Books

Dear /sci/entist recommend me the best book for:

- Infinitesimal calculus
- Linear and non-linear algebra
- Geometry and differential geometry
- Anything else in the field of mathematics and physics

Have a nice day.

The Quran?

>>2
Recommend me at least the best book for infinitesimal calculus...

>>1
What level are you looking for here?  Like freshman calculus or theoretical analysis?

Sheldon Axler's "Linear Algebra Done Right" is a really good textbook.

>>4
Both, please. I'm looking for book(s) that covers the basic topics and moves over to advanced and theoretical topics.

>>6
Probably doesn't exist.  Regular calc books don't do much with epsilon-delta stuff and rigorous development of integration theory, and analysis books don't have whole chapters on how to find antiderivatives using integration by parts.

>>7
Then recommend me the best book for the basic topics, and another book for theoretical analysis.

>>8
most "freshman calculus" books are more or less interchangeable.  To move into more advanced topics, one classic is Rudin's Principles of Mathematical Analysis, and I'll second the Axler recommendation, but what would probably benefit you the most is to pick up random Springer UTMs (undergraduate texts on mathematics) from the university library on stuff that looks interesting to exercise your math reading muscles.  One great book on mathematical topics and physics, which starts at a low level and quickly (!!) jumps into advanced topics is V.I. Arnol'd's Mathematical Methods of Classical Mechanics.

In physics, supposing you know the freshman stuff, the E+M and quantum books by Griffiths are a great start to more advanced topics.  I think by the time you are comfortable with those you'll know enough to figure out where to look. 

Learning any of this stuff will take years of concentrated work, even if you are a genius, (though, chances are you aren't a genius since you're asking for advice on 4chan) so don't get discouraged.  It does get easier as you go along, though it may not seem that way for a long time.  It really helps to have people around to talk to about stuff too.

>>8
While I have heard that Rudin's analysis textbook is very good, I can't vouch for it as I haven't read it.  But Bartle and Sherbert's "Introduction to Real Analysis" is an excellent text for getting introduced to how advanced mathematics in general is going to be, and it should be readable even without being too familiar with the mechanics of calculus.  What you won't learn from it is how to really get the hang of the computations though.

>>9
Thanks, I will look for those.

Not that I wish to hijack the thread, but where would a high school senior who successfully avoided taking maths begin?  I'd like to get a head-start on physics, calculus, geometry, trig- anything and everything before I move up to college. 

Assume I'm a math beginner who only knows a decent amount of algebra. Just for perspective: my math stopped when I completed sophomore algebra II (after taking geometry, but I only made it to geometry because I tested out of algebra I).

>>12
You can begin by not calling it "maths".

>>13
No. Shut up. "Maths" is the correct term in many countries.

>>12
Start at the bottom and work yourself up, obviously. Trigonometry, Precalculus, Calculus. The Calculus text I used in high school was by Larson, Hostetler, and Edwards, if I remember correctly; it was a very good book. I don't think it's that important to look for a particular text for Trig and Precalc, just find ones that cover sufficient content and do a good job of explaining the material.

Saying what you plan on doing in college would help me provide additional recommendations. I'm finishing up my undergrad in chemical engineering. I took differential equations in my senior year of high school (author: Zill), and apart from that I haven't really needed any more math, though I've taken courses in Linear Algebra (author: Strang), Numerical Methods (Gilat), Partial Differential Equations (Strauss), and Advanced Vector Calc (Marsden & Tromba).

>>14
>No. Shut up. "Maths" is the correct term in many countries.

http://whois.domaintools.com/4chan.org

>Registrant Country:US

4chan is in america, your argument is invalid.

>>15
aight nigga this aint not no british board
we be speaking american here!

>>14

The purpose behind teaching myself these MATHS is to see how well I could capitalize on my father's natural talent for MATHS, assuming I inherited it.  See, my dad was a major engineer for Chevron.  He oversaw the production of offshore oil rigs, coordinated undersea robotics, etc.

From what I gather, engineering is fairly mathematics intensive, and my reasoning is that it's better to know the MATHS than to not know the MATHS.  Thus, I'm shooting for a general understanding of MATHS to give myself something to work from and toward later on (not to mention I'm an absolute nerd and find math fun).

That aside, I'm mostly interested in chemistry, biochemistry, computer science, and engineering, with no particular bias toward any one subject.

POST SCRIPT: if you're going to get a stick in the ass over the word MATHS, reread the above and substitute "math" for "MATHS".

>>17
WELL YOU'RE A POOPY HEAD!!! D:<

>>18

Sir, I'll have ya know my head is reg'lar!

>>17
You may wish to read from a college freshman book on mechanics and E+M in physics (something like Gianconi is probably OK, though Serway is a personal favorite.  These books are all more or less the same at this level, though)  in order to motivate a lot of the vector calculus that you will need to end up learning.

not to mention I'm an absolute nerd and find math fun
Then why didn't you lrn it the 1st time around back in high school?  If you find it interesting, you really shouldn't have put math off.  The earlier you lrn, the better.

>>21
Because nobody likes math nerds in high school.

>>22
coolface.jpg