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Designed for advanced undergraduate and beginning graduate students in linear of abstract algebra, Advanced Linear Algebra provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra in many areas of pure and applied mathematics.

Advanced Linear Algebra (Twarda)

This is the second of a two-part set of books for the undergraduate linear algebra sequence. The text is for more advanced courses taught in mathematics departments. This course is based around matrix theory and focused on the theory of linear algebra. Along with the chapters found in Elementary Linear Algebra, he offers seven additional chapters .

Linear Algebra (James R. Kirkwood)(Miękka)

PART I"DETERMINANTS, VECTORS, MATRICES, AND LINEAR EQUATIONS"I. DETERMINANTS  1.1. Arrangements and the Î-symbol  1.2. Elementary properties of determinants  1.3. Multiplication of determinants  1.4. Expansion theorems  1.5. Jacobi's theorem  1.6. Two special theorems on linear equationsII. VECTOR SPACES AND LINEAR MANIFOLDS  2.1. The algebra of vectors  2.2. Linear manifolds  2.3. Linear dependence and bases  2.4. Vector representation of linear manifolds  2.5. Inner products and orthonormal basesIII. THE ALGEBRA OF MATRICES  3.1. Elementary algebra   3.2. Preliminary notions concerning matrices  3.3. Addition and multiplication of matrices  3.4. Application of matrix technique to linear substitutions  3.5. Adjugate matrices  3.6. Inverse matrices  3.7. Rational functions of a square matrix  3.8. Partitioned matricesIV. LINEAR OPERATIONS  4.1. Change of basis in a linear manifold  4.2. Linear operators and their representations  4.3. Isomorphisms and automorphisms of linear manifolds 

An Introduction to Linear Algebra (L. Mirsky)(Miękka)

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject.

Basic Topology (Mark A. Armstrong)(Twarda)

Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate. This second edition has been thoroughly revised and includes a new chapter on C^ and W^ algebras.

Topological Vector Spaces (H.H. Schaefer,M.P. Wolff)(Miękka)

This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. §It includes several major spectral theorems of analysis, showing 

Real and Functional Analysis (Serge Lang)(Twarda)

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Geometrical Methods of Mathematical Physics (Bernard F Schutz)(Miękka)

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections.  It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels.  The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning.  Exercises are selected from a number of different domains, both theoretical and more applied.  Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many.  For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as they move on to more advanced

Exercises in Applied Mathematics (Daniel Alpay)(Twarda)

Math for Data Science presents the mathematical foundations necessary for studying and working in Data Science. The book is suitable for courses in applied mathematics, business analytics, computer science, data science, and engineering. The text covers the portions of linear algebra, calculus, probability, and statistics prerequisite to Data Science.  The highlight of the book is the machine learning chapter, where the results of the previous chapters are applied to neural network training and stochastic gradient descent. Also included in this last chapter are advanced topics such as accelerated gradient descent and logistic regression trainability.Clear examples are supported with detailed figures and Python code; Jupyter notebooks and supporting files are available on the author's website. More than 380 exercises and nine detailed appendices covering background elementary material are provided to aid understanding. The book begins at a gentle pace, by focusing on two-dimensional dat

Math for Data Science (Omar Hijab)(Twarda)

The purpose of this book is to present various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The focus is mostly on analytical techniques, although numerical and statistical techniques for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Some specific applications, such as stochastic resonance and Brownian motors are also discussed. The book is intended for beginning graduate students in these disciplines. Prerequisites include ordinary and partial differential equations, linear algebra, elementary functional analysis and techniques from applied mathematics such as perturbation theory. Basic knowledge of scientific computing and of a programming language or matlab would certainly be very helpful. Some familiarity with probability the

Stochastic Processes and Applications (Grigorios Pavliotis)(Twarda)

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems and Tikhonov regularization, should appeal not only to mathematicians interested in applications but also to researchers in related fields.§Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.§

Functional Analysis (Joseph Muscat)(Miękka)

This book, first published in 2004, provides an introduction to the major mathematical structures used in physics today. It covers the concepts and techniques needed for topics such as group theory, Lie algebras, topology, Hilbert space and differential geometry. Important theories of physics such as classical and quantum mechanics, thermodynamics, and special and general relativity are also developed in detail, and presented in the appropriate mathematical language. The book is suitable for advanced undergraduate and beginning graduate students in mathematical and theoretical physics, as well as applied mathematics. It includes numerous exercises and worked examples, to test the reader's understanding of the various concepts, as well as extending the themes covered in the main text. The only prerequisites are elementary calculus and linear algebra. No prior knowledge of group theory, abstract vector spaces or topology is required.

Course in Modern Mathematical Physics (Peter Szekeres)(Twarda)

Jzyk: Angielski, Oprawa: Piercieniowa, Wydawnictwo: John Wiley & Sons Inc, Autor: Anton,Howard,Kaul,Anton, ISBN-13: 9781119268048, Data wydania: 2019

Elementary Linear Algebra (Anton,Howard,Kaul,Anton)(Pierścieniowa)

Jzyk: Angielski, Oprawa: Piercieniowa, Wydawnictwo: John Wiley & Sons Inc, Autor: Anton,Howard,Rorres,Chris,Kaul,Anton, ISBN-13: 9781119282365, Data wydania: 2019

Elementary Linear Algebra (Anton,Howard,Rorres,Chris,Kaul,Anton)(Pierścieniowa)

Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra.  In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations.  Written at a sophomore level, the text is accessible to students who have completed multivariable calculus.  With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra.  Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebra

Differential Equations with Linear Algebra (Matthew R. Boelkins, Jack L. Goldberg, Merle C. Potter)(Twarda)

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advan

Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing (Roe W. Goodman)(Miękka)

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