“…Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed. …”
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“…The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. …”
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“…This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. …”
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“…."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. …”
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“…Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. …”
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“…PRELIMINARIES Mathematical background Algebraic structures in a nutshellFinite groupsSummary and further readingExercisesBasics on complexity Complexity classesAsymptotic notation and examplesSummary and further readingExercisesCryptology: An introductionA short historical overview     Historical encryption schemes     Public-key cryptographyModern cryptologySummary and further readingExercisesPUBLIC-KEY ENCRYPTIONProvable security guarantees Public-key encryption revisitedCharacterizing secure public-key encryptionOne-way functions and random oraclesThe general Bellare-Rogaway constructionIND…”
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“…First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory…”
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“…The comprehensive review covers all precalculus topics: Algebraic Expressions, Equations, and Inequalities; Functions: Concept, Properties, and Operations; Representations of Functions: Symbolic, Graphical, and Tabular; Analytic Geometry; Trigonometry and its Applications; Functions as Models. …”
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“…Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. …”
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“…This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. …”
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“…Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. …”
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“…Given arbitrary function field k together with a fixed place \infty, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. …”
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“…In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. …”
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“…This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. …”
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“…The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians. …”
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“…Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group G. …”
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“…The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. …”
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“…The author then studies algebraic models and completeness theorems for them. …”
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“…This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics. …”
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“…The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in ReferativnyíZhurnal Matematika from mid-1982 to the end of 1985. …”
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