Summary
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p 2, as well as Hilbertfs irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of regular extensions of Q(T). While proofs are not carried out in full detail, the book contains a number of examples, exercises, and open problems
Details
ISBN: 978-1-56881-412-4
Year: 2007
Format: Hardcover
Pages: 120
Reviews
This is a very stimulating text, which c will attract mathematicians working in group theory, number theory, algebraic geometry, and complex analysis.
*Zentralblatt fur Mathematik
This small book contains a nice introduction to some classical highlights and some recent work on the inverse Galois theory problem. The topics and main theorems are carefully chosen and composed in a masterly manner.
*Mathematical Reviews
ISBN: 978-1-84265-471-2
Publication Year: Forthcoming 2008
Pages: 350
Binding: Hard Back
Dimension: 185mm x 240mm
About the book
Applied Time Series: Analysis and Forecasting provides the theories methods and tools for necessary modeling and forecasting of time series. It includes a complete theoretical development of univariate time series models with each step demonstrated with an analysis of real time data series. The result is clear presentation, quantified subjective judgment derived from selected models applied to time series observations. Utilizing real time series to demonstrate theoretical Approaches, the author explore diverse aspects of time series, including how to identify structure, explain observed behaviour, model structures and behaviours, and interpret analysis to make informed forecast. The book also illustrates concepts such as components decomposition, fundamental model form such as trends cycles seasonality and practical requirement.
Table of content
Scope of the Book / Analysis of Time Series / Classical Time Series Decomposition / Exponential Smoothing Method / Stationary & Nonstationary Time Series / Stationary Stochastic Processes / The Box-Jenkins Arima Methodology / Model Identification and Diagnostics Checking / Applications of Box-Jenkins Methodology / Recursive Estimation of Time Series Models / Recursive Estimation and Time-Varying Parameter / Implementation of Recursive Methods in Excel Spread Sheet.
Audience
Undergraduate ? Postgraduate Students, Researchers & Professionals within business, statistics, economics, engineering, and operations research program
1968; 519 pp; hardcover
ISBN-10: 0-8218-4342-7
ISBN-13: 978-0-8218-4342-0
The theory of finite simple groups enjoyed a period of spectacular activity in the 1950s and 1960s. The first edition of Gorenstein's book was published in 1968, at the time of some of the first major classification results. The second edition was published in 1980, when it was clear that the classification was understood and the proof was within reach. Gorenstein's treatment of the subject proved prescient, as many of the developments between the two editions could be seen as continuations of the material in the book. Even now, the book remains one of the best sources for an introduction to finite groups and the classification of the simple groups. Gorenstein's insight provides a guiding light through the many pages that have been dedicated to the proof.
Readership
Undergraduates, graduate students, and research mathematicians interested in finite groups and the classification of the simple groups.
Table of Contents
Part I: Methods
Preliminaries
Some basic topics
Representations of groups
Character theory
Groups of prime power order
Solvable and $\pi$-solvable groups
Fusion, transfer, and $p$-factor groups
$p$-constrained and $p$-stable groups
Groups of even order
Part II: Applications
Fixed-point-free automorphisms
The Hall-Higman theorem
Groups with generalized quaternion Sylow 2-subgroups
Zassenhaus groups
Groups in which centralizers are nilpotent
Groups with self-centralizing Sylow 2-subgroups of order 4
Part III: General Classification Problems
Simple groups of low rank
The known simple groups
Bibliography
List of symbols
Index
CBMS Issues in Mathematics Education, Volume: 14
2007; 223 pp; softcover
ISBN-10: 0-8218-4194-7
ISBN-13: 978-0-8218-4194-5
University-level mathematicians--whether focused on research or teaching--recognize the need to develop effective ways for teaching undergraduate mathematics. The Mathematics Department of the Korea Advanced Institute of Science and Technology hosted a symposium on effective teaching, featuring internationally distinguished researchers deeply interested in teaching and mathematics educators possessing established reputations for developing successful teaching techniques. This book stems from that symposium.
The book deals with teaching mathematics, a core activity of the contemporary university. It is suitable for the library of every university and mathematician. It features a broad range of topics (technology, pedagogy, philosophy, course content) of interest and value to all who teach university mathematics. This is one of the few books dealing with this essential subject.
The papers describe many different questions of teaching university mathematics. How do we teach about proof? How can we use technology in presenting mathematics? What are key issues of teaching mathematics to students from other disciplines? How do we better equip teaching assistants and new faculty?
Readers keen to learn from the experience of others in teaching university mathematics will benefit from this book. Department heads will find valuable teaching approaches for their faculty.
This series is published in cooperation with the Mathematical Association of America.
Readership
Research mathamaticians interested in teaching and mathematics education.
Table of Contents
K. H. Ko -- Mathematics in general education at KAIST
D. Hughes Hallett -- Harnessing the enthusiasm of our best and brightest students for mathematics
T. Banchoff -- Interactive geometry and multivariable calculus on the internet
C. Stevens -- Helping new mathematics faculty to develop into successful teachers and scholars
W. G. McCallum -- Computer algebra and human algebra
S. Friedberg -- Teaching mathematics graduate students to teach: An international perspective
E. Neuwirth -- Computers supporting mathematical insight--two case studies
T. M. Mills and P. Sullivan -- Mathematics--at your service
H. Arikan -- A leverage in learning
O. N. Kwon -- Towards inquiry-oriented mathematics instruction in the university
W. Page -- The influence of technology on mathematics instruction: Concerns and challenges
C.-K. Li -- Research experiences with undergraduates: A discussion from the mathematical educational point of view
J. Sandefur -- Problem solving: What I have learned from my students
U. Kortenkamp -- Guidelines for using computers creatively in mathematics education
L. H. Seitelman -- Suggestions from the real world on improving math education
R. S. Smith -- Spreadsheets in the mathematics classroom
A. Stanoyevitch -- Incorporating MATLABR into university mathematics programs
E. A. Varbanova -- A CAS supported environment for learning and teaching calculus
G. E. Uchida -- Experience with blended learning: IT support inside the classroom and beyond
S.-O. Kim -- On the mathematics courses for social science majors
S. O. Shilova and N. V. Shilov -- On mathematical contents of computer science contests
M. Narita -- Curriculum for teaching how mathematics is applied to real world in teacher education course at a Japanese college
D. Arganbright, E. Neuwirth, and R. S. Smith -- Workshop in Excel
Mathematical World, Volume: 26
2007; 134 pp; softcover
ISBN-10: 0-8218-4323-0
ISBN-13: 978-0-8218-4323-9
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confocal ellipses.
The book demonstrates the advantage of purely geometric methods of studying conics. It contains over 50 exercises and problems aimed at advancing geometric intuition of the reader. The book also contains more than 100 carefully prepared figures, which will help the reader to better understand the material presented.
Readership
Undergraduate and graduate students interested in geometry.
Table of Contents
Elementary properties of curves of second degree
Some results from classical geometry
Projective properties of conics
Euclidean properties of curves of second degree
Solutions to the problems
Bibliography
Index