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Decidable Theories

Decidable Theories ab 42.99 € als Taschenbuch: Vol. 2: The Monadic Second Order Theory of All Countable Ordinals. Auflage 1973. Aus dem Bereich: Bücher, Taschenbücher, Naturwissenschaft,

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Symbolic Dynamics

Symbolic Dynamics ab 90.99 € als Taschenbuch: One-sided Two-sided and Countable State Markov Shifts. Softcover reprint of the original 1st ed. 1998. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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Combinatorics and Graph Theory

These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline. This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline.The second edition includes many new topics and features: New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. New material on partitions, multinomial coefficients, and the pigeonhole principle. Expanded coverage of Pólya Theory to include de Bruijn s method for counting arrangements when a second symmetry group acts on the set of allowed colors. Topics in combinatorial geometry, including Erdos and Szekeres development of Ramsey Theory in a problem about convex polygons determined by sets of points. Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. Numerous new exercises throughout the book.About the First Edition:". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked." Ioana Mihaila, MAA Reviews

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Ultrafilters and Topologies on Groups

This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters.The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5, introduces to topological groups and ultrafilters insofar as the semigroup operation on ultrafilters is not required. Constructions of some important topological groups are given. In particular, that of an extremally disconnected topological group based on a Ramsey ultrafilter. Also one shows that every infinite group admits a nondiscrete zero-dimensional topology in which all translations and the inversion are continuous.In the second part, Chapters 6 through 9, the Stone-Cêch compactification betaG of a discrete group G is studied. For this, a special technique based on the concepts of a local left group and a local homomorphism is developed. One proves that if G is a countable torsion free group, then betaG contains no nontrivial finite groups. Also the ideal structure of betaG is investigated. In particular, one shows that for every infinite Abelian group G, betaG contains 22 G minimal right ideals.In the third part, using the semigroup betaG, almost maximal topological and left topological groups are constructed and their ultrafilter semigroups are examined. Projectives in the category of finite semigroups are characterized. Also one shows that every infinite Abelian group with finitely many elements of order 2 is absolutely -resolvable, and consequently, can be partitioned into subsets such that every coset modulo infinite subgroup meets each subset of the partition.The book concludes with a list of open problems in the field. Some familiarity with set theory, algebra and topology is presupposed. But in general, the book is almost self-contained. It is aimed at graduate students and researchers working in topological algebra and adjacent areas.

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Price: 51.99 EUR excl. shipping