Problems In Mathematical Analysis Continuity And Differentiation Book Download

Problems in Mathematical Analysis  Continuity and differentiation PDF
Author: Wiesława J. Kaczor
Publisher: American Mathematical Soc.
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 398
View: 6281

Get Book


Problems In Mathematical Analysis Continuity And Differentiation

by Wiesława J. Kaczor, Problems In Mathematical Analysis Continuity And Differentiation Books available in PDF, EPUB, Mobi Format. Download Problems In Mathematical Analysis Continuity And Differentiation books, We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). If you want to hone your understanding of continuous and differentiable functions, this book contains hundreds of problems to help you do so. The emphasis here is on real functions of a single variable. The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided.


Matrix Groups For Undergraduates Book Download

Matrix Groups for Undergraduates PDF
Author: Kristopher Tapp
Publisher: American Mathematical Soc.
Format: PDF, ePub, Docs
Category : MATHEMATICS
Languages : en
Pages : 166
View: 219

Get Book


Matrix Groups For Undergraduates

by Kristopher Tapp, Matrix Groups For Undergraduates Books available in PDF, EPUB, Mobi Format. Download Matrix Groups For Undergraduates books, Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.


Lectures On Generating Functions Book Download

Lectures on Generating Functions PDF
Author: Sergei K. Lando
Publisher: American Mathematical Soc.
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 148
View: 4527

Get Book


Lectures On Generating Functions

by Sergei K. Lando, Lectures On Generating Functions Books available in PDF, EPUB, Mobi Format. Download Lectures On Generating Functions books, In combinatorics, one often considers the process of enumerating objects of a certain nature, which results in a sequence of positive integers. With each such sequence, one can associate a generating function, whose properties tell us a lot about the nature of the objects being enumerated. Nowadays, the language of generating functions is the main language of enumerative combinatorics. This book is based on the course given by the author at the College of Mathematics of the Independent University of Moscow. It starts with definitions, simple properties, and numerous examples of generating functions. It then discusses various topics, such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications of generating functions to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the reader is motivated by interesting examples rather than by general theories. It also contains a lot of exercises to help the reader master the material. Little beyond the standard calculus course is necessary to understand the book. It can serve as a text for a one-semester undergraduate course in combinatorics.


A View From The Top Book Download

A View from the Top PDF
Author: Alex Iosevich
Publisher: American Mathematical Soc.
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 136
View: 6340

Get Book


A View From The Top

by Alex Iosevich, A View From The Top Books available in PDF, EPUB, Mobi Format. Download A View From The Top books, This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another. In teaching his readers a variety of problem solving techniques as well, the author succeeds in enhancing the readers' hands on knowledge of mathematics and provides glimpses into the world of research and discovery. The connections between different techniques and areas of mathematics are emphasized throughout and constitute one of the most important lessons this book attempts to impart. This book is interesting and accessible to anyone with a basic knowledge of high school mathematics and a curiosity about research mathematics. The author is a professor at the University of Missouri and has maintained a keen interest in teaching at different levels since his undergraduate days at the University of Chicago. He has run numerous summer programs in mathematics for local high school students and undergraduate students at his university.The author gets much of his research inspiration from his teaching activities and looks forward to exploring this wonderful and rewarding symbiosis for years to come.


A First Course In Sobolev Spaces Second Edition Book Download

A First Course in Sobolev Spaces  Second Edition PDF
Author: Giovanni Leoni
Publisher: American Mathematical Soc.
Format: PDF, Mobi
Category : Sobolev spaces
Languages : en
Pages : 734
View: 4376

Get Book


A First Course In Sobolev Spaces Second Edition

by Giovanni Leoni, A First Course In Sobolev Spaces Second Edition Books available in PDF, EPUB, Mobi Format. Download A First Course In Sobolev Spaces Second Edition books, This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.


Lectures On Fractal Geometry And Dynamical Systems Book Download

Lectures on Fractal Geometry and Dynamical Systems PDF
Author: Ya. B. Pesin
Publisher: American Mathematical Soc.
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 314
View: 6331

Get Book


Lectures On Fractal Geometry And Dynamical Systems

by Ya. B. Pesin, Lectures On Fractal Geometry And Dynamical Systems Books available in PDF, EPUB, Mobi Format. Download Lectures On Fractal Geometry And Dynamical Systems books, Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.


Plateau S Problem Book Download

Plateau s Problem PDF
Author: Frederick J. Almgren
Publisher: American Mathematical Soc.
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 78
View: 1633

Get Book


Plateau S Problem

by Frederick J. Almgren, Plateau S Problem Books available in PDF, EPUB, Mobi Format. Download Plateau S Problem books, There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book--or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.


Higher Arithmetic Book Download

Higher Arithmetic PDF
Author: Harold M. Edwards
Publisher: American Mathematical Soc.
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 210
View: 4681

Get Book


Higher Arithmetic

by Harold M. Edwards, Higher Arithmetic Books available in PDF, EPUB, Mobi Format. Download Higher Arithmetic books, Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.