Series: Undergraduate Texts in Mathematics
2008, Approx. 200 p., Hardcover
ISBN: 978-0-387-78214-0
Due: July 2008
About this textbook
Makes some basic Lie theory accessible
Unique choice of approach and topics
Introduces an advanced topic to undergraduates, at just the right pace
Author includes exercises and examples
Until recently Lie theory has been reserved for practictioners, with no Lie theory for mathematical beginners. This book aims to fill that gap and it covers all the basics at a level that should be appropriate for junior/senior level undergraduates. The classical groups are introduced via a study of rotations in two, three, and four dimensions, which is also an appropriate place to bring in complex numbers and quaternions. From there it is only a short step to studying rotations in real, complex, and quaternion spaces of any dimension. In so doing, one has already introduced the classical simple Lie groups, in their most geometric form, using only basic linear algebra. Then calculus intervenes to find the tangent spaces of the classical groups?their Lie algebras?and to move back and forth between the group and its algebra via the log and exponential functions.
Most books at this level rely on deep ideas from outside Lie Theory, such as the inverse function theorem. However, this book actually proves simplicity of the classical Lie algebras can be done by basic matrix arithmetic, and there is an amazing elementary proof of Campbell-Baker-Hausdorff due to Eichler in 1968. The naive approach to Lie theory is due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics, particularly the results of linear algebra.
To compensate for the lack of technical power which is inherent to the naive approach, the end-of-chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. While naive methods might not afford the same insights as more sophisticated methods, they do offer another insight that is often undervalued?some important theorems are not as difficult as they look!
Table of contents
Preface.- Geometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of lie algebras.- The matrix logarithm.- Topology.- Simply-connected Lie groups.- Bibliography.- Index.
Series: Universitext
2008, 350 p., Softcover
ISBN: 978-3-540-78571-2
Due: September 2008
About this textbook
The book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. The calculus is presented both for the Brownian noise and for Levy type of noise.
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions of stochastic differential equations mainly within the Brownian frame, this book has another goal: it presents the development of the theory and its use in new fields of application such as stochastic integral representations and stochastic control. The applications presented in the environment of mathematical finance include: hedging, in complete and incomplete markets, optimization in the presence of asymmetric information and also pricing and sensitivity analysis.
Besides, the book presents very new developments in anticipating calculus. Included is a presentation of forward integration originally introduced for Brownian motion and here extended to Poisson random measures, and its applications to the study of some insider trading problems.
Moreover extensions of the Malliavin calculus to the white noise framework are presented, allowing some more flexibility in the treatment of the operators and tools presented in this book.
ISBN: 9781597180405
Publication Date: 2/7/2008
Explores regression modeling of clustered or hierarchical data
Explains various models and their assumptions
Applies methods to real data using Stata and shows how to interpret the results
Contains new chapters and updates for Stata 10
Includes new exercises and data sets that span an array of disciplines
Multilevel and Longitudinal Modeling Using Stata, Second Edition discusses regression modeling of clustered or hierarchical data, such as data on students nested in schools, patients in hospitals, or employees in firms. Longitudinal data are also clustered with, for instance, repeated measurements on patients or several panel waves per survey respondent. Multilevel and longitudinal modeling can exploit the richness of such data and can disentangle processes operating at different levels.
Assuming some knowledge of linear regression, this bestseller explains models and their assumptions, applies methods to real data using Stata, and shows how to interpret the results. The applications and exercises span a wide range of disciplines, making the book suitable for courses on multilevel and longitudinal modeling in the medical, social, and behavioral sciences and in applied statistics. This extensively revised second edition includes 3 new chapters, comprehensive updates for Stata 10, 38 new exercises, and 27 new data sets.
Contents
Series: Chapman & Hall/CRC Biostatistics Series Volume: 25
ISBN: 9781584888871
Publication Date: 2/22/2008
Number of Pages: 824
Provides comprehensive coverage of the wide range of biostatistical methods used in evidence-based patient management, medical research, and health administration
Demonstrates how biostatistics helps manage many types of medical uncertainties
Explains various statistical methods step-by-step
Contains a large number of real-world examples that elucidate the medical meaning of the results
Includes guide charts in the beginning of the book to enable immediate retrieval of statistical procedures
Emphasizing statistical concepts used in medicine, the interpretation of methods, and applications, Medical Biostatistics, Second Edition shows how biostatistical methods are important tools in managing uncertainties in medicine and the health sciences. With coverage ranging from elementary topics, such as mean and standard deviation, to advanced approaches, such as logistic regression and multivariate methods, this edition is even more far-reaching in scope than its predecessor.
Contents
Series: Chapman & Hall/CRC Biostatistics Series Volume: 26
ISBN: 9781420067279
Publication Date: 4/21/2008
Number of Pages: 248
Addresses DNA methylation studies using microarrays
Requires only basic knowledge of statistics and programming
Features examples based on real firsthand data
Illustrates the numerous results through graphics
Written from the perspective of an analyst who interacts closely with biology colleagues who have only minimal knowledge of statistics and programming, DNA Methylation Microarrays provides a solid understanding of methodological foundations and enables critical thinking for advanced studies. Using graphics to illustrate the results, the book presents examples based on real biological data from a variety of cellular samples with array hybridizations performed in the laboratory. It covers quality control, experimental design, normalization, significant differential methylation, clustering, dependence networks, and online annotations.
Table of Contents
Statistics. Quality Control. Experimental Design. Normalization. Significant Differential Methylation. Clustering. Classification. Dependence Networks. Online Annotations. Public Microarray Repositories. Open-source Software for Microarray Data Analysis.