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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?"
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!
http://webcast.berkeley.edu/courses.php?semesterid=27
Once you start down the path to astrophysics you'll be swarming in the ladies, and you need to know how to deal with them.
ftw
"Well, with one degree in maths and another in astrophysics, it was either that or back to the dole queue on Monday" DNA
Don't forget; Astrophysics requires a solid grounding in geophysics. any good advanced books in Geology and Geophysics will help you cover the math for Astrophysics, too.
"The mind works quicker than you think!"
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.
licet differant, aequabitur
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
The Tao of Physics
The Dancing Wu Li Masters
To get you thinking the right way, then, for a new classic, try:
The Road to Reality
For some seriously heavy slogging.
No folly is more costly than the folly of intolerant idealism. - Winston Churchill
http://books.slashdot.org/article.pl?sid=05/05/09/2145236
Coincidentally, I started reading it last night, so a review will have to wait weeks/months(/years?)
Physics for Dummies might help u.
hilarious
Three words: "The Feynman Lectures". If you get through all three volumes, you will have a good grounding.....and they're an entertaining read too!!
Ah, an American with an inferiority complex. What a refreshing change. /deadpan
You should cover all of the foundation physics. At least mechanics, electromagnetism, classical radiation, a ground course in modern physics, and heat theory.
Depending on your research topic, also pick up more advanced books in necessary fields. Eg. for cosmology, you'd want to be familiary with relativity and prior work in this area, while for plasma physics a strong knowledge of thermodynamics and radiation is necessary.
Actually, radiation is the thing to know anyway:)
...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: $$)...
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.
In that case, I recommend:
Get a Financial Life
Dating For Dummies
Paint the Sky with Stars: The Best of Enya
Getting Things Done: The Art of Stress-Free Productivity
There is a lot of books, actually too many to mention, in the end it's not about the book it's what you are learning...
I would recommend, that you study some Thermodynamics, quantum mechanics, statistical physics, analytical mechanics, and special relativity, at this point i think you will have a good base in things you will probably need to know later and a starting point to learn General relativity and actually start learning about astrophysics and cosmology.
the Feynman lectures on physics.
Michael Spivak is a mathematician who wrote the very popular math textbook, Calculus on Manifolds, which you've probably used in a class. Apparently he has given some video lectures on elementary mechanics. I haven't watched them, but he's an excellent teacher so they are probably great.
http://www.math.hc.keio.ac.jp/coe/videos/spivak2004/
Letters to a young Mathematician by Ian Stewert? I'm a Biologist working in the Microfab Industry and it really inspired me. Hope you didn't pick the maverick guru as your advisor. But really just read it, it takes about 5 hours.
If you're scared of the subject, maybe you're approaching learning the wrong way?
I understand that you're getting an MS(wtf is an MS"c"? Is that asshole for MS?) But as a Math BSer, Astro/Physics should just be application. (not exactly but hopefully someone gets my Doppler shift.)
I'll shamelessly hijack this post.
What books would you recommend for a molecular biologist who always wanted to study computer science but decided not to and now turns to software engineering?
I know lots of stuff, but lack some of the fundamentals and also applications of computer science and software engineering. I am currently reading those books, which are really helpful:
* The Elements of Computing Systems, Noam Nisan & Shimon Shocken
http://www1.idc.ac.il/tecs/
* Head First: Design Patterns
http://oreilly.com/catalog/9780596007126/
Could anyone recommend other books that "complete" my knowledge? Classics? Stuff about data structures, algorithms, programming theory.
I prefer books written in a fresh, modern style, if possible :-)
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.
Frederick W. Byron, Jr and Robert W Fuller
Mathematics of Classical and Quantum Physics
1992, Dover Books
ISBN 0-486-67164-X
This is a reprint of an original 1969 2 volume set by Addison Wesley, which will probably have a different ISBN.
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.
hi,
you should know that I have nothing more than a high school diploma, but physics was my favorite area of geekery for many years during and after school I had an awesome physics teacher for three years in high school.. actually the best teacher I ever had, so you may be way ahead of me on this stuff, but I have a couple of tips to pass on that helped me to understand some fairly advanced physics stuff. it is very important when you are getting started in physics, that you understand the historical time line of which theories were popular at different times.
I would recommend digging through a couple of those paperback physics overview kind of books. I don't know what the latest popular ones are, but I am talking about the ones that you find at a regular book store in the science section. I have read a bunch of these, they cover nothing in detail but discuss chronologically how each important physicist built on previous works. usually they start with newtonian stuff and work forward to present day.
since you already have a math background, I would say it is more important to go over stuff conceptually in the beginning. The most important book I can recommend, if you haven't already read it, is in search of shrodinger's cat: quantum physics and reality. by John Gribbin
that book will get your mind around the important ideas in quantum physics, making it much easier to apply math to it later.
good luck, --k
Obama is a twitter sock puppet
Fundamentals of Physics (Extended) by Halliday, Resnick, and Walker
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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"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#
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
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
Goldstein/Poole/Safko - Classical Mechanics
Kittel/Kroemer - Thermal Physics
Bransden/Joachain - Physics of Atoms and Molecules
Sakurai - Modern Quantum Mechanics
Have a good summer!
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.
Learning about the basic theories on how galaxies form is going to be underlying a lot of your work if you would like to more than dabble in cosmology. I found this book rather useful.
An Education is the Font of All Liberty
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.
Any self-respecting graduate student should read all of Landau and Lifshitz. There are no errors and the scope is complete. Of course the level far exceeds that of Feynman, but that is because of the audience these books are intended for. Please do not overlook this series.
http://en.wikipedia.org/wiki/Lev_Landau
Good Luck in your studies!
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.
Though nominally it does not assume any mathematical knowledge on the onset, the Road to Reality gives an unadulterated description of modern physics in more mathematical detail than any other book for common consumption. Unlike most physics books, which give a roughly chronological description of physics (teaching the classical Newtonian approximations before the correct modern theories), this book races through teaching math and then shows how general relativity and the standard model plop right out.
The book is quite dense and not for the faint hearted. If I recall, chapter 1 is the introduction, chapter 2 is on non-euclidean geometry, chapter 15 is gauge theory and fibre bundles, and they cover the basics of complex analysis, topology, and 10 billion other things. This is a book that will make you feel stupid. I never did slog my way through the whole thing, but for someone of your background and goals, it seems perfect.
If you want to go over classical mechanics and are a CS type person, may I suggest Structure and Interpretation of Classical Mechanics, from the people who brought you Scheme. It's main strength, in my view, is cleaned up notation (I hate most mathematical notation) and a nice environment to "play" around in, which for a person of your background may not be as useful as it is to me. Still, it's free.
His Philosophiæ Naturalis Principia Mathematica contains his 3 laws of motion, everything follows from there.
one thing i find when talking to mathematicians is that they often have little knowledge of maths for physicists, though they can acquire this knowledge very quickly. for this reason, i'd recommend you have a look at something like "mathematical methods in the physical sciences" by Mary L. Boas. she also covers a great deal of physics from a mathematical perspective.
