Textbook, MCCME, Moscow, 2000, 300 pp., ISSBN 5-900916-57-X
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
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.
Special smooth functions on Rn
Algebras and points
Smooth manifolds (algebraic definition)
Charts and atlases
Equivalence of coordinate and algebraic definitions
Spectra and ghosts
Differential calculus as an aspect of a commutative algebra
Vector bundles and projective modules
Appendix. A. M. Vinogradov
The observability principle, the set theory, and
"foundations of mathematics"