Whittaker-Watson or Rudin: Which is the better book for self-studying analysis?

[jk]

I have an undergraduate degree in physics and am looking to go to graduate school in math (for a Masters) in the next couple of years. I have been out of school almost a decade and half but I recently took a couple of classes at my alma mater to refresh my musty mind: a course in Advanced Calculus taught using the Moore Method (which I can't recommend highly enough -I wish all Math classes were taught this way) and a year long Advanced Linear Algebra at the senior/beginning graduate level.
I still have another year or so before I can enroll full time in school and I am planning to use that time for some self study. I want to study analysis and I am torn between Whitaker Watson and baby Rudin. WW has been on my todo list for fifteen years so I really want to get it done. Plus its a good book for those interested in applications. I also want to read Rudin since it is a good introduction to the modern language of analysis. My question is which one should I read first?

 

[snipez90]

Um Whittaker looks like it starts with complex analysis and then moves onto special functions. Probably best to get Rudin under your belt unless you want to learn real and complex analysis simultaneously.

 

[mathwonk]

i think if my goal were to read those two books, i would probably read rudin first. but it would make interesting reading to alternate between them as suitable.

 

[jk]

Thanks for the quick replies. I had one semester real analysis 15 years ago but I hardly remember any of it now. I will start with Rudin then go to Whittaker.
If time permits, I may then move on to papa Rudin

 

[jk]

On a somewhat tangential topic, are there any schools that use the Moore Method heavily?

 

[mathwonk]

I have only heard of it being used in the past, first at Texas where Moore was I think, and then at a few schools where his own students taught, such as University of Georgia in the 1970's, and maybe Utah, also a long time ago. Such classes seem limited to subjects like point set topology where the subject is very basic and only a few definitions are needed, and there is not much content to cover. Of course it would work with elementary number theory too for the same reasons. But the need to reinvent the wheel makes them move really slowly. The students emerge with a deep grasp of a very few things and a strengthened ability to do proofs. The teacher also gets a sense of which students could do research, but the courses don't cover much content. At least that's my impression. They also require really a lot of work from the students who must be very committed. I am also curious to know if the method is still used.

 

[mathwonk]

Moore's method apparently only works well if the instructor is good at it. I once heard Moore's secret described simply as "he was just so PLEASED when you presented a good proof." Here is a description from graduates of the method:

"The Motivation in Moore's system was provided partly by the student's curiosity and sense of intellectual play. Good-natured competition was also a motivation. Capping everything for Moore's students was his great respect for them and for their ideas. This led to a sense of common intellectual striving that served his students well in their careers.

Martin Ettlinger, who took an MA with Moore before going on to graduate study at Harvard and a distinguished career as a plant products chemist, recently described the atmosphere in Moore's classes as extraordinary. Every student's ideas were listened to carefully and critically. No sniping or discourtesy was tolerated, but every idea was tested before being accepted. Ettlinger said the only other place he encountered this atmosphere was as a Junior Fellow of Harvard's Society of Fellows.

The Discovery in Moore's classes took place mainly outside the classroom, while Presentation lay at the heart of the classroom experience. Moore would ask one of the students whether he or she could present the next item at the board. If the answer was "Yes, sir," the student became the lecturer. Fellow students formed an interested and critical audience. The experience of seeing your dream proof collapse under careful examination by your fellows might be chastening, but the success of a difficult matter disposed of nicely was gratifying."the site for this quote has a few examples of current Moore type teachers:

http://legacyrlmoore.org/reference/FOCUS.htmloops i guess we are off - topic.

 

[jk]

The one class I had that was taught using this method was advanced calculus at the University of Houston. I know the instructor also teaches all his classes using the Moore method so I know it can successfully be applied to a variety of topics. The pace is slow in the beginning but it gets faster as the students get into it. It is the most intellectually exhilarating math class I have ever taken. You emerge from the experience with a confidence that you can tackle any problem. Mathematics becomes a living discipline that you "create", instead of something that is handed to you. It was fascinating to see the differences in the ways different students proved the same thing. Another interesting aspect was that the class wad composed of students with different backgrounds: from old graduates like me to math juniors to a few engineering types. Most did very well and the atmosphere was very collegial even if there was some element of competition. You really get to absorb the spirit of mathematical practice