Useful maths & physics books to read before starting university?

[lizzie96]

Sorry if this question has been asked a lot before, but...

What books would be particularly useful to read before starting university?
What books explain tricky undergraduate-level topics really well?

My course will hopefully be Mathematical Physics, so any recommendations of maths books (pure or applied) for a beginning student would be particularly useful, as I tend to find maths harder than physics. I tried looking on the university's website, but they don't seem to have any recommended reading lists.

Thank you for any advice.

 

[micromass]

If you already know some calculus, then going through Apostol would be a very nice idea. His two volumes cover calculus very indepth and many exercises are truly challenging.

If you're new to calculus, then I think Lang's "first course in calculus" would be very suitable.

If you're up for a challenge, then there's always Spivak's calculus. But this is more a real analysis book, I recommend doing Apostol first anyway.

You can also get into linear algebra. A good first introduction is Lang's "Introduction to Linear Algebra" (don't confuse this with his more difficult "Linear Algebra"). This book teaches matrices, vector spaces, etc. A good follow-up book is probably "Linear Algebra done wrong", which you can get freely here: http://www.math.brown.edu/~treil/papers/LADW/LADW.html

Since you're interested in mathematics, you might also be interested in a bit of abstract algebra. Pinter is a very readable and easy introduction (be sure to do all the exercises, since it contains much good stuff). Artin's Algebra is more challenging, but very well-written.

For physics. I don't think you can really ignore the wonderful Kleppner & Kolenkow. It's an amazing introduction to classical mechanics (do get the very first edition, the later editions are much less good). I do hope your calculus is good and I do hope you're already a bit acquainted to physics. If not, then Halliday & Resnick should be a good first introduction (although I find the book very boring, I don't think it's "real" physics).

Finally, a book you should certainly buy are the Feynman lectures. They're simply amazing. It's good to read them right now, you'll learn a lot. But if you got yourself a PhD in physics and then read the Feynman lectures, then you'll still learn a lot! Don't treat the Feynman lectures as a textbook though, they're just supplementary.
Mathematics has its own Feynman lectures called the "Princeton companion to mathematics" written by Timothy Gowers. If you're into pure math, then I certainly recommend this as well.

Well, I think these books should keep you busy for a long while

 

[mathwonk]

micromass's books are very very wonderful, but if you want something less formal i suggest looking at courant's what is mathematics?

 

[BOAS]

If you already know some calculus, then going through Apostol would be a very nice idea. His two volumes cover calculus very indepth and many exercises are truly challenging.

If you're new to calculus, then I think Lang's "first course in calculus" would be very suitable.

If you're up for a challenge, then there's always Spivak's calculus. But this is more a real analysis book, I recommend doing Apostol first anyway.

You can also get into linear algebra. A good first introduction is Lang's "Introduction to Linear Algebra" (don't confuse this with his more difficult "Linear Algebra"). This book teaches matrices, vector spaces, etc. A good follow-up book is probably "Linear Algebra done wrong", which you can get freely here: http://www.math.brown.edu/~treil/papers/LADW/LADW.html

Since you're interested in mathematics, you might also be interested in a bit of abstract algebra. Pinter is a very readable and easy introduction (be sure to do all the exercises, since it contains much good stuff). Artin's Algebra is more challenging, but very well-written.

For physics. I don't think you can really ignore the wonderful Kleppner & Kolenkow. It's an amazing introduction to classical mechanics (do get the very first edition, the later editions are much less good). I do hope your calculus is good and I do hope you're already a bit acquainted to physics. If not, then Halliday & Resnick should be a good first introduction (although I find the book very boring, I don't think it's "real" physics).

Finally, a book you should certainly buy are the Feynman lectures. They're simply amazing. It's good to read them right now, you'll learn a lot. But if you got yourself a PhD in physics and then read the Feynman lectures, then you'll still learn a lot! Don't treat the Feynman lectures as a textbook though, they're just supplementary.
Mathematics has its own Feynman lectures called the "Princeton companion to mathematics" written by Timothy Gowers. If you're into pure math, then I certainly recommend this as well.

Well, I think these books should keep you busy for a long while

Quick question (i'm interested in looking into linear algebra before the new academic year);

For books such as Lang's introduction to linear algebra, should I worry about the publication date? I can pay £4.00 for a 1971 version or £35.00 for a 2012 edition.

Was it as good back then as it is now?

 

[TomServo]

Math is the easy part, IMO. I suggest focusing on building physical intuition.

