Download or read book Encounters with Chaos and Fractals Third Edition written by DENNY. FORD GULICK (JEFF.) and published by . This book was released on 2018-09-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encounters with Chaos and Fractals Third Edition written by Denny Gulick and published by CRC Press. This book was released on 2018-08 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This popular text provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines. A set of concept-oriented problems for each chapter, and new examples and exercises are included in this edition.
Download or read book Encounters with Chaos and Fractals written by Denny Gulick and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications. The Third Edition updates this classic book for a modern audience. New applications on contemporary topics, like data science and mathematical modelling, appear throughout. Coding activities are transitioned to open-source programming languages, including Python. The text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the authors introduce famous infinitely complicated fractals. How to obtain computer renditions of them are explained. The book concludes with Julia sets and the Mandelbrot set"--
Download or read book Encounters with Chaos and Fractals written by Denny Gulick and published by CRC Press. This book was released on 2024-05-10 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications. The Third Edition updates this classic book for a modern audience. New applications on contemporary topics, like data science and mathematical modelling, appear throughout. Coding activities are transitioned to open-source programming languages, including Python. The text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the authors introduce famous infinitely complicated fractals. How to obtain computer renditions of them are explained. The book concludes with Julia sets and the Mandelbrot set. The Third Edition includes: v More coding activities included in each section. The code is expanded to include pseudo-code, with specific examples in MATLAB (or it's open-source cousin Octave) and Python. v Many more and updated exercises from previous editions. v Proof writing exercises for a more theoretical course. v Sections revised to include historical context. v Short sections added to explain applied problems developing the mathematics. This edition reveals how these ideas are continuing to be applied in the 21st century, while connecting to the long and winding history of dynamical systems. The primary focus is the beauty and diversity of these ideas. Offering more than enough material for a one-semester course, the authors show how these subjects continue to grow within mathematics and in many other disciplines.
Download or read book Encounters with Chaos and Fractals Second Edition written by Denny Gulick and published by CRC Press. This book was released on 2012-04-26 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.
Download or read book Advanced Linear Algebra written by Nicholas A. Loehr and published by CRC Press. This book was released on 2024-06-21 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author begins with chapters introducing basic notation for vector spaces, permutations, polynomials, and other algebraic structures. The following chapters are designed to be mostly independent of each other so that readers with different interests can jump directly to the topic they want. This is an unusual organization compared to many abstract algebra textbooks, which require readers to follow the order of chapters. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint, while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. A wide array of topics is included, ranging from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra). The book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.
Download or read book Intuitive Axiomatic Set Theory written by José L Garciá and published by CRC Press. This book was released on 2024-04-04 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
Download or read book Fundamentals of Abstract Algebra written by Mark J. DeBonis and published by CRC Press. This book was released on 2024-04-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained. Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
Download or read book Mathematical Biology written by Christina Alvey and published by CRC Press. This book was released on 2024-08-09 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text serves as an exploration of the beautiful topic of mathematical biology through the lens of discrete and differential equations. Intended for students who have completed differential and integral calculus, Mathematical Biology: Discrete and Differential Equations allows students to explore topics such as bifurcation diagrams, nullclines, discrete dynamics, and SIR models for disease spread, which are often reserved for more advanced undergraduate or graduate courses. These exciting topics are sprinkled throughout the book alongside the more typical first- and second-order linear differential equations and systems of linear differential equations. This class-tested text is written in a conversational, welcoming voice, which should help invite students along as they discover the magic of mathematical biology and both discrete and differential equations. A focus is placed on examples with solutions written out step by step, including computational steps, with the goal of being as easy as possible for students to independently follow along. Rich in applications, this book can be used for a semester-long course in either differential equations or mathematical biology. Alternatively, it can serve as a companion text for a two-semester sequence beginning with discrete-time systems, extending through a wide array of topics in differential equations, and culminating in systems, SIR models, and other applications.