There's one for every Slashdot discussion !
http://www.xkcd.com/435/
I don't know about the field of astrophysics, but my experience from 4 years of studying physics is clearly to avoid "all in one"-style intro books. They may give you a smoother introduction, and they may keep a persistent style introducing you to many fields, but the quality just isn't the same as specialized books.
Other than that, the best advice is certainly: Talk to professors and other students. The problem is of course that a lot of the decision is about taste, but once you've had a few recommendations, you'll find out what you like, and know what style to go for next time.
I can fully recommend the 10 books of Landau & Lifshitz.
Feynman's are great, but not very mathematical and deep. They are more like a introduction for experimental physics. (So maybe just the right for you)
So I'd buy all three Feynman books and then depending on the topic choose one Landau & Lifshitz. Depending on the topic there I can also recommend other books, for example Jackson with classical electrodynamics.
For deep theoretical understanding you won't get far with Feynman's books.
To get a broad, overview of higher math and its role in physics, as well as to understand major themes of theoretical physics, I would suggest "A Road to Reality" by Sir. Roger Penrose.
It's meant to be a recreational physics book, but doesn't pull any punches when it comes to math in physics. Your math background should be sufficient to know what he is generally talking about when he omits details.
It's a great, thick book!
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
I did a BSc in Physics with Astrophysics, and the astro classes were more maths than even my friends who were doing maths had in their mathiest maths classes.
For our stellar structure course the lecturer used every letter of the alphabet in his equations. Upper and lower case. Latin and Greek. He may even have sneaked in an aleph when we weren't looking (which was often). We used to test ourselves by someone picking a random letter, say 'p' and someone else going 'partial gas pressure!' or whatever it was.
Okay, I suppose the equations were all based on physical properties of fusion plasmas, but with a maths degree you shouldn't have any trouble with the numbers.
Good to see people calling it 'maths' and not 'math' in this thread - I don't think the USA has woken up yet :)
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.
If the Government becomes a lawbreaker, it breeds contempt for law;
Having graduated in astrophysics - i'll recommend the Feynman Lectures. They don't treat astrophysics specificly - but they'll get you into the physicists way of thinking.
Do NOT use the Feynman lectures as a starting point. They are fun to read and will give you a lot of insight if you already know what he is talking about, but I don't know anyone who learned intro physics for the first time from them. I tried it myself in the 11th/12th grade, and didn't get very far. I would suggest you try books that are somewhere between upper level undergrad and beginning grad level. The main obstacle undergrads face while reading this books is not having the requisite math background; but this should not be a problem for you. So for class mech, use Goldstein. For QM, Sakurai's Modern QM. For EM, use Griffiths, I don't think you should jump into Jackson just yet. For thermo, Schroeder. Supplement all of these with Boas' Mathematical Methods, if there is any math you need to review or learn. After you've skimmed through Goldstein, you might also wanna try Hartle's Gravity, this will probably be the most useful for astrophysics.
I used this text for a physics class of the same name during my undergraduate studies in geophysics. I think it would be an excellent bridge, since you're coming from a mathematics background. Some of the criticisms of the book (not being complete, mathematically, in its treatments) wouldn't be relevant.
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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
You should have totally mastered:
classical: Landau vol. I (amazingly beautiful and concise)
E&M: Griffiths
quantum: Griffiths
stat mech: Reif
And have moved on to learning:
E&M: Jackson
quantum: Sakurai supplemented with Schiff
stat mech: Landau vol. V (check the footnote on Jacobian methods).
Work lots of problems!
A lot of people seem to be recommending the Feynmann lectures, but I'd recommend that you use those to supplement other reading rather than as your main text.
If you want to get up to speed quickly, try University Physics by Young and Freedman. It's a well written general physics textbook, contains plenty of exercises and diagrams (important!) and should get you up to a basic 2nd-year (UK) physics undergrad level.
After that, look towards the Manchester physics series. Electromagnetism (Grant and Phillips), Statistical Physics (Mandl) and Optics (Smith and Thomson) are all pretty good, and cover the bulk of classical physics. (University Physics covers dynamics well enough by itself.)
For quantum mechanics, I found the early chapters of Molecular Quantum Mechanics (Atkins) instructive. There are a few good relativity textbooks out there, but I can't remember the names of any...
For astrophysics textbooks, Introductory Astronomy and Astrophysics (Zeilik and Gregory) covers the basics. For high energy astrophysics, Longair is the most comprehensive textbook I've found. For galactic astrophysics I read Combes et al., which I found quite average.
Good luck!
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.
Actually, as an English clever person with a doctorate and everything (I has a smarts, I do), I've found myself using just 'Math' recently as it seems to make more sense. Certainly in tutorial material.
It just sounds better really, not least because the word it's shortened form of isn't 'Mathsematics'. I may be committing an Englishness sin by doing this, but since I never studied Mathematics as a single subject, I may be able to plead insanity.
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
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.
Your Professor?
A quick check on your universities web site should also furnish a list of your prof's group, (Phds and post-docs). Track them down. What you don't really need at this stage is a full physics degree. That is why they chose a mathematician, right? So find out the specifics of your project, and read around that.
Also, it shows the people who count that you're interested.....
Introduction to Quantum Mechanics, 2nd Ed. is good clear guide to first and second year material.
Tough material, great book. Remember that Einstein had the physical theory first and then looked to mathematicians to help him put it into formal equations. One can't help but feel closer to "God" (whatever that may be) after learning about GR and seeing the implications as truths in our telescopes. Good luck to you!
Intel transfer the difficult from Hadware to software, for get more power, programmer need more technology. -- chinaitn
A good statistical mechanics book, I can't think of one off the top of my head, but I've used serveral, there doesn't seem to be much of a shortage of good stat-mech books.
Since you are going into astro I'd suspect it would be good to either/or/both read a GR or fluid mechanics book. I'd go with the fluid mechanics because it shares a lot of the math with both GR and EM, (Poisson and Laplace equations, Fourier methods, conservation laws etc). It is also nice to see classical physics in a non-block sliding down a ramp frame of reference :)
For a very lightweight text that goes surprisingly deep into the physics theory, I suggest this book: "Astrophysics With a PC - An Introduction to Computational Astrophysics". It's intended for amateur astronomers with an interest in astrophysics, source code in Basic is printed along with the text.
Take a look at the table of contents in the link I gave and see what you think, it costs only $19.95, which is a very low cost for a book these days.
We haven't, but we are tossing and turning uneasily, restlessly sensing all you Brits writing maths "whilst" we try to sleep.
Done a PhD on theoretical astrophysics myself.
Now, the trouble with astrophysics is that you find (and must understand) every area of physics included in there. You will need thermodynamics, nuclear and particle physics for star formation; gravitation and fluid dynamics for galaxies; relativity and quantum physics for cosmology; electrodynamics and optics for interstellar fields; and so on.
