Good analysis/calculus book?
Florian Gyarfas
I'm looking for a really good book on advanced Analysis/Calculus. The books
I have had so far are really bad! They're either too detailed, too brief or
too hard to understand (especially the ones my professors recommended). I
need a book that covers all common analysis topics, like
differential/integral calculus with one and more variables, limits, (taylor)
series, metric spaces, differential equations etc.... just the common stuff!
I'd prefer a book with lots of examples... I don't need exercises, though.
And, most importantly, it shouldn't be boring... I need a book that I enjoy
to read!
Does anybody know such a book?
By the way, what is the most popular analysis book??
thanks!! bye!
Florian
Whigdon2
research papers?
Seriously, you may as well learn to like reading of this sort, or go into
something like computer science where the reading is generally a little easier
(and frequently sloppier too..but that's another matter).
My favorite advanced calculus book is "Advanced Calculus" by Loomis and
Sternberg. It discusses many of the topics that you mentioned. I can't think
of a book that I have **enjoyed** reading more! However it is moderately
challenging, and at least temporarily, out of print.
Whichever texts that you choose, I suggest that you prefer books with exercises
to those without them. Practically all undergraduate students could use more
practice at writing proofs. Admittedly, I don't know you, so you may be an
exception.
Best wishes,
Bill Higdon,
Florian Gyarfas
Hello,
thanks for your answer.
> What are you going to do when you get to the point where you need to read
> research papers?
> Seriously, you may as well learn to like reading of this sort, or go into
> something like computer science where the reading is generally a little
easier
I AM a Computer Science student, but I gotta take all those math classes.
However, as a CS student I'll never get to the point where I have to read
math research papers.
And by the way, you may have misunderstood me. I don't care if a book is
difficult; it just has to be interesting and not too abstract.
See, I'm from Germany (that's why I have some difficulties expressing myself
in English) and most scientific books written by U.S. authors are way easier
to read than the ones written by European authors (at least that's my
experience). Some American authors seem to be a little humorous, too,
something I really appreciate and something you'd never find here.
>
> (and frequently sloppier too..but that's another matter).
>
> My favorite advanced calculus book is "Advanced Calculus" by Loomis and
> Sternberg. It discusses many of the topics that you mentioned. I can't
think
> of a book that I have **enjoyed** reading more! However it is moderately
> challenging, and at least temporarily, out of print.
Okay, I'll check out that one.
> Whichever texts that you choose, I suggest that you prefer books with
exercises
> to those without them.
Yes, in general that's true; however, I didn't mention that I get more than
enough exercises from my teachers, so I don't have the time to solve even
more. What I really need are examples.
> Practically all undergraduate students could use more
> practice at writing proofs. Admittedly, I don't know you, so you may be
an
> exception.
I agree with you. I guess I'm not an exception:-)
regards,
Florian
Dave L. Renfro
[sci.math Wed, 31 May 2000 21:51:08 +0200]
<http://forum.swarthmore.edu/epigone/sci.math/twangskooyoi>
wrote
> Hi everybody,
>
> I'm looking for a really good book on advanced Analysis/Calculus.
> The books I have had so far are really bad! They're either too
> detailed, too brief or too hard to understand (especially the
> ones my professors recommended). I need a book that covers all
> common analysis topics, like differential/integral calculus with
> one and more variables, limits, (taylor) series, metric spaces,
> differential equations etc.... just the common stuff! I'd prefer
> a book with lots of examples... I don't need exercises, though.
> And, most importantly, it shouldn't be boring... I need a book
> that I enjoy to read!
> Does anybody know such a book?
> By the way, what is the most popular analysis book??
>
> thanks!! bye!
> Florian
I was going to say something about exercises, but your follow-up
post gave an adequate explanation. I don't think anyone could
honestly tell you the most popular analysis book. If "most
popular" means "most titles sold", this would require sales
information about several dozen books from over a dozen
book publishers--information I doubt would be available.
Someone mentioned "Advanced Calculus" by Loomis and Sternberg.
This was once used at Harvard University (late 1960's?) for
an honors advanced calculus course designed for their most
mathematically capable undergraduates. I was told by someone
about 20 years ago (who received his Ph.D. at Harvard back in
the 1960's) that this book was discontinued because it was
too difficult. Thus, this is hardly a text for someone having
difficulty with some of the books their professors have recommended.
However, for the mature student, Loomis/Sternberg is an excellent
survey of many important topics. [For those who are interested,
another book designed for an honors advanced calculus course is
by Nickerson and Steenrod (I think--I wasn't able to find it at
amazon.com).]
I strongly recommend the following book:
Victor Bryant, YET ANOTHER INTRODUCTION TO ANALYSIS, Cambridge
University Press, 1990. [Hardback and paperback available.]
Here's what a reviewer at amazon.com has to say about it:
<< Reviewer: Carl McLaren (cmcl...@cyberstreet.com) from
Florida USA While there have been countless introductions
to mathematical analysis (calculus) this is my favorite.
The author does a brilliant job of making the subject
matter interesting and very understandable with excellent
exercises along the way which have solutions in the back!
A must read for bright high school seniors and college
freshman that are taking calculus or will be. >>
I agree with McLaren's comments, except maybe for his comments
about high school seniors and college freshmen (at least with
regard to those in the U.S.).
I think Bryant's book is better suited for individual study than
any other book on introductory real analysis that I'm aware of.
It's written in a very engaging manner, gives very detailed
explanations, is excellent in providing motivation for new
concepts, and has detailed solutions to all exercises.
Dave L. Renfro
Ed Ngai
read, ever? I used Kreyszig 6th ed. of Advanced mathematics
when I was at grad school. Humm, there is the REA series of
math books. REA puts the questions down and then does a good
job of laying out all steps on how to solve the problem.
I hate Schaums, they are too difficult, they leave out alot
of steps of the eq.s and I couldn't follow the problem thru,
way too hard, not fun.
How about the Dover series of books? I remember the Lapalce
Eq.s Solver book and that was kinda interesting.
Steven E. Landsburg
Dave L. Renfro writes::
> [For those who are interested,
> another book designed for an honors advanced calculus course is
> by Nickerson and Steenrod (I think--I wasn't able to find it at
> amazon.com).]
It's Nickerson, Spencer and Steenrod, and it's a great book if you can
find it. It was published by Van Nostrand. When I wanted to teach a
course out of this book several years ago, I called Van Nostrand and
asked for permission to photocopy it for my students, since it was
out of print and unavailable. Van Nostrand said they had no record of
ever having published this book (though I was holding a copy with
their imprint in my hands) and advised me to go ahead and photocopy
it on the grounds that they'd never recognize it as theirs anyway.
Steven E. Landsburg
ste...@landsburg.com
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