This second edition of Alexander Sofier’s Geometric Etudes in Combinatorial Mathematics provides supplementary reading materials to students of all levels interested in pursuing mathematics, especially in algebra, geometry, and combinatorial geometry. Within the text, the author outlines an introduction to graph theory and combinatorics while exploring topics such as the pigeonhole principle, Borsuk problem, and theorems of Helly and Szokefalvi—Nagy.
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored.
1st published 1975, Second Printing 1978. The book contains a collection of 1351 problems (with answers) in plane and solid geometry for technical schools and colleges. The problems are of varied content, involving calculations, proof, construction of diagrams, and determination of the spatial location of geometrical points. It gives sufficient problems to meet the needs of students for practical work in geometry, and the requirements of the teacher for varied material for tests, etc.
Mathematical Problems and Puzzles from the Polish Mathematical Olympiads
This book is a translation of the second Polish edition, published in 1960, in which various improvements were made. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. The problems set at the contests require only a knowledge of school mathematics (i.e., elementary algebra, geometry and trigonometry) but are on the whole more difficult than the usual school exercises.
The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metric, the theory of Hilbert polynomials, and projective and affine geometries. This comprehensive volume is unusual in its extensive use of applications in physics to clarify each topic. This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics.
