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| uconn linear algebra: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| uconn linear algebra: The Finite Element Method: Theory, Implementation, and Applications Mats G. Larson, Fredrik Bengzon, 2013-01-13 This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics. |
| uconn linear algebra: Numerical Linear Algebra in Signals, Systems and Control Paul Van Dooren, Shankar P. Bhattacharyya, Raymond H. Chan, Vadim Olshevsky, Aurobinda Routray, 2011-05-21 The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices. |
| uconn linear algebra: Elliptic Curves, Modular Forms, and Their L-functions Alvaro Lozano-Robledo, Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. This book is an introduction to some of these problems. |
| uconn linear algebra: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves. |
| uconn linear algebra: Linear Algebra With Machine Learning and Data Crista Arangala, 2023-05-09 This book takes a deep dive into several key linear algebra subjects as they apply to data analytics and data mining. The book offers a case study approach where each case will be grounded in a real-world application. This text is meant to be used for a second course in applications of Linear Algebra to Data Analytics, with a supplemental chapter on Decision Trees and their applications in regression analysis. The text can be considered in two different but overlapping general data analytics categories: clustering and interpolation. Knowledge of mathematical techniques related to data analytics and exposure to interpretation of results within a data analytics context are particularly valuable for students studying undergraduate mathematics. Each chapter of this text takes the reader through several relevant case studies using real-world data. All data sets, as well as Python and R syntax, are provided to the reader through links to Github documentation. Following each chapter is a short exercise set in which students are encouraged to use technology to apply their expanding knowledge of linear algebra as it is applied to data analytics. A basic knowledge of the concepts in a first Linear Algebra course is assumed; however, an overview of key concepts is presented in the Introduction and as needed throughout the text. |
| uconn linear algebra: The Arithmetic of Elliptic Curves Joseph H. Silverman, 2013-03-09 The preface to a textbook frequently contains the author's justification for offering the public another book on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery. |
| uconn linear algebra: Computer Science (IT) Advice , The best Computer science (IT) tips for PCs, Smartphones, Tablets for Maintenance and Optimization, Internet Security (Account protection, how to defend yourself from Viruses, make online purchases safely, speed up surfing), tips for Digital Marketing, for the more experienced the Programming, and finally Video Games.) |
| uconn linear algebra: Advanced Topics in Linear Algebra Kevin O'Meara, John Clark, Charles Vinsonhaler, 2011-09-26 The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the Jordan form. Developing an understanding of both forms will allow students and researchers to exploit the mathematical capabilities of each in varying situations. Weaving together ideas and applications from various mathematical disciplines, Advanced Topics in Linear Algebra is much more than a derivation of the Weyr form. It presents novel applications of linear algebra, such as matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. Among the related mathematical disciplines from which the book draws ideas are commutative and noncommutative ring theory, module theory, field theory, topology, and algebraic geometry. Numerous examples and current open problems are included, increasing the book's utility as a graduate text or as a reference for mathematicians and researchers in linear algebra. |
| uconn linear algebra: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| uconn linear algebra: Practical Flow Cytometry Howard M. Shapiro, 2005-02-25 From the reviews of the 3rd Edition... The standard reference for anyone interested in understandingflow cytometry technology. American Journal of Clinical Oncology ...one of the most valuable of its genre and...addressed to awide audience?written in such an attractive way, being bothinformative and stimulating. Trends in Cell Biology This reference explains the science and discusses the vastbiomedical applications of quantitative analytical cytology usinglaser-activated detection and cell sorting. Now in its fourthedition, this text has been expanded to provide full coverage ofthe broad spectrum of applications in molecular biology andbiotechnology today. New to this edition are chapters on automatedanalysis of array technologies, compensation, high-speed sorting,reporter molecules, and multiplex and apoptosis assays, along withfully updated and revised references and a list of suppliers. |
| uconn linear algebra: Calculus, Volume I, 2nd Ed One-variable Calculus, with an Introduction to Linear Algebra Tom M. Apostol, 2007 · Some Basic Concepts Of The Theory Of Sets · A Set Of Axioms For The Real Number System · Mathematical Induction, Summation Notation, And Related Topics · The Concepts Of The Integral Calculus · Some Applications Of Differentiation · Continuous Functions · Differential Calculus · The Relation Between Integration And Differentiation · The Logarithm, The Exponential, And The Inverse Trigonometric Functions · Polynomial Approximations To Functions · Introduction To Differential Equations · Complex Numbers · Sequences, Infinite Series, Improper Integrals · Sequences And Series Of Functions · Vector Algebra · Applications Of Vector Algebra To Analytic Geometry · Calculus Of Vector-Valued Functions · Linear Spaces · Linear Transformations And Matrices |
| uconn linear algebra: Parameter Estimation and Inverse Problems Richard C. Aster, Brian Borchers, Clifford H. Thurber, 2018-10-16 Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. - Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method - Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems - Covers updated information on adjoint methods that are presented in an accessible manner |
| uconn linear algebra: Advanced Engineering Mathematics Lawrence Turyn, 2013-09-25 Beginning with linear algebra and later expanding into calculus of variations, Advanced Engineering Mathematics provides accessible and comprehensive mathematical preparation for advanced undergraduate and beginning graduate students taking engineering courses. This book offers a review of standard mathematics coursework while effectively integrating science and engineering throughout the text. It explores the use of engineering applications, carefully explains links to engineering practice, and introduces the mathematical tools required for understanding and utilizing software packages. Provides comprehensive coverage of mathematics used by engineering students Combines stimulating examples with formal exposition and provides context for the mathematics presented Contains a wide variety of applications and homework problems Includes over 300 figures, more than 40 tables, and over 1500 equations Introduces useful MathematicaTM and MATLAB® procedures Presents faculty and student ancillaries, including an online student solutions manual, full solutions manual for instructors, and full-color figure sides for classroom presentations Advanced Engineering Mathematics covers ordinary and partial differential equations, matrix/linear algebra, Fourier series and transforms, and numerical methods. Examples include the singular value decomposition for matrices, least squares solutions, difference equations, the z-transform, Rayleigh methods for matrices and boundary value problems, the Galerkin method, numerical stability, splines, numerical linear algebra, curvilinear coordinates, calculus of variations, Liapunov functions, controllability, and conformal mapping. This text also serves as a good reference book for students seeking additional information. It incorporates Short Takes sections, describing more advanced topics to readers, and Learn More about It sections with direct references for readers wanting more in-depth information. |
| uconn linear algebra: Numerical Methods for Structured Matrices and Applications Dario Andrea Bini, Volker Mehrmann, Vadim Olshevsky, Eugene Tyrtsyhnikov, Marc van Barel, 2011-02-09 This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements. |
| uconn linear algebra: Signals and Systems Analysis In Biomedical Engineering, Second Edition Robert B. Northrop, 2010-03-26 The first edition of this text, based on the author’s 30 years of teaching and research on neurosensory systems, helped biomedical engineering students and professionals strengthen their skills in the common network of applied mathematics that ties together the diverse disciplines that comprise this field. Updated and revised to include new material as the field has grown, Signals and Systems Analysis in Biomedical Engineering, Second Edition continues to provide a ready source of information on those specialized mathematical techniques most useful in describing and analyzing biomedical signals. New chapters on nonlinear and complex systems Enriched with many examples that promote sound practical analysis, this volume covers classical linear systems theory and its applications to biomedicine. It examines the important use of joint time-frequency analysis to characterize non-stationary physiological signals, and explores the mathematics of tomographic imaging (the Radon transform, the Fourier slice theorem, and the filtered back-projection algorithm). It also describes the analytical signal and the Hilbert transform and some of its biomedical applications. New chapters in this edition include one on the analysis of nonlinear biochemical systems and biochemical oscillators, as well as one introducing complex systems and illustrating ways to best model them. Four appendices with additional material Extensive appendices supplement the text, including Simnon® Programs Used in Chapters 11 and 12, How to use Root Locus to Determine the Stability of SISO Linear Systems, Signal Flow Graphs and Mason’s Rule, and Computational Tools for Biomedical Signal Processing and Systems Analysis. An extensive glossary is included as well as an ample listing of sources for further study. A solutions manual is available for instructors wishing to convert this refrence to classroom use. |
| uconn linear algebra: Parallel Curriculum Units for Mathematics, Grades 6–12 Jann H. Leppien, Jeanne H. Purcell, 2011-04-07 Parallel Curriculum Units for Mathematics, Grades 6–12 combines four essential models for improving student understanding and growth in mathematics. The lessons provided in the textbook build on students′ abilities, so they can see all parts of a math problem and are able to tackle and understand it at various levels. —Elizabeth Alvarez, Assistant Principal John C. Dore Elementary, Chicago, IL Maximize your mathematics curriculum to challenge all students This collection of lessons, building on material presented in the best-selling The Parallel Curriculum, is written by experienced teachers who provide innovative and challenging learning opportunities for students in Grades 6–12. The four sample units focus on fractions, linear programming, geometry, and quadratic relationships. The authors provide user-friendly methods for creating high-quality lessons and demonstrate how to differentiate these lessons for the benefit of all students. Included are field-tested and standards-based strategies that guide students through: Understanding secondary-level mathematics concepts Discovering connections between mathematics and other subjects Developing critical thinking skills Connecting mathematics learning to society through the study of real-world data, proportional reasoning, and problem solving Each unit includes subject matter background, a content framework, study components, teacher reflections, and sample lessons. Learn from the experts and enhance your mathematics curriculum with these proven strategies. |
| uconn linear algebra: Essentials of Stochastic Processes Richard Durrett, 2016-11-07 Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance. |
| uconn linear algebra: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| uconn linear algebra: Undergraduate Algebra Serge Lang, 2013-06-29 This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the linear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory. |
| uconn linear algebra: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| uconn linear algebra: Rational Points on Elliptic Curves Joseph H. Silverman, John Tate, 2013-04-17 In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of Rational Points on Cubic Curves. These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is readable by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove. |
| uconn linear algebra: Geometry of Derivation with Applications Norman L. Johnson, 2023-06-06 Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment. The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications. |
| uconn linear algebra: Commutative Algebra Aron Simis, 2023-08-07 The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth). |
| uconn linear algebra: Real Analysis for Graduate Students Richard F. Bass, 2013-01-04 This book is a course on real analysis (measure and integration theory plus additional topics) designed for beginning graduate students. Its focus is on helping the student pass a preliminary or qualifying examination for the Ph.D. degree. |
| uconn linear algebra: Symbolic Data Analysis Lynne Billard, Edwin Diday, 2012-05-14 With the advent of computers, very large datasets have become routine. Standard statistical methods don’t have the power or flexibility to analyse these efficiently, and extract the required knowledge. An alternative approach is to summarize a large dataset in such a way that the resulting summary dataset is of a manageable size and yet retains as much of the knowledge in the original dataset as possible. One consequence of this is that the data may no longer be formatted as single values, but be represented by lists, intervals, distributions, etc. The summarized data have their own internal structure, which must be taken into account in any analysis. This text presents a unified account of symbolic data, how they arise, and how they are structured. The reader is introduced to symbolic analytic methods described in the consistent statistical framework required to carry out such a summary and subsequent analysis. Presents a detailed overview of the methods and applications of symbolic data analysis. Includes numerous real examples, taken from a variety of application areas, ranging from health and social sciences, to economics and computing. Features exercises at the end of each chapter, enabling the reader to develop their understanding of the theory. Provides a supplementary website featuring links to download the SODAS software developed exclusively for symbolic data analysis, data sets, and further material. Primarily aimed at statisticians and data analysts, Symbolic Data Analysis is also ideal for scientists working on problems involving large volumes of data from a range of disciplines, including computer science, health and the social sciences. There is also much of use to graduate students of statistical data analysis courses. |
| uconn linear algebra: Random Walk and the Heat Equation Gregory F. Lawler, 2010-11-22 The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas. |
| uconn linear algebra: Riemannian Foliations Molino, 2012-12-06 Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of plaques. 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is simple. For an arbitrary foliation, it is only l- u L ally [on a simpIe open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques. |
| uconn linear algebra: Visual Group Theory Nathan Carter, 2021-06-08 Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. |
| uconn linear algebra: Analytic Pro-P Groups J. D. Dixon, M. P. F. Du Sautoy, A. Mann, D. Segal, 2003-09-18 An up-to-date treatment of analytic pro-p groups for graduate students and researchers. |
| uconn linear algebra: A First Course in Linear Model Theory Nalini Ravishanker, Zhiyi Chi, Dipak K. Dey, 2021-10-18 Thoroughly updated throughout, A First Course in Linear Model Theory, Second Edition is an intermediate-level statistics text that fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the authors introduce to students the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models. In addition to adding R functionality, this second edition features three new chapters and several sections on new topics that are extremely relevant to the current research in statistical methodology. Revised or expanded topics include linear fixed, random and mixed effects models, generalized linear models, Bayesian and hierarchical linear models, model selection, multiple comparisons, and regularized and robust regression. New to the Second Edition: Coverage of inference for linear models has been expanded into two chapters. Expanded coverage of multiple comparisons, random and mixed effects models, model selection, and missing data. A new chapter on generalized linear models (Chapter 12). A new section on multivariate linear models in Chapter 13, and expanded coverage of the Bayesian linear models and longitudinal models. A new section on regularized regression in Chapter 14. Detailed data illustrations using R. The authors' fresh approach, methodical presentation, wealth of examples, use of R, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models. |
| uconn linear algebra: A Celebration of the EDGE Program’s Impact on the Mathematics Community and Beyond Susan D'Agostino, Sarah Bryant, Amy Buchmann, Michelle Craddock Guinn, Leona Harris, 2019-08-31 The Enhancing Diversity in Graduate Education (EDGE) Program began twenty years ago to provide support for women entering doctoral programs in the mathematical sciences. With a steadfast commitment to diversity among participants, faculty, and staff, EDGE initially alternated between Bryn Mawr and Spelman Colleges. In later years, EDGE has been hosted on campuses around the nation and expanded to offer support for women throughout their graduate school and professional careers. The refereed papers in A Celebration of the EDGE Program’s Impact on the Mathematics Community and Beyond range from short memoirs, to pedagogical studies, to current mathematics research. All papers are written by former EDGE participants, mentors, instructors, directors, and others connected to EDGE. Together, these papers offer compelling testimony that EDGE has produced a diverse new generation of leaders in the mathematics community. This volume contains technical and non-technical works, and it is intended for a far-reaching audience, including mathematicians, mathematics teachers, diversity officers, university administrators, government employees writing educational or science policy, and mathematics students at the high school, college, and graduate levels. By highlighting the scope of the work done by those supported by EDGE, the volume offers strong evidence of the American Mathematical Society’s recognition that EDGE is a program that makes a difference.” This volume offers unique testimony that a 20-year old summer program has expanded its reach beyond the summer experience to produce a diverse new generation of women leaders, nearly half of whom are underrepresented women. While some books with a women-in-math theme focus only on one topic such as research or work-life balance, this book's broad scope includes papers on mathematics research, teaching, outreach, and career paths. |
| uconn linear algebra: Elliptic Curves (Second Edition) James S Milne, 2020-08-20 This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated. |
| uconn linear algebra: Non-Invasive Instrumentation and Measurement in Medical Diagnosis Robert B. Northrop, 2019-12-10 Non-Invasive Instrumentation and Measurement in Medical Diagnosis, Second Edition discusses NIMD as a rapidly growing, interdisciplinary field. The contents within this second edition text is derived from Professor Robert B. Northrop's experience teaching for over 35 years in the Biomedical Engineering Department at the University of Connecticut. The text focusses on the instruments and procedures which are used for non-invasive medical diagnosis and therapy, highlighting why NIMD is the preferred procedure, whenever possible, to avoid the risks and expenses associated with surgically opening the body surface. This second edition also covers a wide spectrum of NIMD topics including: x-ray bone densitometry by the DEXA method; tissue fluorescence spectroscopy; optical interferometric measurement of nanometer tissue displacements; laser Doppler velocimetry; pulse oximetry; and applications of Raman spectroscopy in detecting cancer, to name a few. This book is intended for use in an introductory classroom course on Non-Invasive Medical Instrumentation and Measurements taken by juniors, seniors, and graduate students in Biomedical Engineering. It will also serve as a reference book for medical students and other health professionals intrigued by the topic. Practicing physicians, nurses, physicists, and biophysicists interested in learning state of the art techniques in this critical field will also find this text valuable. Non-Invasive Instrumentation and Measurement in Medical Diagnosis, Second Edition concludes with an expansive index, bibliography, as well as a comprehensive glossary for future reference and reading. |
| uconn linear algebra: Geometric Methods in Physics XXXVII Piotr Kielanowski, Anatol Odzijewicz, Emma Previato, 2019-11-26 The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Białowieża Workshops have been complemented by a School on Geometry and Physics comprising a series of advanced lectures for graduate students and early-career researchers. The book also includes abstracts of the five lecture series that were given at the seventh school. |
| uconn linear algebra: The Cauchy-Schwarz Master Class J. Michael Steele, 2004-04-26 This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics. |
| uconn linear algebra: College Physics Paul Peter Urone, Roger Hinrichs, 2018-01-05 This is part two of two for College Physics. This book covers chapters 18-34. Please note: The text and images in this textbook are grayscale and the format size has been reduced from 8.5 x 11 to 7.44 x 9.69. This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. College Physics includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems. |
| uconn linear algebra: The William Lowell Putnam Mathematical Competition Problems and Solutions Andrew M. Gleason, R. E. Greenwood, Leroy Milton Kelly, 1980 Back by popular demand, the MAA is pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas.--Back cover. |
| uconn linear algebra: Truth as One and Many Michael P. Lynch, 2011-03-31 What is truth? Michael Lynch defends a bold new answer to this question. Traditional theories of truth hold that truth has only a single uniform nature. All truths are true in the same way. More recent deflationary theories claim that truth has no nature at all; the concept of truth is of no real philosophical importance. In this concise and clearly written book, Lynch argues that we should reject both these extremes and hold that truth is a functional property. To understand truth we must understand what it does, its function in our cognitive economy. Once we understand that, we'll see that this function can be performed in more than one way. And that in turn opens the door to an appealing pluralism: beliefs about the concrete physical world needn't be true in the same way as our thoughts about matters -- like morality -- where the human stain is deepest. |
| uconn linear algebra: Linear Algebra Kenneth Hoffman, Ray Alden Kunze, 2015 |
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