Author: Fine Benjamin,Gaglione Anthony,Baginski Paul
Publisher: World Scientific
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography
Author: Jae Choon Cha
Publisher: American Mathematical Soc.
The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann $L2$-signature invarian
Author: George E. Martin
Publisher: Springer Science & Business Media
Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
Author: Phillip W. Bean,Jack C. Sharp,Thomas J. Sharp
Publisher: Pws Publishing Company
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
Author: Peter Fletcher,C. Wayne Patty
Publisher: Pws Pub Co
This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking.
Author: Earl William Swokowski,Jeffery Alan Cole
Publisher: Arden Shakespeare
Through eight editions, Swokowski's mathematical accuracy continues to be a trademark. Swokowski's unique problem sets present a variety of challenging and motivating exercises for students. Currently, the Seventh Edition is used at more than sixty U.S. schools.
an early functions approach
Author: W. Roy Fraser
Publisher: PWS Pub. Co.
* Features an early introduction of relations/functions and their inverses.* Emphasizes domain, range, symmetry, roots, graphs, notation, and algebra of functions throughout.* A variety of exercises with real-world applications from business, geology, archeology, and psychology.* A strong emphasis on geometry throughout, in keeping with the MCTM and AMATYC standards.
Author: American Mathematical Society