The Feynmann lectures are an excellent entry point. The rest depends on the direction you want to take. Theory? Then the Landau-Lifschitz volumes will be your friends. Observational? That will depend of the area, ask your majors.
it's hard to believe no one has recommended Gravitation yet. This comprehensive, well-written, and authoritative book on general relativity is tailor-made for the mathematically sophisticated. One of its strong points is it does everything twice using both coordinate-free and coordinate-based differential geometry to help solidify your understanding and so you can do both theory (coord-free) and calculations (coords).
I will recommend three books at three distinct levels. First, to give you a basic familiarity with the night sky, I recommend, Nightwatch: A Practical Guide to Viewing the Universe, it has been one of my favourites. No astrophysics in this one, just decades' worth of experience in star gazing. Also, for a familiarity with the solar system and planetary geology, I recommend Moons and Planets. Finally, for rigour, I recommend Introduction to Cosmology, it is clear, concise, and introduces elements from general relativity without much of the required differential geometry. These books were all part of required classes in my undergrad and I really enjoyed them. Hope they serve you well!
Charles Kittel, Herbert Kromer, Thermal Physics
Consise, a small set of problems, at least look at every one
Hans Ohanian, Gravitation and Spacetime
Could prevent you from boggling at Misner, Thorne and Wheeler
Stephane Mallat, A Wavelet Tour of Signal Processing
Thorough, a math processor here told us that the demand for rigor could invariably be handled by saying "Lebesgue limit theorem."
Cornelius Lanczos, The Variational Principles of Mechanics (a paperback from Dover books)
Classic introduction to the calculus of variations and analytic mechanics
Paul Horowitz, Winfield Hill, The Art of Electronics
The first edition, before they threw in all the microprocessor stuff, is focused on what experimental physicists need to know.
One of the grand old men of analog chip design, Bob Pease, has written a column for years that you can read on the web.
http://www.elecdesign.com/Departments/DepartmentID/6/6.html
http://www.national.com/rap/
My favorite undergraduate physics texts (as a physics and math B.A.):
Fundamentals of Physics by Halliday, Resnick, and Walker - Great intro book (very basic). I still go back to it as a great intro level reference.
Classical Mechanics by John R. Taylor - A very good book covering all of the 'basics' of Classical Mechanics. This is basically an introductory treatment of some of the higher level concepts of classical mechanics, including air resistance, the lagrangian and hamiltonian, rotational frames of reference, etc.
Introduction to Electrodynamics by Griffiths - Probably *the* standard text for 3rd year undergraduate E&M. A very well written, readable introduction to higher level E&M concepts.
Introduction to Quantum Mechanics by Griffiths - Not as standard as his electrodynamics book, but still a very good introduction to quantum mechanics, from the schrodinger equation and particle in a box through time dependent perturbation theory and more.
An Introduction to Modern Astrophysics by Carroll and Ostlie - A very broad treatment of almost everything you could ever think of in astrophysics. I'd personally consider it a must have reference for astrophysicists, but I'm not one, so take that with a grain of salt. The second edition may be worth shelling out the extra cash, because a *lot* has changed in astrophysics in the last 15 years (for example, WMAP, to name just one of the many important experiments that have changed our view of the cosmos)
In addition to these textbooks, as others have already mentioned, there are the Feynman lectures, which many people take as gospel. They're good, but in my opinion they don't beat a good textbook devoted to the topic, like the ones I've listed above.
Other books that I don't think are quite as good, but you might consider, depending on your needs: Modern Physics by Serway, Moses, and Moyer - Not a great text, but I haven't encountered *any* good modern physics texts. Really, I'd say you're better off ignoring this, and going straight to quantum.
Solid State Physics by Hook and Hall - A fine solid state text. Not the standard one by any means, but I find it fairly readable and easy to follow.
An Introduction to Thermal Physics by Schroeder - I don't have much experience with thermal physics texts. This one was adequate.
None of the above texts are graduate level, but no doubt you'll have to buy the appropriate graduate level texts as you take the classes. Between all of them, if you understand the material, you'll have a more than adequate background in physics to start your degree. Cherry pick as best fits your needs.
or go to this link:
http://www.holoscience.com/synopsis.php
you will find the answer you are actually looking for.
Hello!
Since you're a mathematician, maybe you'll be interested in cosmology (=theoretical astrophysics).
Here is one recommendation:
Cosmology: A Very Short Introduction - Peter Coles (1)
http://www.oup.com/uk/catalogue/?ci=9780192854162
OTOH, the following book is quite provocative:
The Trouble With Physics - Lee Smolin (2)
http://backreaction.blogspot.com/2006/08/lee-smolins-trouble-with-physics.html
BTW, http://fliptomato.wordpress.com/2007/03/09/the-trouble-with-smolin/
------------
(1) Professor of Astrophysics, University of Nottingham
(2) Researcher at the Perimeter Institute for Theoretical Physics, Waterloo, Ontario
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.
http://books.google.com/books?isbn=0880292512
Introduction to Mechanics is a freshman/sophomore level text based on vector calculus, so it doesn't do the kind of dancing around to avoid the math that you see in other intro texts. Schools often assume that the student is enrolled in vector calculus in parallel. Still in its first edition from 1973 (I just checked) - and the price is roughly one million dollars.
j/k. Buy it used, it only costs you half a million.
Two of the books I kept after graduating in nuclear physics might help to get a quick rough overview in about 10% of the pages of the Feynman lectures. None of them replace the other suggestions, but they might work well as a kick start and quick reference.
-From Newton to Mandelbrot. The fractals section is probably completely out of fashion now, but the first 2/3rds of the book are a lightning fast course through most of theoretical mechanics, electrodynamics, relativity and quantum physics
-Princeton Guide to Advanced Physics--a 400 page almost pure math romp through all kinds of physics. It's ok for getting a quick overview. Be a bit careful with this one, all the content is sound, but the editing is fairly sloppy. But it's the only place I know where you can get, for example, the basic equations for fluid dynamics in 15 pages, rather than 150.
Course of Theoretical Physics by Landau and Lifshitz
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
I retired from a thirty year career as a software engineer to do the same thing you are doing. I am in my 4th semester towards my MSc in astrophysics and astronomy with grades of High Distinction each semester. If you know math up through calculus and advanced differential equations, then the physics will come easily! Your first semester may require some spherical trigonometry (which even most math majors aren't familiar with), but essentially you've got it made with your math background. I'm familiar with practically all of the books that others have recommended to you in other comments, but I've found that the most relevant are the David McMahon "Demystified" books such as Relativiy Demystified , Quantum Mechanics Demystified , etc. These books assume you are familiar with advanced math but not necessarily physics (though be warned I have found some mistakes in these, but these errors are easily recognizable). I honestly think you don't have much to worry about given your math background.
The Feynman lectures on physics are nice because they contain more insight than actual grindstone physics. And in the long run insight wins, though you still need to know the mechancis.
The nice part for you is you understand Maths already which is really the connective tissue of physics. Most textbooks are geared toward students who are still learning math. So in your search for books aim for ones taught in first year graduate courses rather than undergrad. (e.g. Jackson for Eletcrodynamics).
I'd also reccomend reading Fear and Loathing in Las Vegas by hunter S thompson and shakespeare in the original klingon.
