On another note, the version of the inverse function theorem in the book discusses differentiability of f^{-1} only at f(x_0). In applications one would like to know that f^{-1} is differentiable on the neighbourhood V. How should one think about this discrepancy?

*[Fair enough. I’ve added a few exercises to explore these statements in the errata for the book. -T]*

I have been using your Analysis text book this semester. It has been generally great. One shortcoming I have noticed is with the multivariable section. I have found that the students need a good amount of discussions about continuity and limits. This is because some subtle issues arise; e.g., it could happen that a limit does not exist, even if it exists if one approaches on any line, or one can have a discontinuous function which is continuous in both variables x and y (if one fixes the other variable), etc.

It would be great if a chapter is devoted to discussing multivariable limits and continuity before diving into derivatives. Some examples such as xy/(x^2+y^2) or x^2y/(x^4+y^2) as (x,y)–>(0,0) would help students.

Thanks,

Masoud

University of Queensland

The only connections are: 1. The ability of our brains to work seems to depend on nature, the ability of our minds via our brains to formulate and comprehend mathematics … might do so too. 2. In physics (which is NOT the same field as maths, but has a lot of overlaps), the laws of nature seem to be governed by mathematics, which MIGHT mean, that some mathematics is embedded in nature herself. BUT that does nothing to say that mathematics comes from Nature.

Finally, Mathematics is not invented. It is a purely formal analysis of ideal structures, which cannot be subject to the arbitrary whims of people. This indicates that it is mind-independent.

]]>Do you know if the books (Analysis I & II) will be printed in the future by Springer ? If so, when ?

Thank you.

]]>i would like you to see the doubt that i have stated above because i am interested in knowing any approximation to the nth prime related to or dependent on the harmonic number. And any book about prime number ]]>

I tried to purchase your Analysis I and II (published by springer). Unfortunately, they say it is out of print. It appears it was never printed by Springer, since I cannot find it on Amazon either. This is unfortunate because I want to make it a required text for our analysis class! Of course, students have access to the electronic book through the library, but sometimes it is nice to have a physical copy to scheme through. I found scheming to be very useful when I was a student, as it led to reading sections that were not necessarily covered in class (granted I’m old-fashioned).

Best wishes,

Masoud

University of Queensland