Timeline for Text for an introductory Real Analysis course.
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Sep 4, 2018 at 21:49 | comment | added | user46189 | Rudin was the book from which my introductory analysis course was taught. I do admit that Rudin would be rather callous if the students had no background with proof and rigor. And I say Rudin's chapters on multi-variables, differential forms, and the Lebesgue Theory are rather rushed. But the criticism against his proofs is unfair. Although they are unmotivated, they are either follow-your-nose or easily reverse engineered by keeping in mind what you want or what you want to avoid. "Why is this proof easy to reconstruct?" is a question I don't mind asking myself reading through a text though. | |
| Dec 2, 2017 at 9:09 | comment | added | The Mathemagician | @FrankScience I can't speak for Glenn, but I sure as hell didn't. I didn't understand forms and their integrals until I began a serious study of differential manifolds using Conlon's DIFFERENTIABLE MANIFOLDS and Munkres' ANALYSIS ON MANIFOLDS. Then I went back to Rudin,reread it and wondered what the hell he was thinking when he wrote this train wreck. | |
| S Nov 30, 2015 at 16:50 | history | suggested | foobar | CC BY-SA 3.0 |
added list of books, spaces after commas
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| Nov 30, 2015 at 16:36 | review | Suggested edits | |||
| S Nov 30, 2015 at 16:50 | |||||
| Jul 20, 2014 at 4:20 | comment | added | user20948 | @Glenn I'm quite curious whether you understood the statement and the proof of The Rank Theorem in multivariable calculus while reading Baby Rudin, or the introduction to differential forms and their integrals? | |
| Feb 28, 2014 at 18:07 | comment | added | Glenn | If students are floundering with the notion of proof in "baby" Rudin then I think the problem is with their curriculum and not Rudin. | |
| Oct 22, 2013 at 4:42 | review | Late answers | |||
| Oct 22, 2013 at 7:21 | |||||
| Sep 17, 2013 at 9:31 | comment | added | lightalchemist | I haven't read any of the books suggested by @AndrewL so I'm not going to comment on whether they are any good. However, I concur 100% that students entering college now are not as well prepared as those from earlier generations. Rudin is too difficult for a first course simply because they have not been prepared well enough (just look up any recent high school text). It would certainly make a great text for a follow-up course after one has acquired the fundamentals of analysis though. | |
| Aug 14, 2010 at 21:11 | comment | added | The Mathemagician | @Anonymous High school geometry is VERY poorly taught at most high schools in the US now-if,indeed,it's taught at all. The collapse of the American secondary school system has sadly affected incoming 1st year math students more then any group.We need to adjust the analysis texts accordingly.The students are NOT "dumber" then in previous generations-as a lot of better trained students snark nowadays-they're simply very poorly prepared.@Daniel Take a good,careful look at Pugh's book,especially the exercises. I think you'll find it far superior to Rudin while still remaining terse and concise. | |
| Aug 14, 2010 at 12:20 | comment | added | Daniel Miller | I have to say, that Rudin was the best thing that happened to me. While it may not be "user-friendly," it forced me to actually understand the concepts, instead of just parroting the proofs the prof did in class. | |
| Mar 11, 2010 at 4:12 | comment | added | The Mathemagician | A great deal of point set theory is covered in Pugh and done more clearly then in Rudin. I don't know where Anonymous was trained,but clearly came from a better system then most students come from. Most high schools in America in 2010 have trouble graduating students who can READ,let alone know geometry.It's easy to like slick proofs when you're experienced and well-versed in rigor.Most instructors don't remember what it was like struggling with that fundamental change in thinking that proof creates the first time.Worse,gifted students think anyone that doesn't find it easy is an imbecile. | |
| Mar 10, 2010 at 19:04 | comment | added | Anonymous | Your first sentence on Rudin's book is very bad, unfair and very likely not true. Any serious college student who approaches analysis for the first time must know what a proof is, having seen it in Euclidean Geometry back in junior middle school. And I personally like Rudin's, read it when I was still in high school and found it clear, to-the-point, and with a good supply of excellent problems. Also, one cannot fault an author for giving slick proofs. I for one prefer slick proofs over tedious, drawn-out proofs (unless they're the correct conceptual ones). | |
| Mar 10, 2010 at 18:56 | comment | added | Harry Gindi | Rudin covers some important points of point-set topology that are simply not covered in any other introductory analysis book. Students in an "honors calculus" course at the level of math 55 at Harvard (real analysis in disguise) who do not see a fairly significant portion of point-set topology by the end of the first semester are in my opinion being done a huge disservice. | |
| Mar 10, 2010 at 18:41 | history | answered | The Mathemagician | CC BY-SA 2.5 |