Download or read book Taking the Oof Out of Proofs written by Alexandr Draganov and published by CRC Press. This book was released on 2024-04-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high-school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one. Readers will see how various mathematical concepts are tied and will see that mathematics is not a pile of formulas and facts; rather, it has an orderly and beautiful edifice. The author begins with basic rules of logic and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader. Reviewer Comments: I find the book very impressive. The choice and sequence of topics is excellent, and it is wonderful to have all of these things together in one volume. Theorems are clearly stated, and proofs are accurate. – Michael Comenetz The thoroughness of the narrative is one of the main strengths of the book. The book provides a perfect illustration of mathematical thinking. Each step of a given derivation is precise and clear. – Julie Gershunskaya Draganov’s book stands out from the many competing books. Draganov’s goal is to show that mathematics depends on the notion of proof. Unlike other transition books, he addresses mathematical topics at an accessible level, rather than topics studied later in the university curriculum. – Ken Rosen
Download or read book Vector Calculus written by Steven G. Krantz and published by CRC Press. This book was released on 2024-05-28 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using meaningful examples, credible applications, and incisive technology, Vector Calculus strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. This text is intended to be a cornerstone of that process. An engaging style and clear writing make the language of mathematics accessible, understandable, and enjoyable, with a high standard for mathematical rigor. A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject, and offers a sense of what mathematics is all about. Technique is presented, yet so are ideas. The authors help students to master basic methods and discover and build their own concepts in a scientific subject. There is an emphasis on using modeling and numerical calculation. Additional features include: A Quick Quiz and Problems for Practice, Further Theory and Practice, and Calculator/Computer Exercises appear at the end of each section All exercise sets are step laddered A Look Back and A Look Forward help students put the ideas in context Every chapter ends with a Genesis and Development section, giving history and perspective on key topics in the evolution of calculus Boxed Insights clear up points or answer commonly asked questions The text has an extra-large offering of examples Examples are illustrated with meaningful and useful graphics The pedagogical features make the subject more interesting and accessible to students than other texts, while maintaining an appropriate rigor. —Daniel Cunningham, CSU-Fresno This text is truly well written and organized. I do like the fact the book is quite rigorous, yet full of illustrative examples. —Bob Devaney, Boston University
Download or read book Differential Calculus in Several Variables written by Marius Ghergu and published by CRC Press. This book was released on 2024-02-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle, who wrote in his Nicomachean Ethics that “For the things we have to learn before we can do them, we learn by doing them”. The theory is illustrated through many relevant examples, followed by a large number of exercises whose requirements are rendered by action verbs: find, show, verify, check and construct. Readers are compelled to analyze and organize analytical skills. Rather than placing the exercises in bulk at the end of each chapter, sets of practice questions after each theoretical concept are included. The reader has the possibility to check their understanding, work on the new topics and gain confidence during the learning activity. As the theory unfolds, the exercises become more complex – sometimes they span over several topics. Hints have been added in order to guide the reader in the process. This book stems from the Differential Calculus course which the author taught for many years. The goal of this book is to immerse the reader in the subtleties of Differential Calculus through an active perspective. Particular attention was paid to continuity and differentiability topics, presented in a new course of action.
Download or read book A Bridge to Higher Mathematics written by James R. Kirkwood and published by CRC Press. This book was released on 2024-05-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this unique text is to provide an “experience” that would facilitate a better transition for mathematics majors to the advanced proof-based courses required for their major. If you feel like you love mathematics but hate proofs, this book is for you. The change from example-based courses such as Introductory Calculus to the proof-based courses in the major is often abrupt, and some students are left with the unpleasant feeling that a subject they loved has turned into material they find hard to understand. The book exposes students and readers to some fundamental content and essential methods of constructing mathematical proofs in the context of four main courses required for the mathematics major – probability, linear algebra, real analysis, and abstract algebra. Following an optional foundational chapter on background material, four short chapters, each focusing on a particular course, provide a slow-paced but rigorous introduction. Students get a preview of the discipline, its focus, language, mathematical objects of interest, and methods of proof commonly used in the field. The organization of the book helps to focus on the specific methods of proof and main ideas that will be emphasized in each of the courses. The text may also be used as a review tool at the end of each course and for readers who want to learn the language and scope of the broad disciplines of linear algebra, abstract algebra, real analysis, and probability, before transitioning to these courses.
Download or read book Fractals Chaos Power Laws written by Manfred Schroeder and published by Courier Corporation. This book was released on 2009-08-21 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
Download or read book Discrete Encounters written by Craig Bauer and published by CRC Press. This book was released on 2020-05-14 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated
Download or read book Fractal Worlds written by Michael Frame and published by Yale University Press. This book was released on 2016-01-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this essential primer, mathematician Michael Frame, a close collaborator with Benoit Mandelbrot, the founder of fractal geometry, and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology
Download or read book An Introduction To Chaotic Dynamical Systems written by Robert Devaney and published by CRC Press. This book was released on 2018-03-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