Some drink at the fountain of knowledge. Others just gargle.
by Carroll and Ostlie is a very nice and self-contained introduction to many aspects of astronomy and the physics required to study the stars.
I bought it as a student and still use it today as reference.
http://www.amazon.com/Introduction-Modern-Astrophysics-Bradley-Carroll/dp/0201547309/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1215960371&sr=8-2
He's not from Kansas it seems, otherwise he'd have recommended the Bible :)
Hey! If you master the basics you'll be fine. I got my undergrad in math & physics and my grad in astronomy so I can attest to this. Pick up a good calc-based freshman physics book and go through it. Halliday & Resnick or Knight will cover everything you need to know from the physics world - mechanics, waves, optics, electromagnetism, and introductions to atomic, nuclear and quantum physics. Round it off by reading a freshman-level astronomy book like The Cosmic Perspective. And like others suggested, do some of the problems, don't just read and pretend you're really absorbing it. Physics problem solving can be quite a bit different from math problem solving at first. It sounds like a lot of people are trying to recommend the junior and senior level textbooks but if you've thoroughly mastered the first year stuff that will make more of a difference than having skimmed Jackon's E&M or Carroll & Ostlie. Apart from that, when you get to grad school go to a lot of colloquia to pick up the jargon. Good luck!
IMHO this is the best current physics series (http://www.amazon.com/Walter-Greiner-course-of-Physics/lm/R3M2ZCCYYHV24S). There 14 comprehensive volumes, from classical mechanics to nuclear models. Lots of solved exercises, consistent notation across the volumes, etc. Some people complain about the typos, but you need try to learn to spot them since almost every book has them.
If you want something more old school ( and challenging), try the Landau series.
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!
The books I would recommend are:
1) Misner, Thorne, and Wheeler's "Gravitation",
2) Arnold's "Mathematical Methods of Classical Mechanics"
3) Mandl and Shaw's excellent introductory text "Quantum Field Theory"
4) Peskin and Schroeder's "An Introduction to Quantum Field Theory"
5) Sakurai's "Advanced Quantum Mechanics"
6) Messiah's "Quantum Mechanics"
7) Goldstein's "Classical Mechanics"
8) Wald's "General Relativity"
9) Alan P. Lightman, William H. Press, Saul A. Teukolsky, "Problem Book in Relativity and Gravitation"
10) Landau's "The Classical Theory of Fields"
11) Theodore Frankel, "The Geometry of Physics: An Introduction"
12) Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick, "Analysis, Manifolds and Physics, Pt. I: Basics"
13) Kerson Huang, "Quarks, leptons & gauge fields"
14) Teiteilboim and Henneaux "Quantization of Gauge Systems"
15) P. J. E. Peebles "The large-scale structure of the universe"
16) Pierre Cartier, Cecile DeWitt-Morette "Functional Integration: Action and Symmetries"
I have an MSc (and BSc) in mathematics and sometimes study physics as a hobby (though I am mainly interested in the foundations of quantum mechanics, not astrophysics). A couple of years ago I tried learning classical mechanics from
"Mathematical Methods in Classical Mechanics" by V.I. Arnold. I stopped for various reasons not related to the book's quality, which is excellent (in fact as far as I can tell most of V.I. Arnold's books are top-notch). It is fairly heavy-going though as it develops mechanics in its full (non-relativistic) generality on manifolds. The Springer undergraduate mathematics series also has a General Relativity text based on a course at Oxford, and it has at least one positive from a reader at amazon.co.uk though I have not looked at it myself. There is also free stuff such as the following set of lecture notes from a Cambridge general relativity course: http://www.damtp.cam.ac.uk/user/gr/about/members/partiipublic-2006.pdf, but again I have not read over these.
For the math to physics transition, you can't do better than (at least Volume I of) Dubrovin/Fomenko/Novikov's Modern Geometry GTM.
Buy some previous editions of textbooks. For less than the price of one new textbook, you can probably get a whole undergraduate course of learning, as long as you read a lot.
But, make sure any books you buy have answers to problem sets in the back. I learned that lesson the hard way.
Not sure if this was covered above... I suppose it depends on what areas you will focus on. As in most fields, astrophysics and astronomy have many sub-fields that would require a more extensive background in that area. It also depends on which route you are taking (experimental or theoretical). With a math background, I would expect a theoretical route would be very appropriate. Additionally, some schools have different notions of what to include in an Astro grad program. I know someone in one now in which the program assumes little or no previous Astro experience, while some assume extensive undergraduate coursework. I completely encourage you to pursue this, but it may be a daunting task. If you made it through math, it is likely that you have the brain juice to do the physics. There is just a lot of physics out there to learn... so keep a pot of coffee on at all times... :)
For the basics (as most have suggested) check out the Feynman Lectures.
The Schaum's Outline series provides a good overview of many subjects.
Your instructors will probably tell you what to read for your particular astronomy and astrophysics courses.
Most basic and intro areas in astro or physics have a wide variety of books to choose from. Yes, some are better that others, but they all have the information you're looking for, so just grab a few and dive in!
(just a few thoughts from a fellow astrophysicist / college professor)
Rocket Propulsion Elements - Sutton
I'm a Physics Major concentrating in Mathematics. Get books called Mathematical Methods in Physics. This will be your best friend. Then you need to get Quantum Mechanics books, Electrodynamics books, and Classical physics. these, i would just say look at what your strengths are in math, like Matrices or DE's and PDE's, and choose from there.
I recommend "physics" by Halliday, Resnick, Krane.
Good Luck
http://www.amazon.com/Physics-Robert-Resnick/dp/0471568988
Try Straumann's General Relativity: With Applications to Astrophysics: http://www.amazon.com/General-Relativity-Applications-Astrophysics-Mathematical/dp/3540219242/ref=sr_1_1?ie=UTF8&s=books&qid=1215965048&sr=1-1
Well, just a word of warning. It seems like the hardest thing for Math majors to do when switching to Physics is to remember that Rho and Phi are switched when using Cylindrical and Spherical coordinates. Weird, huh?
maths would there for be mathematicses...
If I try to say "maths" I end up with spit all over my screen.
I've strayed a bit from physics, but did physics as well as maths as an undergrad, in quite a good (rigorous) department.
There are many good recommendations here, but there is a lot of overlap and some noise.
With a decent maths background, some parts of the material that give physics undergrads trouble will be relatively easy for you. However, be careful because other parts will be the opposite. Your main problem is that you haven't learned to think like a physicist does.
Concrete recommendations:
The Feynman lecutures will be good to read, with a couple of caveats. First, he doesn't track well with many other intro books (intentional) so jumping back and forward will be harder at first. Second, the third book isn't nearly as good as the first two, and there are better quantum intros.
The Landau & Lifshitz stuff: These two undertook a very ambitious program to cover "all" of physics. The results are somewhat mixed. The books are mostly pitched a bit high level for you to start with, but some are beautiful (e.g. classical theory of fields, which is the classic text in the area, but probably a bit much for you straight off). Some others you can give a miss.
