Textbook, MCCME, Moscow, 2000, 300 pp., ISSBN 5-900916-57-X
(in Russian).
The book is available at the Independent
University of Moscow (B. Vlasijevskij 11, bookstore at the ground floor,
for details and to order click
here) and at the
FizMatKniga Web-Shop.
The second (electronic) edition is now available on-line.
In this edition (likewise English one) new exercises were added (mostly)
to the first half of the book, thus achieving a better balance with
the second half. Besides, some typos
and minor errors, noticed in the first edition, were corrected.
Contents
Foreword
Chapter 1
Introduction
Chapter 2
Special smooth functions on Rn
Chapter 3
Algebras and points
Chapter 4
Smooth manifolds (algebraic definition)
Chapter 5
Charts and atlases
Chapter 6
Smooth maps
Chapter 7
Equivalence of coordinate and algebraic definitions
Chapter 8
Spectra and ghosts
Chapter 9
Differential calculus as an aspect of a commutative algebra
Chapter 10
Smooth bundles
Chapter 11
Vector bundles and projective modules
Afterword
Appendix. A. M. Vinogradov
The observability principle, the set theory, and
"foundations of mathematics"
