epsilon-delta book
Vigual
advanced calculus)?
Dave L. Renfro
[alt.math.undergrad 2003-01-05 02:15:30 PST]
http://groups.google.com/groups?th=c3649e80393b253a
wrote
> can anyone recommend a book for an introduction to analysis
> (epsilon delta advanced calculus)?
Bryant [3] would be my recommendation if you're fresh out of the
calculus/ODE sequence and studying on your own. If your background
is a little stronger (i.e. you've had one of those "transition to
advanced mathematics" courses at the Sophomore or Junior level),
then Bressoud [2] might be better. Finally, you should take a look
at Abbott [1] regardless -- I think it's the best written
introductory analysis book that's appeared in the past couple
of decades.
[1] Stephen Abbott, "Understanding Analysis", Springer-Verlag, 2001.
http://www.maa.org/reviews/understand.html
http://makeashorterlink.com/?K4E6158F2 [amazon.com reviews]
http://community.middlebury.edu/~abbott/UA/UA.html
http://www.wkonline.com/a/Understanding_Analysis_0387950605.htm
[2] David M. Bressoud, "A Radical Approach to Real Analysis",
Classroom Resource Materials Series #2, Mathematical Association
of America, 1994.
http://www.maa.org/pubs/books/ran.html
http://makeashorterlink.com/?G2F6128F2 [amazon.com reviews]
http://www.macalester.edu/~bressoud/
http://www.macalester.edu/~bressoud/books/aratra-correct.html
[3] Victor Bryant, "Yet Another Introduction to Analysis", Cambridge
University Press, 1990.
http://makeashorterlink.com/?S6D6528F2 [amazon.com reviews]
http://makeashorterlink.com/?T6B6138F2
Dave L. Renfro
Raymond Ka Wai Cheng
review and others on amazon.com
r.
Cameron Zwarich
> can anyone recommend a book for an introduction to analysis (epsilon delta
> advanced calculus)?
For a nice, inexpensive book, there is Introduction to Analysis by
Rosenlicht. It is published by Dover. The "classic" in the field is
Principles of Mathematical Analysis by Rudin. However, the ability to
use it as an introduction is a bit questionable. Check it out for
yourself.
Paul Guertin
> can anyone recommend a book for an introduction to analysis (epsilon delta
> advanced calculus)?
I really enjoyed "Calculus" by Michael Spivak. Despite its title,
it's really an analysis book. Get the answer book too -- there's
lots of meat in the exercices.
Paul Guertin
p...@sff.net
Michael J Hardy
> can anyone recommend a book for an introduction to analysis
> (epsilon delta advanced calculus)?
That depends on what you're ready for. For Rudin's _Principles_
_of_Mathematical_Analysis_, you need to know how to write and under-
stand rigorous proofs, and it's a lot of work to go through the
exercises. Spivak's unusual calculus text is much less demanding
prerequisite-wise, and is very good. -- Mike Hardy
Charlie Johnson
also recommend Stephen Lay's book "Introduction to Analysis". He introduces
proofs, then goes on to develop basic analysis. Not many people seem to
know of this book, but it is very good. It will prepare you for Rudin's
books. He also has answers in the back of the book, which may or may not be
to your liking depending on your "maturity". I have tried a lot of books on
Analysis: baby Rudin, Apostol's, Strichartz's, Rosenlicht's, Kolomorgorov
(sp ?). On the whole, for self-study, and a beginner, try Lay's book I
have also heard good things about Spivak and Courant. Check them out!
.
"Vigual" <ele...@gmu.edu> wrote in message
news:5BTR9.101310$I23.6...@news1.east.cox.net...
Cameron Zwarich
We used Spivak in our first semester analysis class. I didn't
particularly like it.
1) The completeness property of the reals is introduced around chapter
seven. Most introductions to real analysis have it in the first
chapter. There are simpler motivations for the idea than the
intermediate and extreme value theorems.
2) Spivak hates sequneces. He really does. He doesn't cover them until
he needs them for series. This doesn't only leave the reader slightly
unprepared; it also obscures the proofs of several important theorems
earlier in the book. The Bolzano-Weierstrass Theorem makes many things
trivial.
Ironically, our teacher taught everything in the same order as Rudin,
only using Spivak for problems.
Amanda
> advanced calculus)?
I recommend Introduction to Real Analysis, by Robert Bartle and Donald
Sherbert. Though it only covers analysis on the real line, the book
provides an excelent treatment of the basic concepts used in general
analysis and prepares you for more advanced books.
Amanda
wgempel
I am working on Bartle and Sherbert now on my own. I like the
presentation specifically because it is very concrete. Occassionally
the early exercises seem to me to ask for a proof of a definition.
Maybe that is just their way of gently introducing proofs. The reason
I am using this text is because I am interested in the
Henstock/Kurzweil integral presented in Chapter 10. This is an
integral supposedly more general than Lebesgue that can be defined
with a slight alteration of Riemann. I am only in chapter 4, so I
can't give a full review, but so far I find the experience to be fun.
There are many cool little techniques that I didn't learn in high
school or calculus, but are too simple for most analysis books to
cover. Such as how to convert any repeating decimal into a fraction
(please don't laugh, I got 780 on my math SAT without knowing that).
If you went to a typical American H.S. and had a typical American
Calculus course, this book can fill in a lot of holes. Another plus,
this book has Cauchy's first proof of the uncountability of the reals
(By the nested interval property) along with the diagonal slash
argument. If you have trouble with the diagonal slash an alternate
viewpoint can be helpful.
Does anyone here have a negative opinion of this text?
wgempel
[snip]
> this book has Cauchy's first proof of the uncountability of the reals
> (By the nested interval property) along with the diagonal slash
> argument. If you have trouble with the diagonal slash an alternate
> viewpoint can be helpful.
Obviously, I was refering to arguments by Cantor, not Cauchy.
Sorry.