mechanics and Thermodynamics:
There are really no agreed upon texts here (sorry), I used Baierlein [amazon.com] 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 [amazon.com] and Karadar 2 [amazon.com]
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 [amazon.com]
Linear Algebra: Griffiths [amazon.com] - Best Book in this list in my opinion.
Special Relativity and General Relativity:
Special: French [amazon.com]
General: Carroll [amazon.com]
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.
Astronomy and theoretical physics (Score:4, Informative)
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 [netlib.org] 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.
Texts from a PhD Student (Score:5, Informative)
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!
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One in fact wonders how large a percentage of buyers of Neil Strauss' The Game [amazon.com] were math or physics majors. Male academics working in other fields are usually so surrounded by women, due to the high proportion of female to males in universities nowadays, that there's not much challenge.
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Try that: http://en.wikipedia.org/wiki/Bioship [wikipedia.org] 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.
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...so don't worry about it! I've had complete IDIOT friends go to what are considered top UK universities (not top-5, like Oxford or Cambridge, more like top-10) and breeze through the programs without actually learning anything.
So, you don't really need to learn any Astrophysics to get your degree, I mean they already accepted you without any background, right?
Yes, it looks like obvious trolling so mod away, but I don't have the time to analyze for those who don't know how the UK higher education system works (hint: $$)...
Not so much as political targets to have 50% of young people attend university. They can't make people more intelligent, so instead university has to be easier.
I don't know how much easier it gets as you go from a top-5 to a top-10, top-20 university (mostly because I go to a top-5 university and rarely discuss work with students who don't go to a similar place).
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Wish I had mod points here. Goldstein, Sakurai, and Griffiths are the books the questioner missed while taking a math degree instead of a physics degree. Throw in Carrol & Ostlie for the astrophysics side of things, and he's covered.
However, I disagree about the "skimming" part. The only way any of these things will be useful is if you actually work through some of the problems. Do a few random problems from each chapter and they'll make a whole heck of a lot more sense.