الصفحة 11
الصفحة 11
Introduction to Singularities and Deformations
This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete.
Introduction to Scientific Programming with Python
This book offers an initial introduction to programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming.
Introduction to Probability with Statistical Applications
This textbook is an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. Main statistical concepts considered are point and interval estimates, hypothesis testing, power function, various statistical tests: z, t, chi-square and Kolmogorov-Smirnov.
Introduction to Plane Algebraic Curves
This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed.IT focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading.
Introduction to Partial Differential Equations: A Computational Approach
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.
Introduction to Numerical Methods in Differential Equations
This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets.
Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Introduction to Mathematical Systems Theory : Linear Systems, Identification and Control
This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The focus is on discrete time systems, which are the most relevant in business applications, as opposed to continuous time systems, requiring less mathematical preliminaries. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.
Introduction to Lie Algebras
This book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics.The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality.
Introduction to Empirical Processes and Semiparametric Inference
This book provides a self-contained, linear, and unified introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. The targeted audience includes statisticians, biostatisticians, and other researchers with a background in mathematical statistics who have an interest in learning about and doing research in empirical processes and semiparametric inference but who would like to have a friendly and gradual introduction to the area. The book can be used either as a research reference or as a textbook. The level of the book is suitable for a second year graduate course in statistics or biostatistics, provided the students have had a year of graduate level mathematical statistics and a semester of probability.
Introduction to Complex Analysis in Several Variables
This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem.
Introduction to Classical Geometries
This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions.
Introduction to Calculus and Classical Analysis
This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This second edition includes corrections as well as some additional material.The text is completely self-contained and starts with the real number axioms; the integral is defined as the area under the graph, while the area is defined for every subset of the plane; there is a heavy emphasis on computational problems.
Introduction to Bayesian Scientific Computing : Ten Lectures on Subjective Computing
Inverse problems are closely related to statistical inference problems, where the observations are used to infer on an underlying probability distribution. This connection between statistical inference and inverse problems is a central topic of the book. Inverse problems are typically ill-posed: small uncertainties in data may propagate in huge uncertainties in the estimates of the unknowns. To cope with such problems, efficient regularization techniques are developed in the framework of numerical analysis. The counterpart of regularization in the framework of statistical inference is the use prior information.
Introduction to Applied Optimization
This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter.
Introduction aux méthodes numériques
Au cours de l’histoire, les méthodes de calcul ont été l’expression de pratiques sans cesse renouvelées. Le développement de l’informatique a largement contribué à une rapide progression de l’ensemble des techniques numériques. En moins de cinquante ans, le paysage algorithmique a été complètement transformé. Aujourd’hui, la plupart des logiciels que nous employons font appel à des méthodes de plus en plus efficaces. Dans les simulations, comme dans les modélisations, l’analyse numérique occupe une place centrale. Composants essentiels de la vie scientifique, les méthodes et algorithmes qui sont présentés ici, illustrés par de nombreux exemples, sont mis à la portée de tous. De l’approximation polynomiale à la résolution d’équations aux dérivées partielles par des méthodes de différences, de volumes et d’éléments finis, ce livre offre un large panorama des méthodes numériques actuelles.
Introduction à la résolution des systèmes polynomiaux = Introduction to solving polynomial systems
This book is an introduction to algebraic methods for solving this type of equations. We show how the geometry of algebraic varieties defined by these equations, their dimension, their degree, or their components can be deduced from the properties of the corresponding quotient algebras. For this, we approach methods of effective algebraic geometry, such as Grobner bases, resolution by eigenvalues and vectors, resultants, bezoutians, duality, Gorenstein algebras and algebraic residues.
Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1
This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half contains a complete account of the technique initiated by Swinnerton-Dyer in 1993 for studying rational points on pencils of curves of genus 1, while incorporating and generalising most of its subsequent refinements. The second half, which builds upon the first, is devoted to quartic del Pezzo surfaces and higher-dimensional intersections of two quadrics.
Interpolation, Schur Functions and Moment Problems
In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
International Symposium on Mathematics, Quantum Theory, and Cryptography ; Proceedings of MQC 2019
This book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan.
