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Elementary Topology.
Textbook in Problems,
by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and
N.Y.Netsvetaev.
Configurations
of Skew Lines in the 3-Dimensional Space
by J.Viro and O.Viro
This is about links made of lines. One has to require that the lines are
not only disjoint, but also non-parallel. This gives the lines an ability
to be linked with each other. As long as the number of lines is not large (less
than 6), the linking numbers rule. Then the Jones polynomial comes.
On a horizont the Khovanov homology can be recognized...
Introductions into Topology of Real Algebraic Varieties
Dequantization of real algebraic geometry on logarithmic paper
A talk by Oleg Viro at the Third European Congress
of Mathematicians (Barcelona, 2000). It bridged patchworking and
Litvinov - Maslov dequantization of positive real numbers and started up
a broad development of Tropical geometry.
What is an Amoeba?
Notices
AMS, 49:8
(2002), 916-917, [pdf]
On Euler's footsteps,
Evgeny Shchepin's Uppsala lectures on Calculus.
During the Fall Semester of
2001 Prof. Evgeny Shchepin (Moscow Steklov Institute) gave
lectures on Calculus for an advanced group of first year
undergraduate students at Uppsala University.
The course followed the historical development of Analysis: it
started with series, but limits appeared only in the middle,
after integrals. Complex analysis appeared on an early stage motivated
by the needs of real analysis. All turns of the course are internally
motivated.
Each lecture contains something surprising. For instance, in the first
lecture it is proved that the sum of all the non-negative integer powers of
two (i.e., 1+2+4+8+16+32+...) equals -1, and a practical interpretation of
this equality is presented.