Piotr Mikusinski's Books

A Bridge To Linear Algebra

By: Dragu Atanasiu,Piotr Mikusinski

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The last section is an interesting collection of geometry problems and their solutions from various International Mathematics Olympics … There are a sufficient number of exercises at the end of each chapter, and the answers to half of them are included at the end of the book, with an occasional full solution here and there. The book prepares the reader for a traditional introductory textbook in linear algebra.'CHOICEThe book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor.While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems.Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student's view of the subject.

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Page Count

507

Publisher

World Scientific

Published Date

ISBN 10

9811200246

ISBN 13

9789811200243

Introduction to Hilbert Spaces with Applications

By: Lokenath Debnath,Piotr Mikusinski

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Introduction to Hilbert Spaces with Applications

By: Lokenath Debnath,Piotr Mikusinski

Continuing on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory complemented by a variety of applications. Students and researchers will benefit from the enhanced presentation of results and proofs and new and revised examples. A completely new section on Sobolev spaces has been added, and the treatment of finite dimensional normed spaces has been expanded. The chapter on wavelets has been updated."--BOOK JACKET.

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Page Count

600

Publisher

Academic Press

Published Date

ISBN 10

0122084381

ISBN 13

9780122084386

Linear Algebra: Core Topics For The Second Course

By: Dragu Atanasiu,Piotr Mikusinski

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Linear Algebra: Core Topics For The Second Course

By: Dragu Atanasiu,Piotr Mikusinski

This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.

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Page Count

333

Publisher

World Scientific

Published Date

ISBN 10

9811258562

ISBN 13

9789811258565

An Introduction to Multivariable Analysis from Vector to Manifold

By: Piotr Mikusinski,Michael D. Taylor

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An Introduction to Multivariable Analysis from Vector to Manifold

By: Piotr Mikusinski,Michael D. Taylor

Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index.

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Page Count

300

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461200733

ISBN 13

9781461200734

An Introduction To Analysis

By: Piotr Mikusinski,Jan Mikusinski

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An Introduction To Analysis

By: Piotr Mikusinski,Jan Mikusinski

The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.

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Page Count

318

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813202637

ISBN 13

9789813202634

Introduction to Functional Data Analysis

By: Piotr Kokoszka,Matthew Reimherr

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Introduction to Functional Data Analysis

By: Piotr Kokoszka,Matthew Reimherr

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

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Page Count

371

Publisher

CRC Press

Published Date

ISBN 10

1498746691

ISBN 13

9781498746694

Białowieża Primeval Forest: Nature and Culture in the Nineteenth Century

By: Tomasz Samojlik,Anastasia Fedotova,Piotr Daszkiewicz,Ian D. Rotherham

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Białowieża Primeval Forest: Nature and Culture in the Nineteenth Century

By: Tomasz Samojlik,Anastasia Fedotova,Piotr Daszkiewicz,Ian D. Rotherham

Understanding the current state and dynamics of any forest is extremely difficult - if not impossible - without recognizing its history. Białowieża Primeval Forest (BPF), located on the border between Poland and Belarus, is one of the best preserved European lowland forests and a subject of myriads of works focusing on countless aspects of its biology, ecology, management. BPF was protected for centuries (15th-18th century) as a game reserve of Polish kings and Lithuanian grand dukes. Being, at that time, a part of the Grand Duchy of Lithuania, BPF was subject to long-lasting traditional, multi-functional utilisation characteristic for this part of Europe, including haymaking on forest meadows, traditional bee-keeping and fishing in rivers flowing through forest. This traditional model of management came to an abrupt end due to political change in 1795, when Poland and Grand Duchy of Lithuania ceased to exist in effect of partitioning by neighbouring countries, and the territory of BPF was taken over by the Russian Empire. The new Russian administration, influenced by the German trends in forestry, attempted at introducing the new, science-based forestry model in the BPF throughout the 19th century. The entire 19th century in the history of BPF is a story of struggle between new trends and concepts brought and implemented by new rulers of the land, and the traditional perception of the forest and forest uses, culturally rooted in this area and originating from mediaeval (or older) practices. The book will show the historical background and the outcome of this struggle: the forest’s history in the long 19th century focusing on tracking all cultural imprints, both material (artificial landscapes, introduced alien species, human-induced processes) and immaterial (traditional knowledge of forest and use of forest resources, the political and cultural significance of the forest) that shaped the forest’s current state and picture. Our book will deliver a picture of a crucial moment in forest history, relevant not only to the Central Europe, but to the continent in general. Moment of transition between a royal hunting ground, traditional type of use widespread throughout Europe, to a modern, managed forest. Looking at main obstacles in the management shift, the essential difference in perceptions of the forest and goods it provides in both modes of management, and the implications of the management change for the state of BPF in the long 19th century could help in better understanding the changes that European forests underwent in general.

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Page Count

230

Publisher

Springer Nature

Published Date

ISBN 10

3030334791

ISBN 13

9783030334796

Problems and Examples in Differential Equations

By: Piotr Biler,Tadeusz Nadzieja

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Problems and Examples in Differential Equations

By: Piotr Biler,Tadeusz Nadzieja

This book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.

