pugh

What pedagogy is it that Pugh (and Spivak) care enough to get right, where nearly all others fail?

But is it worth spending hundreds of hours working through Spivak and Pugh from the standpoint of developing a professional skill?

There have been a lot of implied-in-fact exceptions to the at-will doctrine (see Pugh v.

For anyone looking for a Real Analysis textbook, I’ve heard several recommendations for Pugh as an alternative to Rudin.

The Bill Pugh Singleton: Using the Holder Idiom for thread-safe instances.

In contrast, Pugh focuses on building up the surrounding constructs and techniques to the point where you can apply the same tactics to a wide variety of problems.

In the end I had to lead e Pugh and read enough to be able to ask it with the right vocabulary to make it work.

It is this: Pugh has carefully crafted his book into what I'd call a 'mind expansion tool': almost everything there is crafted to be read, internalized, and meditated on.

Well, if you really take to heart what Spivak and Pugh have to say (and are thinking hard about the problems), there is a very good chance that you will be inspired enough to do further research that will lead you to tangentially related mathematics.

Coming from very little formal math training, and trying to self-study analysis, I would bounce from Rudin if I got stuck, go to Abbott for a confidence boost, and try out some Pugh for a different viewpoint.

Here's another interesting quote about Helium: *Moses Chan, Evan Pugh Professor of Physics at Penn State, explains that the world's supply of helium is a byproduct of natural gas production, with the Texas Panhandle arguably being the helium capital of the world.

(Taking this to the extreme, Paul Halmos once pointed out that a good way to learn a great deal of mathematics is to read the first chapter of many different books.) It's certainly not the case that Spivak and Pugh are the only books out there which help you develop the "mathematical maturity" that will allow you to apply mathematics creatively in other areas.

I absolutely, positively second the recommendation of "Real Mathematical Analysis" by Charles Pugh (don't miss the advice he relates from his colleague, on pages 9&10, with the heading "Metaphor and Analogy", which could easily form the basis for a dissertation on the psychology of mathematical intuition and inspiration).

As mentioned in another subthread, Pugh's Real Mathematical Analysis is great, and better motivated than baby Rudin.

Pugh taught my ODEs course in college and basically turned it into a dynamical systems party.

If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh.