Mathematics. It's content, methods, and meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev, S. H.

By A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev, S. H. Gould

There is not any paintings in English that compares with this significant survey of arithmetic. Twenty leading topic parts in arithmetic are taken care of when it comes to their basic origins, and their subtle advancements, in twenty chapters by means of eighteen extraordinary Soviet mathematicians. every one quantity of the second one variation has been amended to incorporate the entire index to the set.

Show description

Read or Download Mathematics. It's content, methods, and meaning PDF

Best science & mathematics books

Semi-Inner Products and Applications

Semi-inner items, that may be clearly outlined normally Banach areas over the genuine or advanced quantity box, play a big function in describing the geometric houses of those areas. This new publication dedicates 17 chapters to the examine of semi-inner items and its purposes. The bibliography on the finish of every bankruptcy incorporates a record of the papers brought up within the bankruptcy.

Plane Elastic Systems

In an epoch-making paper entitled "On an approximate resolution for the bending of a beam of oblong cross-section lower than any method of load with targeted connection with issues of centred or discontinuous loading", acquired by means of the Royal Society on June 12, 1902, L. N. G. FlLON brought the concept of what was once as a consequence referred to as by means of LovE "general­ ized aircraft stress".

Discrete Hilbert-Type Inequalities

In 1908, H. Wely released the well-known Hilbert’s inequality. In 1925, G. H. Hardy gave an extension of it via introducing one pair of conjugate exponents. The Hilbert-type inequalities are a extra extensive type of research inequalities that are together with Hardy-Hilbert’s inequality because the specific case.

Additional resources for Mathematics. It's content, methods, and meaning

Sample text

Find all such colorings. Solutions 1. Color the floor as in Fig. 7. A 4 × 1 tile always covers 0 or 2 black squares. A 2 × 2 tile always covers one black square. It follows immediately from this that it is impossible to exchange one tile for a tile of the other kind. Fig. 7 2. Any rectangle with 20 squares can be colored like a chessboard with 10 black and 10 white squares. Four of the tetrominoes will cover 2 black and 2 white squares each. The remaining 2 black and 2 white squares cannot be covered by the T-tetromino.

3 Fig. 4 Fig. 5 12. A beetle sits on each square of a 9 × 9 chessboard. At a signal each beetle crawls diagonally onto a neighboring square. Then it may happen that several beetles will sit on some squares and none on others. Find the minimal possible number of free squares. 2. Coloring Proofs 27 13. Every point of the plane is colored red or blue. Show that there exists a rectangle with vertices of the same color. Generalize. 14. Every space point is colored either red or blue. Show that among the squares with side 1 in this space there is at least one with three red vertices or at least one with four blue vertices.

Then , 1 , 2 , 3 define a tetrahedron T the remaining n − 4 planes cuts T , so that T is one of the parts, defined by the n planes. If the plane would cut the tetrahedron T , then would have to cut at least one of the edges AD, BD, CD in a point Q having an even smaller distance from than D. Contradiction. This is valid for any of the n planes. If there are vertices on both sides of a plane, at least two tetrahedra then must rest on this plane. It remains to be shown that among the n planes there are at most three, so that all vertices lie on the same side of these planes.

Download PDF sample

Rated 4.79 of 5 – based on 7 votes