Mathematical Analysis And Its Inherent Nature

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Mathematical Analysis and Its Inherent Nature

Hossein Hosseini Giv
Mathematical Analysis and Its Inherent Nature Book PDF

Author : Hossein Hosseini Giv
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 43,7 Mb
Release : 2016-09-28
Category : Calculus
ISBN : 9781470428075

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Mathematical Analysis and Its Inherent Nature by Hossein Hosseini Giv Pdf

Mathematical analysis is often referred to as generalized calculus. But it is much more than that. This book has been written in the belief that emphasizing the inherent nature of a mathematical discipline helps students to understand it better. With this in mind, and focusing on the essence of analysis, the text is divided into two parts based on the way they are related to calculus: completion and abstraction. The first part describes those aspects of analysis which complete a corresponding area of calculus theoretically, while the second part concentrates on the way analysis generalizes some aspects of calculus to a more general framework. Presenting the contents in this way has an important advantage: students first learn the most important aspects of analysis on the classical space R and fill in the gaps of their calculus-based knowledge. Then they proceed to a step-by-step development of an abstract theory, namely, the theory of metric spaces which studies such crucial notions as limit, continuity, and convergence in a wider context. The readers are assumed to have passed courses in one- and several-variable calculus and an elementary course on the foundations of mathematics. A large variety of exercises and the inclusion of informal interpretations of many results and examples will greatly facilitate the reader's study of the subject.

Mathematical Analysis I: Approximation Theory

Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal
Mathematical Analysis I Approximation Theory Book PDF

Author : Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal
Publisher : Springer Nature
Page : 262 pages
File Size : 50,5 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9789811511530

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Mathematical Analysis I: Approximation Theory by Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal Pdf

This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences.

Foundations of Mathematical Analysis

Saminathan Ponnusamy
Foundations of Mathematical Analysis Book PDF

Author : Saminathan Ponnusamy
Publisher : Springer Science & Business Media
Page : 575 pages
File Size : 43,6 Mb
Release : 2011-12-17
Category : Mathematics
ISBN : 9780817682927

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Foundations of Mathematical Analysis by Saminathan Ponnusamy Pdf

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

The Mathematics of Patterns, Symmetries, and Beauties in Nature

Bourama Toni
The Mathematics of Patterns Symmetries and Beauties in Nature Book PDF

Author : Bourama Toni
Publisher : Springer Nature
Page : 150 pages
File Size : 46,8 Mb
Release : 2021-12-06
Category : Science
ISBN : 9783030845964

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The Mathematics of Patterns, Symmetries, and Beauties in Nature by Bourama Toni Pdf

This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations, statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature’s beauty in its various manifestations. This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books.

An Introduction to Analysis

Arlen Brown,Carl Pearcy
An Introduction to Analysis Book PDF

Author : Arlen Brown,Carl Pearcy
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207870

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An Introduction to Analysis by Arlen Brown,Carl Pearcy Pdf

As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form the book has been used in this way at the University of Michigan, Indiana University, and Texas A&M University, and has proved serviceable. In addition to its primary purpose as a textbook for a formal course, however, it is the authors' hope that this book will also prove of value to readers interested in studying mathematical analysis on their own. Indeed, we believe the wealth and variety of examples and exercises will be especially conducive to this end. A word on prerequisites. With what mathematical background might a prospective reader hope to profit from the study of this book? Our con scious intent in writing it was to address the needs of a beginning graduate student in mathematics, or, to put matters slightly differently, a student who has completed an undergraduate program with a mathematics ma jor. On the other hand, the book is very largely self-contained and should therefore be accessible to a lower classman whose interest in mathematical analysis has already been awakened.

A Bridge to Advanced Mathematics

Sebastian M. Cioabă,Werner Linde
A Bridge to Advanced Mathematics Book PDF

Author : Sebastian M. Cioabă,Werner Linde
Publisher : American Mathematical Society
Page : 544 pages
File Size : 55,8 Mb
Release : 2022-12-21
Category : Mathematics
ISBN : 9781470471484

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A Bridge to Advanced Mathematics by Sebastian M. Cioabă,Werner Linde Pdf

Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.

Topics in Applied Mathematics and Modeling

Oscar Gonzalez
Topics in Applied Mathematics and Modeling Book PDF

Author : Oscar Gonzalez
Publisher : American Mathematical Society
Page : 228 pages
File Size : 50,7 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9781470469917

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Topics in Applied Mathematics and Modeling by Oscar Gonzalez Pdf

The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience. Students who use this book will enhance their understanding of mathematics, acquire tools to explore meaningful scientific problems, and increase their preparedness for future research and advanced studies. The highlights of the book are case studies and mini-projects, which illustrate the mathematics in action. The book also contains a wealth of examples, figures, and regular exercises to support teaching and learning. The book includes opportunities for computer-aided explorations, and each chapter contains a bibliography with references covering further details of the material.