People have mentioned stuff like Jackson (E&M) and Goldstein (CM) ... while we used some of these texts in honors courses final year, they are typically 1st year graduate texts, and you can expect to run into them. Don't worry about them on your own, you need to get up to speed to read them.
Your going to need something like Halliday & Resnick as a survey intro (ballpark, 2nd year material. Assumes the calculus but not much else). Beyond that, you'll want a "bridging" text in particular areas: E&M like Lorrain (from memory, not at my books) and CM (Feynman is good there, maybe Griffiths). For QM maybe Resnik & E(somethingorother) as intro), then Liboff or Sakurai (good, a bit less intro). You'll need a GR course and I expect you'll take one from Misner Thorne and Wheeler, but the intro GR stuff is a mess as I recall -- ask someone who works in it.
You'll need a good statistical mechanics course, and thermodynamics (something like Sears and Sallinger can get you started. There's probably a better one.) Depending on how solid your probability background is, you can probably jump from there to classic texts.
There are some classic Dover books you could supplement with, like Byron and Fuller maths of classical and quantum phys. which might be nice as reference.
Get a reference in mathematical methods. I had a good one by a Russian, probably titled "Mathematical Physics", but I can't recall now. You want something that covers lots of techniques: Greens functions, maybe operator theory in QM, some practical PDE stuff, etc.)
hope that helps!
Landau and Lifshitz Classical Mechanics - concise and beautifully written. Might be stylistically appealing for someone with a background in mathematics.
Griffiths Introduction to Electromagnetism - A classic and clear introductory text. Probably his best book.
Griffiths Introduction to Quantum Mechanics - Another classic. It's also a short book. If you are looking for more Dirac notation, check out Shankar, another classic at the undergraduate level.
Reif Fundamentals of Statistical and Thermal Physics - Great and very complete introduction to statistical mechanics and thermodynamics. If you find the text daunting, you could substitute it for Schroeder.
Taylor and Wheeler Spacetime Physics - Great introduction to special relativity. You'll find a more mathematical treatment in Griffiths EM or any GR book.
-----
If you are interested in reading a bit of undergraduate-level general relativity and astrophysics as well, good books are
Hartle Gravity - An UG-level intro to General Relativity. Focuses on the physics and providing you with metrics. Fun book. Try Carroll if you want something more mathematical.
Ryden Introduction to Cosmology - Great, recent introduction to cosmology at the UG level. Will give you a lot of intuition into your later studies of cosmology.
You might want to check out a good UG-level text on stellar astrophysics as well, but there's probably more than enough on your plate, unless you're some sort of robot.
If you've been doing pure math, you might not be as practiced with analysis and applied functions as people who've been doing physics for a while. Just because you know Bessel functions, elliptical integrals, and stuff doesn't mean you're familiar enough with their use to pass a time-limited exam...
The books I have are:
If you don't already have it, I also recommend the Handbook of Mathematical Functions as a classic reference.
I would add the two plasma physics books in print by Lyman Spitzer. There's a reason they named an observatory after him.
I concur with the recommendations of Feynmann and Landau & Lifshitz.
It's been some 37 years since I made the switch from math to plasma physics, then applied superconductivity and now accelerator physics.
Additionally, I like Schutz and D'Inverno's texts for introductions to General Relativity, and Stuart and Shapiro is dense but delicious for learning about compact objects.
These are suggested from a physicist's perspective; I'm sure there are plenty of good classics known to an astronomy grad student that are outside of my purview. Anyway, best of luck!
To follow knowledge like a sinking star, / Beyond the utmost bound of human thought. ("Ulysses", Tennyson)
There are a series of "classic" physics textbooks published by Dover. They're not hardcovers with glossy paper and amazing color diagrams, but they are about $5-$10. They're generally reproductions of text books which went out of print a few decades ago. Given that most core undergraduate physic curricula stop at ~1930, that's not too bad.
A better suggestion may be to ask the professors at your university, that's what they're there for. If you walk in to someone's office, they may just hand you the perfect book right there.
Penrose's "Road to Reality" is quite a bit more than Pop-Sci. I bought it a few months ago as a refresher. It has been 25 years since I got my degree and while I have kept up with the news it has been quite a while since I "practiced".
I'd also recommend "High Energy Astrophysics" V1 and V2 by Longair. Fascinating stuff in there.
Finally, set up a good newsreader and spend some time on the sci.astro and sci.physics newsgroups. If you can't get an education there, at least you will get some more suggestions from a far more qualified audience than here on /. ;-)
Good judgement comes from experience, and experience comes from bad judgement.
- W. Wriston, former Citibank CEO
"Mathematics" is plural? How many mathematics did you study today? Did you find any particular mathematic more difficult than another?
OT: New Math
Shop as usual. And avoid panic buying.
Mathematical Physics by Eugene Butkov, St. John's University, New York. My edition was published by Addison-Wesley. You probably won't find anything in it terribly new to you, but it will give you a clear idea of the kind of mathematics that an undergraduate physicist is expected to know. A good investment in any case, after 20 years, I still find myself referring to it on a regular basis.
As an undergraduate, when I couldn't understand the material in Butkov, I would turn to Advanced Engineering Mathematics by Erwin Kreyszig. It covers most of the same material but at a more basic level. As a maths grad, however I don't expect that you will need it.
Good luck.
It's not as obvious a transition as one would think. I'd say make sure that your differential and partial differential equations are up to speed. Make sure your group theory is in good shape. Take a class in analog and digital circuits early on. Also, take a materials science course early. Physicists have a fetish about reality, and they won't talk to you at parties if you can't trace your ideas back to a physical example.
In general, of course, figure out what kind of physics you want to be doing (don't pretend you're interested in everything longer than you have to), and then make sure you understand the math required for that subsystem.
Physicists typically approach math totally differently than mathematicians. They assume that because there is a reality, that reality assumes the role of an existence proof for the mathematical reasonableness of any tools that they slap together to describe it. Many of them spend a lot of time gaining expertise in using their mathematical tools (kind of like getting fast at Rubik's cube), because that facility enables them to solve their problems; trying to understand the underlying logic of the tool itself rarely does.
Last, if you are a hetero guy, make sure that you take the seat in the front row next to the cute girl on the very first day. Just walk right in and sit down. There is no graceful changing of seats after that, and the social pecking order and graph of intimacy is built from that first day's initialization of the array of seating nodes.
Good luck!
I have not read them in a decade, but from what I remember it is almost all conceptual with little math.
As both a physics and math student, I would say that these are must reading. I don't remember who said it, maybe Feynman himself, but the quote goes something like the following: "If you can't explain a concept to a kindergartner, then you don't understand it yourself". Feynman truly understands the physics behind events.
Principles of Physical Cosmology by P. J. E. Peebles
Full of theory and implications with excellent explanations and problems worked out. This isn't going to have the latest and greatest but it solidly presents the basics of modern cosmology. The big bang, Einstein De Sitter solutions of General Relativity, universal expansion, the cosmic background radiation, the distribution of galaxies, baryon creation, etc.
My math is no better than Diff. Eq. and Lin. Alg. and I found nothing in this book that was over my head.
Life's a tale told by an idiot, full of sound and fury, signifying nothing.
Check out Physics2000. It's aimed at an undergraduate level physics introduction. It's a good read, and is unusual in that they teach relativity first...
http://physics2000.com/
Cheap, too - $10 for the entire text on CD-ROM with videos to boot.
I'll also recommend Halliday, Resnick, & Walker.
When I was a first-year Engineering student 32 years ago, our text in basic Physics was the 2-volume Halliday & Resnick.
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
Out of the books mentioned on QM, I'd recommend Baym's Lectures on Quantum Mechanics for this purpose; it's a more methodical treatment of QM. it should appeal more to the mathemetician looking for understanding QM. The advanced viewpoint starts from examining polarized photons to develop the QM framework. The result is a more intuitive understanding of QM.
The fault of most QM books is the "cookbook" like approach, even the best books sometimes fall in this pedagogical trap. Do these manipulations and the right answer will pop out. Do these types of perturbations, etc. and you can do more complicated problems.
Landau & Lifshitz, I feel, gets too detailed in the grind of the treatment. For a mathemetician trying to get the "essence" of QM, I'd recommend Baym.
Quantum books: Shankar and Baym. Goswami is a good undergrad book at the Griffiths level.
Math methods: Riley, Hobson, and Bence.
If you are doing astro, you might be doing spectroscopy, and that means quantum theory of angular momentum, so then add the book on that topic by Richard Zare to your quantum stack.
My astrophysics friends do a lot of data analysis. They use IDL for everything so a book on IDL applications in astrophysics might be useful. I can't think of anything else that hasn't already been mentioned. Modern Problems in Classical Electrodynamics by Charles Brau is also a good grad level E&M book that's a bit more up to date than Jackson.
Lots of people here are suggesting a super-broad physics education focusing on everything from themo to relativity to quantum mechanics. These are VERY diverse areas and I really don't think you have time to learn any of them very good, let alone all of them. Therefore, I'd focus on the areas you're likely to delve into first - things like relativity and basic mechanics/dynamics.
In that regard, Feynman's Lecture series is excellent. For a quick read, I'd recommend Feynman's Six Not So Easy Pieces. You might be able to blow through it in a day.
After coming up to speed on some of that stuff, delve into thermodynamics and electromagnetics. Save quantum mechanics for the very end - it's probably the furthest thing from what you'll need to know.
----- obSig
At SLAC: http://www.slac.stanford.edu/ I saw an interesting book in a Nobel Winner's book shelf:
Quantum Mechanics - Albert Messiah
Can anyone comment on whether or not this book is just a book cover or if it's for real?
I'm a practicing physicist (in the US). I took a number of math courses (through the graduate level) and flirted a bit with cosmology and astro before moving over to condensed matter--Here are my suggestions for making the transition:
For classical mechanics:
Goldstein and Marion and Thornton--perhaps not the most exciting of books but very readable. Landau if you have time--the classical mechanics book is rather readable. I'm not so sure about the UK system, but I would assume that you would already have the basic knowledge of a typical US freshman for something like Halliday and Resnick.
Now, you probably won't have time to read all of these, but try to understand the idea of langrangians and hamiltonians. Poisson brackets are interesting for when you go into quantum mechanics.
Stat. Mech:
Reif for undergrad. Boring, but very readable.
Grad: Huang is standard, landau is ok.
E&M
Griffiths for undergrad has nice jokes. Jackson is the standard graduate text--the major annoyance is filling in the gaps in the derivations in the text. If it were me, I would go through Griffiths. It's fairly light and enjoyable reading.
Quantum
I never had a real quantum book--just lectures. Some people seem to like Griffiths. I used the Brehme book, "Introduction to the structure of matter" freshman year and loved it. Dirac was also a surprisingly good read.
General Relativity
Ohanian is readable and a good sophomore level text. Otherwise, you can use the "bible" of Misner, Thorne and Wheeler--but that's probably more than you have time to read, even if you already have some background in differential geometry.
Along the way, you might want to skim through an Arfken for mathematical methods. Pay attention to the special functions--they will come in handy for E&M and Quantum.
I would recommend sticking to the undergraduate level texts to gain a physical feeling for physics. If you find yourself with even more free time, the Feynmann lectures are also a delightful read, but to come up to speed to compete at the graduate level, I would focus more on the standard texts.
Good luck!
Agreed about the Feynman Lectures. Halliday and Resnick are ok as well. It's not widely available, but my favorite text book of all time is Thomas M. Helliwell's "Introduction to Special Relativity". Its the only textbook I've ever read cover to cover. The sample problems are great fun, frequently involving a rhinoceros traveling at 0.99c (where c is the speed of light in a vacuum). He also has an excellent two volume introduction to mechanics, but its much harder to find. It basically only exists as spiral bound sets of photocopies made for Harvey Mudd students.
I think you will find this one is right up your ally.
Pricey but worth it.
You might check out John Baez's article, "How to learn physics".
If opportunity came disguised as temptation, one knock would be enough.
3^2 * 67^1 * 977^1
The one I use is "Mathematical Methods in the Physical Sciences" by Boas. Im guessing that all the math will be relatively familiar and friendly but most of the examples and problems have to do with physics. That way you can get a pretty reasonable familiarity with a lot of physics without having to recreate an entire undergrad physics curriculum. They will probably have you do the standard mechanics, e&m, quantum, stat mech, etc curriculum in grad school anyway.
Why do so many people insist on confusing the two? Mathematics is merely the language used to describe the Physics. It's a tool folks, and nothing more.
That said, having a Maths degree can be either a very good or very bad basis for pontgrad physics. If you insist on seeing Physics as nothing more than messy but fun maths, you'll never be a great Physicist. If however you see the Maths as a succinct and powerful way to describe the Physics you are on the way to being good at Physics. A lot has to do with what kind of Maths degree you have - don't expect number theory to be a great help, but if you have done lots of analysis, partial differential equations and statistical mechanics you have a good basis to work from.
I'd suggest that the "pop-sci" books are a good way to get a focus on the physics, and from there start to read subjects that build the maths. Get your head around the Physics - you'll be able to learn the specialised maths as you go IF you keep in mind that the maths is not the same as the physics.
The suggestion to look at Maxwell's Equations is a very good one. If you can "perform the surface integrals without blinking" and move between bases fluently then you'll have a good start to a common point were many freak out.
The above is written from the perspective of a mathematician who used to lecture in maths and physics by the way. Physicists have a different perspective, but all the really good ones I know were great physicists who happened to be good at maths, not the other way around.
Ok, I'm going to say something which should strictly not be said. There is a thing going
around on the net known as "The Library of Everything". It is strictly speaking the embodyment of copyright violation in an archive
(tarball, zip,rar ) file.
It will contain everything a graduate student physics needs ( with one caveat ) I do not know how well it is maintained I would recommend that any physics student today, even if they buy their books, download it.
I suspect that what you really want is to browse through a set of junior ( in US college nomenclature ) level physics books, and many recommended here are pedestrian level or freshman level. So be alert when checking them out.
I wouldn't worry too much about this. What I'd recommend is:
Boas, "Mathematical Methods in the Physical Sciences"
That'll take you from proving things to applying the actual Math that you've learned. Given your background, you should be able to go through this quickly. You'd probably also benefit from:
D'Inverno, "Introducing Einstein's Relativity"
Since Relativity is in there quite a bit. But, as astrophysics applies many different fields of Physics, you'd probably benefit from:
Serway, Jewett "Physics for Scientists and Engineers"
All those are targeted at an Undergrad and should provide a decent foundation for you to take off from. But, you're still going to have a steep hill to climb given your lack of background in your chosen subject area.
That being said, I have a question for you: Why are you asking here instead of you future supervisor? (S)he is going to know *much* better what you're going to have to know than anyone here. Programs differ you know.
I second nearly all of the above listings (especially Penrose's "The Road to Reality" and the Feynman Lectures) but I'm surprised three particular jewels were left out:
"On the Shoulders of Giants" by Stephen Hawking 'illuminates the origins of modern physics and astrononmy' by including the breakthrough papers of Copernicus, Galileo, Kepler, Newton and Einstein with brief introductions to each in a single volume. It's useful that you understand the historical context of what you're getting yourself into and it doesn't get much more convenient than this by requiring only a single [fat] textbook.
"Space-Time-Matter" by Hermann Weyl is his first big treatise on combining general relativity with electromagnetism. Check it out if you intend to get into some heavy stuff but beware the heavy reading!!
"The Physics and Chemistry of the Interstellar Medium" by A.G.G.M. Tielens is an amazingly comprehensive introduction to the crazy complex system we call outer space. I recently obtained it from Amazon and my nose has not been out of its pages much since. Perhaps it's a bit more chemistry than most appreciate (losers!) but you may find it to be one of the most valuable texts on the ISM and the author includes a 'Further Reading' section at the end of every chapter to review each of the chapter's references.
Also, you're going to find that thermodynamic process are the driving forces of space and it doesn't hurt to have a good background in physical chemistry. I recommend the Physical Chemistry texts of Levine or McQuarrie to serve you. I'm sure you, as a mathematician, will appreciate these much more than most chemists I know!
Good luck on your academic journey and I hope these references serve you well!
I seem to be the only one thinking, that maybe if you don't know anything about physics, a Masters in "basically physics" is not a great idea?
I mean, supposing you don't like physics?
When I was doing my Maths degree I foolishly signed up for a physics course. I was learning real rigor in my Maths classes, then had to sit a squirm as the physicists did some terrible things to equations. Should have gone for English instead.
~~~~~ BigLig2? You mean there's another one of me?
Has to be "Mechanics Made Easy (How To Solve Mechanics Problems)" by David Reynolds
A great overview with clear & concise howtos for all the examples and formulas a must me thinks.
Keep it near by and always remember...
http://mechanicsmadeeasy.com/
Grab yourself a copy of Ohanian (Physics, combined, 2nd edition)
After that, go to a Blackwell's, and sit in the physics section. Pick some books off the shelf, examine them, see what resonates. Rinse, repeat.
Coming soon - pyrogyra
A couple of things I've not seen are:
http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1215991937&sr=8-2Clasical Mechanics
and since you're a mathematician and haven't seen errors:
http://www.amazon.com/Introduction-Error-Analysis-Uncertainties-Measurements/dp/0935702423/ref=sr_1_1?ie=UTF8&s=books&qid=1215992101&sr=1-1Error Analysis
And this should just be obvious:
http://www.amazon.com/Introduction-Modern-Astrophysics-Bradley-Carroll/dp/0805304029/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1215992235&sr=1-1Modern Astro
Many of the comments in this thread look as if they come from the US perspective, so might be hard to apply to the UK situation. There are major differences in what people understand by Masters-level in the two places. Being neither an astronomer nor a mathematician I have no way to fully assess the advice, but Jodrell Bank has a sane looking reading list for people doing a UK M.Sc similar to the one you are taking. ( reading list at: http://www.jb.man.ac.uk/postgrad_course/readls.html) Roughly speaking, US undergraduate degrees are less specialized than British ones, so Masters degrees usually have at least two years of course work, and must cover a lot of ground. That's why several of the commenters can't imagine how a Masters degree could be squeezed into just one year. At the same time, the final year of a UK undergraduate degree is often just as intense and focused as a US graduate program, so the jump up in level may be less than some commenters are assumng.
These two books were texts I found particularly good through my course:
http://www.whfreeman.com/universe5e/ - Very good easy to read
http://www.amazon.com/Introduction-Modern-Astrophysics-Bradley-Carroll/dp/0805304029 - This one's heavier reading, but very comprehensive.
Even after finishing my Astronomy masters, I'm finding new insights in this book. It doesn't go into the heavy math though.
http://www.gravityfromthegroundup.org/
These posts express my own personal views, not those of my employer
I have not done a complete MSc level course in astrophysics, but I have done most of a complete MSc level course in Physics, and I have taken a course on astrophysics. In my opinion, you will get the majority of the background that you need from a "modern physics" textbook. (There is a class that most physics students in the US take called "modern physics" that includes a wide variety of topics that is meant to be preparation for some more specific advanced courses. The textbook that I studied from is called "Modern Physics from (alpha) to (Z0)", (with the alpha and z0 substituted for their greek renderings). The author is James William Rohlf. While I haven't looked extensively at other texts, this one is pretty decent in that it gives a good overview of most of what you will need. It is several years old, (at least the version I have), so you might be able to find it cheaply.
If there is a one single topic that I would suggest you study for background, it would be statistical mechanics. I would probably say that about any scientific discipline, however, so perhaps you will find that the core of astrophysics is really something else.
Good luck!
As much as I like listening to some of those webcasts (esp. Physics 10, "Physics for future Presidents and CEOs"), I doubt any of them will be useful for someone with decent background in mathematics trying to give himself a quick course in physics.
I mean, the only "real" physics classes on that list are Physics 8A and 8B, and those are physics for biology majors (not to mention that they are lower division, so they don't include a proper treatment of classical mechanics or quantum mechanics).
I'd agree with the sibling post and say that Feynmann lectures in physics would be better, although as those are also meant for lower division physics, he does not take the advantage of additional mathematics knowledge that someone with a B.S. in Math ought to have.
Quantum Mechanics by PAM Dirac if you can get hold of a copy
Old but still good. as one of my lecturers said - most books have too many words between the formulas. This one doesn't.
The Singularity is closer than you think
Quant
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.
I am offering another answer to your question because my earlier response may not have been useful.
Many people have suggested "Feynman", but I would like to be more specific and suggest you find a copy of "The Character of Physical Law", published by MIT Press. I especially recommend you read Chapter 2, "The Relation of Mathematics to Physics". If you grasp the essence of that chapter, it may illuminate the knowledge you already have in regard to your new choice of study.
Back in the "old days" (early 70's) I was taking a triple major in Math, Physics, and Computer Science at a nice University in Chicago, and I intended to be an Astrophysicist. As I got into upper-level classes I had to study a LOT of Geology, Geography and Geophysics. Since my earlier response I've checked with some of my friends, and they tell me that the great majority of their time is spent analyzing hypotheses at the quantum level. So, my earlier response is somewhat dated.
What you CAN learn from studying a good Geophysics text is the thinking processes and the way they differ from Mathematics.
As I said, many people will talk about the value of "The Feynman Lectures", but most of them won't have actually read them. (The same is true of Korzybski's, "Science and Sanity", Fuller's, "Synergetics", Wolfram's "A New Kind of Science", and De Toqueville's, "Democracy in America".) Information becomes dated, but the value of "The Feynman Lectures" may actually be in the way of thinking about Physics.
Good luck.
"The mind works quicker than you think!"
All these books below are nice, but really who cares about the trees when you need to see the forest from above.
Read Feynman Lectures, if you can understand them and follow them you would have learned mode physics and thinking like one.
George, a physicist for the last 42 years.
Don't click the link, you may learn something... http://www.youtube.com/view_play_list?p=095393D5B42B2266
http://www.amazon.com/gp/product/0072472170/ref=olp_product_details?ie=UTF8&me=&seller= I always recommend this book to the beginning Physics student, and I get thanked by my students often. Another bit of advice: Quite a few of my fellow astronomers have never spent much time actually looking at the night sky, either with the naked eye or through a telescope. Doing so will round out your education. (Of course, if you become a radio astronomer, as I did, you can play frisbee inside your telescope!) Good luck in your new endeavor.
Landau and Lifshitz, Course of Theoretical Physics, volumes 1-10.
I have to confess that sometimes the gentlest intoductions were the best. The most expensive book on my reading list was Astronomy: The Evolving Universe, by Zeilik. I still love reading it to this day. Yes, maybe too many pictures for those that like the heavy stuff. If you really want to understand the basic principles - introduced in an absolutely clear manner - you won't get better.
You've got a tough road.
Many graduate programs have core graduate physics courses, perhaps 4 to 6. The enduring standards over the last few decades are Classical Mechanics by Goldstein, Electromagnetics by Jackson, Statistical physics by Reif, QM (not sure if there are enduring classics there).
You've got to be able to work problems out of these books quite well.
I would reccomend that you read a survey course book in astronomy like Chaison's Astronomy today. It's a gentle introduction into the current astronomy suitable for even a freshman. A good intro to physics is a University physics book such as Sears and Zemansky (now written by Young and Freedman). This covers the calculus version of the basics - 1100 pages covered in two to three semesters.
Then, in order to get to the level of the graduate texts, there are typically one to three courses between the basics and the graduate level. This is in electromagnetics, quantum theory, statistical physics, classical mechanics, thermodynamics. Optics is another probable option.
The feynman lectures are great for explanations and concepts. Use them in concert with other texts for good results.
you also need to learn error analysis and basics of experimental methods taught in undergrad labs.
Remember, math has the principle tools of science but it is not the science.
a book that tells smitty that there is only one math. Start there.
Utilizing the synergization of benchmark e-solutions to pre-workaround action items!
I mean, say I have a BA in medieval history, would I really expect to follow it up with an MA in French literature, or something?
To have a right to do a thing is not at all the same as to be right in doing it
Speaking from experience, I can tell you that one of the most practical texts for nuts-and-bolts astrophysics is Radiative Transfer by S. Chandrasekhar. It provides a foundation for a surprising array of topics. Dover makes an inexpensive paperback edition.
For classical mechanics, I recommend Mechanics by Landau and Lifschitz. It's wonderfully concise.
The U.S. standard for graduate mathematical methods in physics is Arfken & Weber. Covers everything.
Kleppner & Kolenkow, Introduction to Mechanics
Goldstein, Classical Mechanics
Jose & Saletan, Classical Mechanics
Arnold, Mathematical Methods of Classical Mechanics
Griffiths, Introduction To Electrodynamics
Schwinger, Classical Electrodynamics
(Jackson omitted on purpose)
Melia, Electrodynamics
Griffiths, An Introduction to Quantum Mechanics
(Sakurai omitted on purpose)
Ballentine, Quantum Mechanics
Zee, Quantum Field Theory in a Nutshell
Peskin & Schroeder, An Introduction to Quantum Field Theory
Schutz, A First Course in General Relativity
Misner & Thorne & Wheeler, Gravitation
Wald, General Relativity
Fermi, Thermodynamics
Chandler, Introduction to Modern Statistical Mechanics
Most of the series by Landau and Lifshitz
Those are to the best of my knowledge some of the better undergrad and basic grad-level works on the core theoretical physics subjects. As far as mathematical background, Pugh's analysis book is really not that tough and so much cleaner than crap like Stewart or the other mega-undergrad-calculus books. For rigorous linear algebra, Axler or Halmos are good. For less-rigorous multivariable calc, Schey's Div Grad Curl is very well-regarded.
Difficulty: unbounded
Hawking & Ellis, The Large Scale Structure of Space-Time
Weinberg, Quantum Theory of Fields
Dear sexy_flying_yoda, First of all I think it is wonderful to have another math major falling to the dark side. But in answer to your question I have one recommendation for you to start with, Physics for Scientists and Engineers by Serway. It is bit expensive but depending on the university you go to there is a good chance it will have been the intro course book used there. It covers pretty much every topic from vectors to QM (although briefly) but it can help in getting you up to speed. If you start reading now before summer is over then you can jump into the straight E&M and QM texts that will be useful for your courses. With the basics under your belt (assuming you are shaky in them) you should be well prepared by the time classes begin. I have read several comments by others and I have to say that there are a lot of good recommendations being made to you but if you are just starting in Physics this is a good book to have, if only for reference. Good luck in your new major!
By Ian Lawrie:
http://www.amazon.com/review/product/0750306041/ref=dp_top_cm_cr_acr_txt?_encoding=UTF8&showViewpoints=1
is an excellent overview of the key ideas in 20th century physics, with an eye for the unifying mathematical principles that underlie them all.
In your situation I think it would be very useful, because it gives you a big picture of what the main concepts in physics are like, rather than dwelling too much into the details of any one topic. Give it a read first, and then move on to a few more topic-specific books like others recommended here.
Two books that are at a somewhat low level, but provide a really thorough and balanced overview and lots of important background are
Frank Shu's The Physical Universe
James Rohlf's Modern Physics from alpha to Z0
They're both an easy read and a great introduction to their respective fields. If were to go over everything in those two books and selectively work through a set of any of the standard standard advanced undergrad E&M, classical mechanics, and QM texts, you'd start out ahead of most incoming physics and astro grad students. (As far as the coursework goes, I'm a big fan of Cohen-Tannoudji for QM and Purcell supplemented by the advanced text of your choice in E&M. Haven't yet found a classical mechanics book that doesn't suck.)
I think the best overview for you would be George Joos' Theoretical Physics. It's very mathematically based and provides a comprehensive overview of most undergraduate material.
Frosty piss posts are worthless, GNAA posts are worthless and hurtful, but they are the least of this site's neuroses.