Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Mathematics. --- Convex geometry. --- Discrete geometry. --- Polytopes. --- Projective geometry. --- Convex and Discrete Geometry. --- Projective Geometry. --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Geometry, Modern --- Geometry, Plane. --- Plane. --- Plane geometry --- Convex geometry . --- Geometry --- Projective geometry --- Hyperspace --- Topology --- Combinatorial geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

Geometry. --- Mathematics --- Euclid's Elements --- Discrete groups. --- Combinatorics. --- Topology. --- Convex and Discrete Geometry. --- Polytopes. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Discrete geometry. --- Hyperspace --- Topology --- Combinatorial geometry --- Convex geometry. --- Discrete mathematics. --- Discrete Mathematics. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre).

Lie groups. --- Lie algebras. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Topological Groups. --- Group theory. --- Global differential geometry. --- Topological Groups, Lie Groups. --- Group Theory and Generalizations. --- Differential Geometry. --- Polytopes. --- Geometry, Differential --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, Topological --- Continuous groups --- Topological groups. --- Differential geometry. --- Hyperspace --- Topology --- Differential geometry