Mathematical Analysis And Its Inherent Nature

DOWNLOAD

Download Mathematical Analysis And Its Inherent Nature PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Mathematical Analysis And Its Inherent Nature book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Mathematical Analysis And Its Inherent Nature

DOWNLOAD
Author : Hossein Hosseini Giv
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-28

Mathematical Analysis And Its Inherent Nature written by Hossein Hosseini Giv and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-28 with Mathematics categories.

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.

Explorations In Analysis Topology And Dynamics An Introduction To Abstract Mathematics

DOWNLOAD
Author : Alejandro Uribe A.
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-21

Explorations In Analysis Topology And Dynamics An Introduction To Abstract Mathematics written by Alejandro Uribe A. and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Education categories.

This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.

Spaces An Introduction To Real Analysis

DOWNLOAD
Author : Tom L. Lindstrøm
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-28

Spaces An Introduction To Real Analysis written by Tom L. Lindstrøm and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Mathematics categories.

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.

An Introduction To Real Analysis

DOWNLOAD
Author : Yitzhak Katznelson
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-22

An Introduction To Real Analysis written by Yitzhak Katznelson and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-22 with Mathematics categories.

An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome. The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.

Introduction To Analysis In One Variable

DOWNLOAD
Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-11

Introduction To Analysis In One Variable written by Michael E. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Education categories.

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

A Bridge To Advanced Mathematics

DOWNLOAD
Author : Sebastian M. Cioabă
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-21

A Bridge To Advanced Mathematics written by Sebastian M. Cioabă and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-21 with Mathematics categories.

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.

A Course In Cryptography

DOWNLOAD
Author : Heiko Knospe
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-27

A Course In Cryptography written by Heiko Knospe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-27 with Computers categories.

This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.

An Introduction To Game Theoretic Modelling Third Edition

DOWNLOAD
Author : Mike Mesterton-Gibbons
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-05

An Introduction To Game Theoretic Modelling Third Edition written by Mike Mesterton-Gibbons and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-05 with Mathematics categories.

This book introduces game theory and its applications from an applied mathematician's perspective, systematically developing tools and concepts for game-theoretic modelling in the life and social sciences. Filled with down-to-earth examples of strategic behavior in humans and other animals, the book presents a unified account of the central ideas of both classical and evolutionary game theory. Unlike many books on game theory, which focus on mathematical and recreational aspects of the subject, this book emphasizes using games to answer questions of current scientific interest. In the present third edition, the author has added substantial new material on evolutionarily stable strategies and their use in behavioral ecology. The only prerequisites are calculus and some exposure to matrix algebra, probability, and differential equations.

A Discrete Transition To Advanced Mathematics

DOWNLOAD
Author : Bettina Richmond
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-25

A Discrete Transition To Advanced Mathematics written by Bettina Richmond and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-25 with Mathematics categories.

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 Analysis In Several Variables Advanced Calculus

DOWNLOAD
Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-27

Introduction To Analysis In Several Variables Advanced Calculus written by Michael E. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-27 with Education categories.

This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.