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This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. ContentsGeometry and geometric ideasIsometries in Euclidean vector spaces and their classification in ℝnThe conic sections in the Euclidean planeSpecial groups of planar isometriesGraph theory and platonic solidsLinear fractional transformation and planar hyperbolic geometryCombinatorics and combinatorial problemsFinite probability theory and Bayesian analysisBoolean lattices, Boolean algebras and Stone's theorem
Geometry --- Computer science --- Mathematics
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This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.
Infinite groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Infinite
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The Annual High School Mathematics Examination (AHSME) began as a local contest in New York City in 1950. By 1960, 150,000 students throughout the United States and Canada took the AHSME. The 1982 Examination was administered to 418,000 participants in the United States and Canada and to 20,000 students in various countries of other continents. In the United States and Canada, one use of AHSME is to select approximately one hundred participants in the U.S.A. Mathematical Olympiad, and the Olympiads are used in the selection of a student team to represent the United States in the International Mathematical Olympiad. Since the difficulty of problems appearing in the AHSME varies over a wide range, they are a valuable teaching aid for all high school students interested in mathematics.
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