Cohomology of Groups

Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
ISBN: 9781468493276
Release Date: 2012-12-06
Genre: Mathematics

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Manifolds and Differential Geometry

Author: Jeffrey Marc Lee
Publisher: American Mathematical Soc.
ISBN: 9780821848159
Release Date: 2009
Genre: Mathematics

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hyper-surfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.

The Geometry of Algebraic Cycles

Author: Reza Akhtar
Publisher: American Mathematical Soc.
ISBN: 9780821851913
Release Date: 2010
Genre: Mathematics

The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.

A Concrete Introduction to Higher Algebra

Author: Lindsay N. Childs
Publisher: Springer Science & Business Media
ISBN: 9780387745275
Release Date: 2008-11-26
Genre: Mathematics

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

Books in Print

ISBN: STANFORD:36105015915866
Release Date: 1989
Genre: American literature

Local Cohomology

Author: M. P. Brodmann
Publisher: Cambridge University Press
ISBN: 9780521513630
Release Date: 2012-11-15
Genre: Mathematics

This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum-Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton-Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over 300 exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.

Data Mining in Biomedicine

Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
ISBN: 9780387693194
Release Date: 2008-12-10
Genre: Medical

This volume presents an extensive collection of contributions covering aspects of the exciting and important research field of data mining techniques in biomedicine. Coverage includes new approaches for the analysis of biomedical data; applications of data mining techniques to real-life problems in medical practice; comprehensive reviews of recent trends in the field. The book addresses incorporation of data mining in fundamental areas of biomedical research: genomics, proteomics, protein characterization, and neuroscience.

Brilliant Light in Life and Material Sciences

Author: Vasili Tsakanov
Publisher: Springer Science & Business Media
ISBN: 9781402057243
Release Date: 2007-09-18
Genre: Science

This book contains an excellent overview of the status and highlights of brilliant light facilities and their applications in biology, chemistry, medicine, materials and environmental sciences. Overview papers on diverse fields of research by leading experts are accompanied by the highlights in the near and long-term perspectives of brilliant X-Ray photon beam usage for fundamental and applied research.

Principles of Stem Cell Biology and Cancer

Author: Tarik Regad
Publisher: John Wiley & Sons
ISBN: 9781118670583
Release Date: 2015-04-01
Genre: Science

Principles of Stem Cell Biology and Cancer: Future Applications and Therapeutics Tarik Regad, The John van Geest Cancer Research Centre, Nottingham Trent University, UK, Thomas J. Sayers, Centre for Cancer Research, National Cancer Institute, Frederick, USA and Robert Rees The John van Geest Cancer Research Centre, Nottingham Trent University, UK The field of cancer stem cells is expanding rapidly, with many groups focusing on isolating and identifying cancer stem cell populations. Although some progress has been made developing efficient cancer therapies, targeting cancer stem cells remains one of the important challenges facing the growing stem cell research community. Principles of Stem Cell Biology and Cancer brings together original contributions from international experts in the field to present the very latest information linking stem cell biology and cancer. Divided into two parts, the book begins with a detailed introduction to stem cell biology with a focus on the characterization of these cells, progress that has been made in their identification, as well as future therapeutic applications of stem cells. The second part focuses on cancer stem cells and their role in cancer development, progression and chemo-resistance. This section of the book includes an overview of recent progress concerning therapies targeting cancer stem cells. Features: An authoritative introduction to the link between stem cell biology and cancer. Includes contributions from leading international experts in the field. Well-illustrated with full colour figures throughout. This book will prove an invaluable resource for basic and applied researchers and clinicians working on the development of new cancer treatments and therapies, providing a timely publication of high quality reviews outlining the current progress and exciting future possibilities for stem cell research.

Classical and Quantum Cosmology

Author: Gianluca Calcagni
Publisher: Springer
ISBN: 9783319411279
Release Date: 2017-02-02
Genre: Science

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.

Mathematics Under the Microscope

Author: Alexandre Borovik
Publisher: American Mathematical Soc.
ISBN: 9780821847619
Release Date: 2010
Genre: Mathematics

The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word ``microscope'' in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical ``memes'' (genes of culture) to an unusual life of a Hollywood star. --Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

The Scientific Study of General Intelligence

Author: Helmuth Nyborg
Publisher: Elsevier
ISBN: 0080516661
Release Date: 2003-07-11
Genre: Psychology

This book celebrates two triumphs in modern psychology: the successful development and application of a solid measure of general intelligence; and the personal courage and skills of the man who made this possible - Arthur R. Jensen from Berkeley University. The volume traces the history of intelligence from the early 19th century approaches, to the most recent analyses of the hierarchical structure of cognitive abilities, and documents the transition from a hopelessly confused concept of intelligence to the development of an objective measure of psychometric g. The contributions illustrate the impressive power g has with respect to predicting educational achievement, getting an attractive job, or social stratification. The book is divided into six parts as follows: Part I presents the most recent higher-stream analysis of cognitive abilities, Part II deals with biological aspects of g, such as research on brain imaging, glucose uptake, working memory, reaction time, inspection time, and other biological correlates, and concludes with the latest findings in g-related molecular genetics. Part III addresses demographic aspects of g, such as geographic-, race-, and sex-differences, and introduces differential psychological aspects as well. Part IV concentrates on the g nexus, and relates such highly diverse topics as sociology, genius, retardation, training, education, jobs, and crime to g. Part V contains chapters critical of research on g and its genetic relationship, and also presents a rejoinder. Part VI looks at one of the greatest contemporary psychologists, Professor Emeritus Arthur R. Jensen as teacher and mentor.