- Table View
- List View
Lectures in Projective Geometry (Dover Books on Mathematics)
by A. SeidenbergAn ideal text for undergraduate courses in projective geometry, this volume begins on familiar ground. It starts by employing the leading methods of projective geometry as an extension of high school-level studies of geometry and algebra, and proceeds to more advanced topics with an axiomatic approach.An introductory chapter leads to discussions of projective geometry's axiomatic foundations: establishing coordinates in a plane; relations between the basic theorems; higher-dimensional space; and conics. Additional topics include coordinate systems and linear transformations; an abstract consideration of coordinate systems; an analytical treatment of conic sections; coordinates on a conic; pairs of conics; quadric surfaces; and the Jordan canonical form. Numerous figures illuminate the text.
Lectures on Advanced Topics in Categorical Data Analysis (Springer Texts in Statistics)
by Tamás RudasThis book continues the mission of the previous text by the author, Lectures on Categorical Data Analysis, by expanding on the introductory concepts from that volume and providing a mathematically rigorous presentation of advanced topics and current research in statistical techniques which can be applied in the social, political, behavioral, and life sciences. It presents an intuitive and unified discussion of an array of themes in categorical data analysis, and the emphasis on structure over stochastics renders many of the methods applicable in machine learning environments and for the analysis of big data. The book focuses on graphical models, their application in causal analysis, the analytical properties of parameterizations of multivariate discrete distributions, marginal models, and coordinate-free relational models. To guide the readers in future research, the volume provides references to original papers and also offers detailed proofs of most of the significant results. Like the previous volume, it features exercises and research questions, making it appropriate for graduate students, as well as for active researchers.
Lectures on Algebraic Topology
by Albrecht DoldSpringer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.
Lectures on Analytic Function Spaces and their Applications (Fields Institute Monographs #39)
by Javad MashreghiThe focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains.With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions.This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.
Lectures on Bifurcations, Dynamics and Symmetry
by Michael J. FieldThis book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.
Lectures on Categorical Data Analysis
by Tamás RudasThis book offers a relatively self-contained presentation of the fundamental results in categorical data analysis, which plays a central role among the statistical techniques applied in the social, political and behavioral sciences, as well as in marketing and medical and biological research. The methods applied are mainly aimed at understanding the structure of associations among variables and the effects of other variables on these interactions. A great advantage of studying categorical data analysis is that many concepts in statistics become transparent when discussed in a categorical data context, and, in many places, the book takes this opportunity to comment on general principles and methods in statistics, addressing not only the “how” but also the “why.” Assuming minimal background in calculus, linear algebra, probability theory and statistics, the book is designed to be used in upper-undergraduate and graduate-level courses in the field and in more general statistical methodology courses, as well as a self-study resource for researchers and professionals. The book covers such key issues as: higher order interactions among categorical variables; the use of the delta-method to correctly determine asymptotic standard errors for complex quantities reported in surveys; the fundamentals of the main theories of causal analysis based on observational data; the usefulness of the odds ratio as a measure of association; and a detailed discussion of log-linear models, including graphical models. The book contains over 200 problems, many of which may also be used as starting points for undergraduate research projects. The material can be used by students toward a variety of goals, depending on the degree of theory or application desired.
Lectures on Cauchy's Problem in Linear Partial Differential Equations
by Jacques HadamardWould well repay study by most theoretical physicists." -- Physics Today"An overwhelming influence on subsequent work on the wave equation." -- Science Progress"One of the classical treatises on hyperbolic equations." -- Royal Naval Scientific ServiceDelivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent.
Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)
by Dirk J. StruikElementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there.For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text -- ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Lectures on Complex Integration
by Alexander O. GogolinElena G. Tsitsishvili Andreas KomnikThe theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.
Lectures on Constructive Approximation
by Volker MichelLectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.
Lectures on Convex Geometry (Graduate Texts in Mathematics #286)
by Daniel Hug Wolfgang WeilThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Lectures on Convex Optimization: A Basic Course (Springer Optimization and Its Applications #137)
by Yurii NesterovThis book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
Lectures on Dependency: Selected Topics in Multivariate Statistics (SpringerBriefs in Statistics)
by Thorsten DickhausThis short book elaborates on selected aspects of stochastic-statistical dependencies in multivariate statistics. Each chapter provides a rigorous and self-contained treatment of one specific topic, poses a particular problem within its scope, and concludes by presenting its solution. The presented problems are not only relevant for research in mathematical statistics, but also entertaining, with elegant proofs and appealing solutions. The chapters cover correlation coefficients of bivariate normal distributions, empirical likelihood ratio tests for the population correlation, the rearrangement algorithm, covariances of order statistics, equi-correlation matrices, skew-normal distributions and the weighted bootstrap. This book is primarily intended for early-career researchers in mathematical statistics, but will also be interesting for lecturers in the field. Its goal is to rouse the reader’s interest, further their knowledge of the subject and provide them with some useful mathematical techniques.
