Series: Progress in Mathematics , Vol. 277
2010, Approx. 170 p., Hardcover
ISBN: 978-3-0346-0128-3
Due: December 2009
Winner of the Ferran Sunyer i Balaguer Prize 2009
First attempt to systematically survey the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.
Designed to rapidly guide the reader to the many areas of ongoing research in the domain
Provides an extensive bibliography
This book is concerned with counting rational points of bounded height on projective algebraic varieties. This is a fertile and vibrant topic that lies at the interface of analytic number theory and Diophantine geometry. The goal of the book is to give a systematic account of the field with an emphasis on the role that analytic number theory has to play in its development.
Graduate students; mathematicians with an interest in analytic number theory and Diophantine geometry
Preface.- 1. Introduction.- 2. The Manin Conjectures.- 3. The Dimension Growth Conjecture.- 4. Uniform Bounds for Curves and Surfaces.- 5. A1 Del Pezzo Surface of Degree 6.- 6. D4 Del Pezzo Surface of Degree 3.- 7. Siegel's Lemma and Non-singular Surfaces.- 8. The Hardy-Littlewood Circle Method.- Bibliography.- Index.
Series: Contributions to Statistics
2010, Approx. 300 p., Softcover
ISBN: 978-88-470-1385-8
Due: February 2010
The book offers a wide variety of statistical methods and is addressed to statisticians working at the forefront of statistical analysis.
The last years have seen the advent and development of many devices able to record and store an always increasing amount of complex and high dimensional data; 3D images generated by medical scanners or satellite remote sensing, DNA microarrays, real time financial data, system control datasets, ....
The analysis of this data poses new challenging problems and requires the development of novel statistical models and computational methods, fueling many fascinating and fast growing research areas of modern statistics. The book offers a wide variety of statistical methods and is addressed to statisticians working at the forefront of statistical analysis.
Academic, Corporate, Hospital Libraries, Scientists, Researchers, Graduates, Practitioners, Professionals and Undergraduates
Advanced Lectures in Mathematics
2009. Approx. 300 pp. Softc.
ISBN: 978-3-8348-0676-5
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. The two example classes of Hilbert modular surfaces and determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The book consists of an introductory volume on schemes and a second volume on the cohomology of schemes.
The first volume requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix.
Hardback (ISBN-13: 9780980232707)
This second edition has two parts. The first part is the complete classic by Gilbert Strang and George Fix, first published in 1973. The original book demonstrates the solid mathematical foundation of the finite element idea, and the reasons for its success. The second part is a new textbook by Strang. It provides examples, codes, and exercises to connect the theory of the Finite Element Method directly to the applications. The reader will learn how to assemble the stiffness matrix K and solve the finite element equations KU=F. Discontinuous Galerkin methods with a numerical flux function are now included. Strang's approach is direct and focuses on learning finite elements by using them.
* Updated second edition of a popular and successful graduate text on the
Finite Element Method * Suitable for postgraduate teaching as well as a
reference for professionals * Includes problem sets for teaching and MATLAB
codes
Introduction to the second edition; Foreword to the 1997 edition; Preface; Part I: 1. An introduction to the theory; A summary of the theory; 3. Approximation; 4. Variational crimes, 5. Stability; 6. Eigenvalue problems; 7. Initial-value problems; 8. Singularities; Bibliography; Index of notations; Index; Part II: 9. Finite elements in one dimension; 10. The finite element method in 2D and 3D; 11. Errors in projections and eigenvalues; 12. Mixed finite elements: velocity and pressure; Appendix A. Discontinuous Galerkin methods; Appendix B. Fast Poisson solvers; Index for chapters 9-12 and appendices A and B.
Hardback (ISBN-13: 9780980232714)
This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book’s tried and tested approach is direct, offering practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang’s 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned.
* Strang’s online lectures and learning resources freely available via
http://web.mit.edu/18.06/www/ * Gives MATLAB code to implement the key
algorithms * Teaches by inspiration not repetition
1. Introduction to Vectors: 1.1 Vectors and linear combinations; 1.2 Lengths and dot products; 1.3 Matrices; 2. Solving Linear Equations: 2.1 Vectors and linear equations; 2.2 The idea of elimination; 2.3 Elimination using matrices; 2.4 Rules for matrix operations; 2.5 Inverse matrices; 2.6 Elimination = factorization: A = LU; 2.7 Transposes and permutations; 3. Vector Spaces and Subspaces: 3.1 Spaces of vectors; 3.2 The nullspace of A: solving Ax = 0; 3.3 The rank and the row reduced form; 3.4 The complete solution to Ax = b; 3.5 Independence, basis and dimension; 3.6 Dimensions of the four subspaces; 4. Orthogonality: 4.1 Orthogonality of the four subspaces; 4.2 Projections; 4.3 Least squares approximations; 4.4 Orthogonal bases and Gram-Schmidt; 5. Determinants: 5.1 The properties of determinants; 5.2 Permutations and cofactors; 5.3 Cramer's rule, inverses, and volumes; 6. Eigenvalues and Eigenvectors: 6.1 Introduction to eigenvalues; 6.2 Diagonalizing a matrix; 6.3 Applications to differential equations; 6.4 Symmetric matrices; 6.5 Positive definite matrices; 6.6 Similar matrices; 6.7 Singular value decomposition (SVD); 7. Linear Transformations: 7.1 The idea of a linear transformation; 7.2 The matrix of a linear transformation; 7.3 Diagonalization and the pseudoinverse; 8. Applications: 8.1 Matrices in engineering; 8.2 Graphs and networks; 8.3 Markov matrices, population, and economics; 8.4 Linear programming; 8.5 Fourier series: linear algebra for functions; 8.6 Linear algebra for statistics and probability; 8.7 Computer graphics; 9. Numerical Linear Algebra: 9.1 Gaussian elimination in practice; 9.2 Norms and condition numbers; 9.3 Iterative methods for linear algebra; 10. Complex Vectors and Matrices: 10.1 Complex numbers; 10.2 Hermitian and unitary matrices; 10.3 The fast Fourier transform; Solutions to selected exercises; Matrix factorizations; Conceptual questions for review;
This book aims to present a new approach called Flow Curvature Method that
applies Differential Geometry to Dynamical Systems. Hence, for a trajectory
curve, an integral of any n-dimensional dynamical system as a curve in
Euclidean n-space, the curvature of the trajectory * or the flow * may
be analytically computed. Then, the location of the points where the curvature
of the flow vanishes defines a manifold called flow curvature manifold.
Such a manifold being defined from the time derivatives of the velocity
vector field, contains information about the dynamics of the system, hence
identifying the main features of the system such as fixed points and their
stability, local bifurcations of codimension one, center manifold equation,
normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).
In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Differential Equations
Dynamical Systems
Invariant Sets
Local Bifurcations
Slow-Fast Dynamical Systems
Integrability
Differential Geometry
Inverse Problem
Invariant Sets * Integrability
Slow-Fast Dynamical Systems * Singularly Perturbed Systems
Readership: Graduate students, researchers and academics in nonlinear dynamics.
340pp Pub. date: Apr 2009
ISBN 978-981-4277-14-3