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Page Count

261

Publisher

CRC Press

Published Date

ISBN 10

1000104753

ISBN 13

9781000104752

The Biographical Landscapes of Raphael Lemkin

By: Piotr Madajczyk

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The Biographical Landscapes of Raphael Lemkin

By: Piotr Madajczyk

The book is the first biography of Raphael Lemkin to draw on a comprehensive body of research into Lemkin as a person and his background and will be of interest to both non-specialists and academics. Drawing on archival materials, a nuanced description is provided of the ethnically mixed Belarusian-Polish-Jewish border region where Lemkin grew up and which shaped him, clarifying at the same time some of the misinterpretations that have surrounded Lemkin’s life. Lemkin’s professional career and intellectual interests up to the time of his flight from Poland after the German aggression of 1939 are exhaustively described. In the latter part of the book, the author poses, among other things, the question of how Lemkin’s activities in the United States were influenced by the experience of the first almost 40 years of his life.

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Page Count

278

Publisher

Taylor & Francis

Published Date

ISBN 10

1000990095

ISBN 13

9781000990096

Inference for Functional Data with Applications

By: Lajos Horváth,Piotr Kokoszka

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Inference for Functional Data with Applications

By: Lajos Horváth,Piotr Kokoszka

This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.

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Page Count

426

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461436559

ISBN 13

9781461436553

Linear Algebra: Core Topics For The First Course

By: Dragu Atanasiu,Piotr Mikusinski

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Linear Algebra: Core Topics For The First Course

By: Dragu Atanasiu,Piotr Mikusinski

The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.

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Page Count

465

Publisher

World Scientific

Published Date

ISBN 10

9811215049

ISBN 13

9789811215049

Introduction to Hilbert Spaces with Applications

By: Lokenath Debnath,Piotr Mikusinski

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Introduction to Hilbert Spaces with Applications

By: Lokenath Debnath,Piotr Mikusinski

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. - Updated chapter on wavelets - Improved presentation on results and proof - Revised examples and updated applications - Completely updated list of references

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Page Count

599

Publisher

Elsevier

Published Date

ISBN 10

0080455921

ISBN 13

9780080455921

An Introduction to Analysis

From Number to Integral

By: Jan Mikusiński,Piotr Mikusiński

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An Introduction to Analysis

From Number to Integral

By: Jan Mikusiński,Piotr Mikusiński

Based on the lifetime work of leading teacher and researcher Jan Mikusiński, this classroom-tested book provides a thorough grounding in mathematical analysis, calculus and mathematical proofing. It introduces natural numbers through a new mathematical approach; replaces the Riemann integral with the more general Lebesgue integral; and rigorously develops the real number system from four simple axioms of natural numbers. Additional features include a wider range of problems than other texts--including simple and routine as well as problems requiring more in depth creativity, answers to common questions, a new approach to the concept of equivalence relation which simplifies the construction of real numbers, and a large number of computational applications.

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Page Count

290

Published Date

ISBN 10

0471599778

ISBN 13

9780471599777

An Introduction to Multivariable Analysis from Vector to Manifold

By: Piotr Mikusinski,Michael Taylor

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An Introduction to Multivariable Analysis from Vector to Manifold

By: Piotr Mikusinski,Michael Taylor

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Page Count

310

Publisher

Springer Science & Business Media

Published Date

ISBN 10

081764234X

ISBN 13

9780817642341

Linear Algebra: Core Topics For The First Course

By: Dragu Atanasiu,Piotr Mikusinski

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Linear Algebra: Core Topics For The First Course

By: Dragu Atanasiu,Piotr Mikusinski

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Page Count

465

Publisher

World Scientific

Published Date

ISBN 10

9811215049

ISBN 13

9789811215049

Linear Algebra: Core Topics For The Second Course

By: Dragu Atanasiu,Piotr Mikusinski

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Linear Algebra: Core Topics For The Second Course

By: Dragu Atanasiu,Piotr Mikusinski

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Page Count

333

Publisher

World Scientific

Published Date

ISBN 10

9811258562

ISBN 13

9789811258565

Book's by Piotr Mikusinski

A Bridge To Linear Algebra

A Bridge To Linear Algebra

Introduction to Hilbert Spaces with Applications

Introduction to Hilbert Spaces with Applications

Linear Algebra: Core Topics For The Second Course

Linear Algebra: Core Topics For The Second Course

An Introduction to Multivariable Analysis from Vector to Manifold

An Introduction to Multivariable Analysis from Vector to Manifold

An Introduction To Analysis

An Introduction To Analysis

Introduction to Functional Data Analysis

Introduction to Functional Data Analysis

Białowieża Primeval Forest: Nature and Culture in the Nineteenth Century

Białowieża Primeval Forest: Nature and Culture in the Nineteenth Century

Problems and Examples in Differential Equations

Problems and Examples in Differential Equations

The Biographical Landscapes of Raphael Lemkin

The Biographical Landscapes of Raphael Lemkin

Inference for Functional Data with Applications

Inference for Functional Data with Applications

Linear Algebra: Core Topics For The First Course

Linear Algebra: Core Topics For The First Course

Introduction to Hilbert Spaces with Applications

Introduction to Hilbert Spaces with Applications

An Introduction to Analysis

An Introduction to Analysis

An Introduction to Multivariable Analysis from Vector to Manifold

An Introduction to Multivariable Analysis from Vector to Manifold

Linear Algebra: Core Topics For The First Course

Linear Algebra: Core Topics For The First Course

Linear Algebra: Core Topics For The Second Course

Linear Algebra: Core Topics For The Second Course

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