Lectures on Elementary Mathematics (Dover Books on Mathematics)
by Joseph Louis LagrangeOne of the eighteenth century's greatest mathematicians, Lagrange made significant contributions to all fields of analysis and number theory. He survived the French Revolution to deliver these lectures in 1795 at the École Normale, a training school for teachers. An exemplar among elementary expositions, Lagrange's talks feature both originality of thought and elegance of expression.The five lectures begin with discussions of arithmetic that focus on fractions and logarithms as well as theory and applications. Subsequent talks consider algebra, with emphasis on the resolution of equations of the third and fourth degree, the resolution of numerical equations, and the employment of curves in the solution of problems. Students, teachers, and others with an interest in mathematics will find this volume a unique reading book in mathematics, with fascinating historical and philosophical remarks by a distinguished mathematician.
Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories (SpringerBriefs in Mathematical Physics #39)
by Hiro Lee TanakaThis book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
Lectures on Formal and Rigid Geometry
by Siegfried BoschThe aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Lectures on Functional Analysis and the Lebesgue Integral
by Vilmos KomornikThis textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small â,,"p spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul ErdÅ's and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
Lectures on Gaussian Processes
by Mikhail LifshitsGaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
Lectures on Geometry (UNITEXT #158)
by Lucian Bădescu Ettore CarlettiThis is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics. In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some branches of engineering and computer science. Chapter 11 may be useful as an elementary introduction to algebraic geometry for advanced undergraduate and graduate students of mathematics. Chapters 12 and 13 may be a part of a course on non-Euclidean geometry for mathematics students. Chapter 13 may be of some interest for students of theoretical physics (Galilean and Einstein’s general relativity). It provides full proofs and includes many examples and exercises. The covered topics include vector spaces and quadratic forms, affine and projective spaces over an arbitrary field; Euclidean spaces; some synthetic affine, Euclidean and projective geometry; affine and projective hyperquadrics with coefficients in an arbitrary field of characteristic different from 2; Bézout’s theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.
Lectures on Graph Theory: Insights into Feynman Diagrams (Lecture Notes in Physics #1035)
by Ray D. SameshimaThis book introduces foundational topics such as group theory, fields, linear algebra, matrix theory, and graph theory, providing readers with the essential background needed to understand Feynman diagrams and their integral representations. The book highlights Feynman's parametrization as a central tool for studying Feynman integrals, starting with the traditional momentum representation. Schwinger and Lee-Pomeransky parametrizations are covered in a supplementary chapter. Readers will develop a clear understanding of the mathematical properties and practical applications of these techniques, with a particular emphasis on Feynman’s approach. Advanced topics such as integration-by-parts identities and intersection number theory are explored in the final chapter, offering readers a gateway to key mathematical structures. The prerequisites are minimal—only a basic familiarity with algebra and calculus is recommended. The content begins with introductory concepts and gradually progresses to more advanced material, ensuring a balanced learning curve. Practical examples throughout the book reinforce the main ideas, allowing readers to apply what they’ve learned and deepen their understanding as they move through the material.
Lectures on Infinitary Model Theory
by David MarkerInfinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
Lectures on Integral Equations (Dover Books on Mathematics)
by Harold WidomThis concise and classic volume presents the main results of integral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. The self-contained treatment requires only some familiarity with elementary real variable theory, including the elements of Lebesgue integration, and is suitable for advanced undergraduates and graduate students of mathematics.Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake. A helpful index concludes the text.
Lectures on K3 Surfaces
by Daniel HuybrechtsK3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Lectures on Kinetic Processes in Materials
by Han-Ill YooThis book provides beginning graduate or senior-level undergraduate students in materials disciplines with a primer of the fundamental and quantitative ideas on kinetic processes in solid materials. Kinetics is concerned with the rate of change of the state of existence of a material system under thermodynamic driving forces. Kinetic processes in materials typically involve chemical reactions and solid state diffusion in parallel or in tandem. Thus, mathematics of diffusion in continuum is first dealt with in some depth, followed by the atomic theory of diffusion and a brief review of chemical reaction kinetics. Chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions are examined. Through this course of learning, a student will become able to predict quantitatively how fast a kinetic process takes place, to understand the inner workings of the process, and to design the optimal process of material state change.Provides students with the tools to predict quantitatively how fast a kinetic process takes place and solve other diffusion related problems;Learns fundamental and quantitative ideas on kinetic processes in solid materials;Examines chemical diffusion in metals and ionic solids, diffusion-controlled kinetics of phase transformations, and kinetics of gas-solid reactions, among others;Contains end-of chapter exercise problems to help reinforce students' grasp of the concepts presented within each chapter.
Lectures on Logarithmic Algebraic Geometry (Cambridge Studies in Advanced Mathematics #178)
by Arthur OgusThis graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and number theory. It features a systematic exposition of the foundations of the field, from the basic results on convex geometry and commutative monoids to the theory of logarithmic schemes and their de Rham and Betti cohomology. The book will be of use to graduate students and researchers working in algebraic, analytic, and arithmetic geometry as well as related fields.