Mathematics of Optimization: How to do Things Faster

Steven J. Miller
Mathematics of Optimization How to do Things Faster Book PDF

Author : Steven J. Miller
Publisher : American Mathematical Soc.
Page : 327 pages
File Size : 55,9 Mb
Release : 2017-12-20
Category : Management science
ISBN : 9781470441142

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Mathematics of Optimization: How to do Things Faster by Steven J. Miller Pdf

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.

A Passage to Modern Analysis

William J. Terrell
A Passage to Modern Analysis Book PDF

Author : William J. Terrell
Publisher : American Mathematical Soc.
Page : 607 pages
File Size : 45,6 Mb
Release : 2019-10-21
Category : Education
ISBN : 9781470451356

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A Passage to Modern Analysis by William J. Terrell Pdf

A Passage to Modern Analysis is an extremely well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition. The examples, problems, and exposition open up a student's intuition but still provide coverage of deep areas of real analysis. A yearlong course from this text provides a solid foundation for further study or application of real analysis at the graduate level. A Passage to Modern Analysis is grounded solidly in the analysis of R and Rn, but at appropriate points it introduces and discusses the more general settings of inner product spaces, normed spaces, and metric spaces. The last five chapters offer a bridge to fundamental topics in advanced areas such as ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. Thus, the book introduces interesting and useful developments beyond Euclidean space where the concepts of analysis play important roles, and it prepares readers for further study of those developments.

Real Analysis: A Constructive Approach Through Interval Arithmetic

Mark Bridger
Real Analysis A Constructive Approach Through Interval Arithmetic Book PDF

Author : Mark Bridger
Publisher : American Mathematical Soc.
Page : 302 pages
File Size : 44,7 Mb
Release : 2019-07-05
Category : Continuity
ISBN : 9781470451448

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Real Analysis: A Constructive Approach Through Interval Arithmetic by Mark Bridger Pdf

Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering. The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material—including an introduction to complex variables and Fourier series—to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects—many with hints—at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout.

Linear Algebra for the Young Mathematician

Steven H. Weintraub
Linear Algebra for the Young Mathematician Book PDF

Author : Steven H. Weintraub
Publisher : American Mathematical Soc.
Page : 389 pages
File Size : 51,6 Mb
Release : 2019-10-29
Category : Education
ISBN : 9781470450847

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Linear Algebra for the Young Mathematician by Steven H. Weintraub Pdf

Linear Algebra for the Young Mathematician is a careful, thorough, and rigorous introduction to linear algebra. It adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject. It begins at the beginning, assuming no prior knowledge of the subject, but goes quite far, and it includes many topics not usually treated in introductory linear algebra texts, such as Jordan canonical form and the spectral theorem. While it concentrates on the finite-dimensional case, it treats the infinite-dimensional case as well. The book illustrates the centrality of linear algebra by providing numerous examples of its application within mathematics. It contains a wide variety of both conceptual and computational exercises at all levels, from the relatively straightforward to the quite challenging. Readers of this book will not only come away with the knowledge that the results of linear algebra are true, but also with a deep understanding of why they are true.

A Discrete Transition to Advanced Mathematics

Bettina Richmond,Thomas Richmond
A Discrete Transition to Advanced Mathematics Book PDF

Author : Bettina Richmond,Thomas Richmond
Publisher : American Mathematical Society
Page : 540 pages
File Size : 49,6 Mb
Release : 2023-08-25
Category : Mathematics
ISBN : 9781470472047

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A Discrete Transition to Advanced Mathematics by Bettina Richmond,Thomas Richmond Pdf

This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity. Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio. A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.

Introduction to Mathematics

Scott A. Taylor
Introduction to Mathematics Book PDF

Author : Scott A. Taylor
Publisher : American Mathematical Society
Page : 445 pages
File Size : 45,6 Mb
Release : 2023-09-13
Category : Mathematics
ISBN : 9781470471880

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Introduction to Mathematics by Scott A. Taylor Pdf

This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge.

Spaces: An Introduction to Real Analysis

Tom L. Lindstrøm
Spaces An Introduction to Real Analysis Book PDF

Author : Tom L. Lindstrøm
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 53,5 Mb
Release : 2017-11-28
Category : Functional analysis
ISBN : 9781470440626

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Spaces: An Introduction to Real Analysis by Tom L. Lindstrøm Pdf

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.

Applied Mathematical Analysis: Theory, Methods, and Applications

Hemen Dutta,James F. Peters
Applied Mathematical Analysis Theory Methods and Applications Book PDF

Author : Hemen Dutta,James F. Peters
Publisher : Springer
Page : 810 pages
File Size : 53,7 Mb
Release : 2019-02-21
Category : Technology & Engineering
ISBN : 9783319999180

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Applied Mathematical Analysis: Theory, Methods, and Applications by Hemen Dutta,James F. Peters Pdf

This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications.