**Author**: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

**Publisher:** American Mathematical Soc.

**ISBN:** 0821886258

**Category:** Mathematics

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**View:** 539

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This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the proofs at the end of the chapter or skip them altogether. This style also caters to the expert who needs a handbook and prefers formulations not overshadowed by proofs. Most of the proofs are simple and easy to discover. The book can be useful and enjoyable for readers with quite different backgrounds and interests. The text is structured in such a way that it is easy to determine what to expect from each piece and how to use it. There is core material, which makes up a relatively small part of the book. The core material is interspersed with examples, illustrative and training problems, and relevant discussions. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology.
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
The aim of Problems and Solutions for Undergraduate Real Analysis I, as the name reveals, is to assist undergraduate students or first-year students who study mathematics in learning their first rigorous real analysis course. The wide variety of problems, which are of varying difficulty, include the following topics: Elementary Set Algebra, the Real Number System, Countable and Uncountable Sets, Elementary Topology on Metric Spaces, Sequences in Metric Spaces, Series of Numbers, Limits and Continuity of Functions, Differentiation and the Riemann-Stieltjes Integral. Furthermore, the main features of this book are listed as follows: 1. The book contains 230 problems, which cover the topics mentioned above, with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied. 2. Each chapter starts with a brief and concise note of introducing the notations, terminologies, basic mathematical concepts or important/famous/frequently used theorems (without proofs) relevant to the topic. 3. Three levels of difficulty have been assigned to problems so that you can sharpen your mathematics step-by-step. 4. Different colors are used frequently in order to highlight or explain problems, examples, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) 5. An appendix about mathematical logic is included. It tells students what concepts of logic (e.g. techniques of proofs) are necessary in advanced mathematics.
Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. Most can be solved with elementary mathematics. Complete solutions.
These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.
This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

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**Author**: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

**Publisher:** American Mathematical Soc.

**ISBN:** 0821886258

**Category:** Mathematics

**Page:**

**View:** 539

*longest, consists of solutions: proofs, answers, or constructions, depending on *

the nature of the problem. ... To get maximum profit from the book the reader

should know the elementary techniques and results of general topology,

measure ...

**Author**: P.R. Halmos

**Publisher:** Springer Science & Business Media

**ISBN:** 9781468493306

**Category:** Mathematics

**Page:** 373

**View:** 412

*Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint.*

**Author**: C. R. F. Maunder

**Publisher:** Courier Corporation

**ISBN:** 0486691314

**Category:** Mathematics

**Page:** 375

**View:** 259

*The wide variety of problems, which are of varying difficulty, include the following topics: Elementary Set Algebra The Real Number System Countable and Uncountable Sets Elementary Topology on Metric Spaces Sequences in Metric Spaces Series ...*

**Author**: Kit-Wing Yu

**Publisher:** 978-988-78797-5-6

**ISBN:** 9887879754

**Category:**

**Page:** 212

**View:** 984

*Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. Most can be solved with elementary mathematics. Complete solutions.*

**Author**: A. M. Yaglom

**Publisher:** Courier Corporation

**ISBN:** 9780486318578

**Category:** Mathematics

**Page:** 239

**View:** 591

*In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990).*

**Author**: M. Husek

**Publisher:** Elsevier

**ISBN:** 9780080934433

**Category:** Mathematics

**Page:** 808

**View:** 352

*The answers seem to be yes, provided the problems are neither too hard nor too *

easy. The book is addressed to students (and teachers) of undergraduate linear

algebra–it might supplement but not (I hope) replace ... problems, and the

introductions that precede and the solutions that follow them sometimes

laboriously explain elementary concepts, ... and carefully explain the associative

law, but at other times I assume that the word —topology“, while it may not refer to

something that ...

**Author**: Paul R. Halmos

**Publisher:** American Mathematical Soc.

**ISBN:** 9781614442127

**Category:** Mathematics

**Page:** 333

**View:** 470

*This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa ...*

**Author**: J. de Vries

**Publisher:** Springer Science & Business Media

**ISBN:** 0792322878

**Category:** Mathematics

**Page:** 748

**View:** 796

*This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.*

**Author**: Christian Bär

**Publisher:** Cambridge University Press

**ISBN:** 9780521896719

**Category:** Mathematics

**Page:** 317

**View:** 861

*The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for ...*

**Author**: Pablo Amster

**Publisher:** Springer Science & Business Media

**ISBN:** 9781461488934

**Category:** Mathematics

**Page:** 226

**View:** 491

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