The Flying Circus of Physics (full of real world examples)

The Cartoon Guide to Physics

Mad About Physics

Mad About Modern Physics


The above books are full of physics riddles to build your understanding, mainly of classical physics, but you'll fall back on your classical understanding a lot.
I just started "The Refrigerator and the Universe" to develop my understanding of entropy and it's pretty good so far.

 

[micromass]

Quick question (i'm interested in looking into linear algebra before the new academic year);

For books such as Lang's introduction to linear algebra, should I worry about the publication date? I can pay £4.00 for a 1971 version or £35.00 for a 2012 edition.

Was it as good back then as it is now?

With math and physics books, you will often find that the older editions are better than the new editions. So I wouldn't worry about getting a 1971 version.

 

[homeomorphic]

If you've done calculus, I would recommend Visual Complex Analysis.

 

[Perpetuella]

Hey Mathwonk o/ and anyone else with advice. I figured I would ask this question here rather than start another thread of basically the same topic. I've been going through your "so you want to be a mathematician thread" and recently I've started becoming more interested in mathematics. So the 2nd semester of my freshman year is coming to a close and I'm starting to realize that I don't really know much at all about math besides the "plug n chug" stuff. I'm in cal b and have been making b's due to lack of effort. I was wondering if you have any suggestions on what "maths" I should go back and get a more theoretical understanding of. For instance I have a general understanding of algebra and geometry/trigonometry, but would you advise going back and looking at some more rigorous books on these subjects besides the basic cookie cutter textbooks in school? I really want to come at it from a proof/theorem perspective and then tackle some examples. I've seen almost countless books linked all over the place. I figure going through Apostol's books for calculus would be a good place to start but I honestly think those are probably over my head right now. Also I'm a CS/physics double major if that helps at all.

 

[homeomorphic]

For instance I have a general understanding of algebra and geometry/trigonometry, but would you advise going back and looking at some more rigorous books on these subjects besides the basic cookie cutter textbooks in school?

Typically, you wouldn't really need to review those subjects, unless there is some major gap in your skills. If you wanted a warm-up for more theoretical math, you'd probably be better off with something like naive set theory for a subject where you can explore proofs without a lot of the difficulty of coming up with analysis arguments or some linear algebra for something that's sort of transitional. Also, as always, I attribute a lot of earlier success at classes like real analysis to reading Visual Complex Analysis, which you should be ready for, if you can get a B in calculus due to lack of effort.

 

[Ripley]

What is mathematics? By courant is very good. The road to reality by penrose is very interesting and can often be picked up cheaply.
Most of all enjoy some time off before your studies begin.

 

[omega500]

Feynman lectures

The Feynman Lectures are available online here: http://www.feynmanlectures.caltech.edu/

 

[lizzie96]

Thank you for all the suggestions. I have already read the Feynman Lectures (and agree that they are fantastic!) but I will definitely (try to..) read Visual Complex analysis, Spivak's calculus, and Kleppner & Kolenkow. Hopefully these books will fill some of the major gaps in my knowledge by the time I start university.
By the way, I have also seen recommendations of a series of books by Landau and Lifshitz, which are meant to be hard but good for theory students. Would these be appropriate reading to gain a deeper level of understanding before university, or would they be ridiculously advanced and need lots of prerequisites?

 

[jtbell]

Landau and Lifshitz are graduate-school level, and I think most grad students consider them rather challenging even at that level!

 

[SredniVashtar]

Get a copy of A. P. French "Newtonian Mechanics". I believe this to be the best intro to physics (no, not just to Newtonian mechanics, to physics) one could hope for.
French is a truly gifted teacher and leaves nothing unexplained, especially in this very first volume of the MIT Physics Series. Do not be misled by the age of the book [*], it is a timeless masterpiece. Some think it's a tad too verbose, but this is a strength if you are having your first serious encounter with university physics. This book tells you what other books usually give for granted.
Kleppner is good, but can wait. Feynman is amazing, but not quite the best choice for an introduction to physics. French gives you a solid foundation.

Also, French's volume on waves, "Vibrations and Waves" from the same series, is a must read.
Lucid explanations, well thought out exposition, and a -in contrast with the first volume - a wonderful synthesis.
.

[*] Micromass is dead right: older editions are usually far better than newer ones. There's an alarming trend in watering down (and uselessly over-coloring) physics books that keep reminding me of the that movie... "Idiocracy". :-/

 

[Daverz]

Second the French books. There is also a QM book and a special relativity book in the series. I'm not familiar with the QM book, and for relativity I'd start with the old red paperback edition of Spacetime Physics.