Fundamentals For Advanced Mathematics

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Fundamentals of Advanced Mathematics 1

Author : Henri Bourles
Publisher : Elsevier
ISBN 13 : 0081021127
Total Pages : 268 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics 1 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics 1 written by Henri Bourles and published by Elsevier. This book was released on 2017-07-10 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. Part of the New Mathematical Methods, Systems, and Applications series Presents the notions, results, and proofs necessary to understand and master the various topics Provides a unified notation, making the task easier for the reader. Includes several summaries of mathematics for engineers

Fundamentals of Advanced Mathematics V3

Author : Henri Bourles
Publisher : Elsevier
ISBN 13 : 0081023863
Total Pages : 424 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics V3 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics V3 written by Henri Bourles and published by Elsevier. This book was released on 2019-10-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems. Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems Provides theory as well as practical information

Fundamentals of Advanced Mathematics 2

Author : Henri Bourles
Publisher : Elsevier
ISBN 13 : 0081023855
Total Pages : 360 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics 2 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics 2 written by Henri Bourles and published by Elsevier. This book was released on 2018-02-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and Picard Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Foundations of Advanced Mathematics

Author : William E. Kline
Publisher :
ISBN 13 : 9780278469198
Total Pages : 583 pages
Book Rating : 4.4/5 (691 download)

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Book Synopsis Foundations of Advanced Mathematics by : William E. Kline

Download or read book Foundations of Advanced Mathematics written by William E. Kline and published by . This book was released on 1975 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Advanced Mathematics

Author : Zhien Ma
Publisher :
ISBN 13 : 9787040177947
Total Pages : 453 pages
Book Rating : 4.1/5 (779 download)

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Book Synopsis Fundamentals of Advanced Mathematics by : Zhien Ma

Download or read book Fundamentals of Advanced Mathematics written by Zhien Ma and published by . This book was released on 2005 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elements of Advanced Mathematics, Third Edition

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1439898340
Total Pages : 368 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Elements of Advanced Mathematics, Third Edition by : Steven G. Krantz

Download or read book Elements of Advanced Mathematics, Third Edition written by Steven G. Krantz and published by CRC Press. This book was released on 2012-03-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant. This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques. Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.

Basic Category Theory

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1107044243
Total Pages : 193 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Basic Category Theory by : Tom Leinster

Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.

Advanced Calculus: Fundamentals of Mathematics

Author : Carlos Polanco
Publisher : Bentham Science Publishers
ISBN 13 : 9811415072
Total Pages : 212 pages
Book Rating : 4.8/5 (114 download)

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Book Synopsis Advanced Calculus: Fundamentals of Mathematics by : Carlos Polanco

Download or read book Advanced Calculus: Fundamentals of Mathematics written by Carlos Polanco and published by Bentham Science Publishers. This book was released on 2019-07-31 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.

Advanced Mathematics for Engineering Students

Author : Brent J. Lewis
Publisher : Butterworth-Heinemann
ISBN 13 : 0128236825
Total Pages : 432 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Advanced Mathematics for Engineering Students by : Brent J. Lewis

Download or read book Advanced Mathematics for Engineering Students written by Brent J. Lewis and published by Butterworth-Heinemann. This book was released on 2021-05-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics courses at the author’s university, the book delivers the mathematical foundation needed in an engineering program of study. Other treatments typically provide a thorough but somewhat complicated presentation where students do not appreciate the application. This book focuses on the development of tools to solve most types of mathematical problems that arise in engineering – a “toolbox” for the engineer. It provides an important foundation but goes one step further and demonstrates the practical use of new technology for applied analysis with commercial software packages (e.g., algebraic, numerical and statistical). Delivers a focused and concise treatment on the underlying theory and direct application of mathematical methods so that the reader has a collection of important mathematical tools that are easily understood and ready for application as a practicing engineer The book material has been derived from class-tested courses presented over many years in applied mathematics for engineering students (all problem sets and exam questions given for the course(s) are included along with a solution manual) Provides fundamental theory for applied mathematics while also introducing the application of commercial software packages as modern tools for engineering application, including: EXCEL (statistical analysis); MAPLE (symbolic and numeric computing environment); and COMSOL (finite element solver for ordinary and partial differential equations)

All the Mathematics You Missed

Author : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
ISBN 13 : 9787302090854
Total Pages : 380 pages
Book Rating : 4.0/5 (98 download)

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Book Synopsis All the Mathematics You Missed by : Thomas A. Garrity

Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Scientific Mathematics

Author : George E. Owen
Publisher : Courier Corporation
ISBN 13 : 0486164586
Total Pages : 288 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Fundamentals of Scientific Mathematics by : George E. Owen

Download or read book Fundamentals of Scientific Mathematics written by George E. Owen and published by Courier Corporation. This book was released on 2012-12-03 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.

Advanced Calculus

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Proofs and Fundamentals

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
ISBN 13 : 1461221307
Total Pages : 434 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Proofs and Fundamentals by : Ethan D. Bloch

Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Galois Groups and Fundamental Groups

Author : Tamás Szamuely
Publisher : Cambridge University Press
ISBN 13 : 1139481142
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Galois Groups and Fundamental Groups by : Tamás Szamuely

Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.

A Transition to Proof

Author : Neil R. Nicholson
Publisher : CRC Press
ISBN 13 : 0429535473
Total Pages : 323 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis A Transition to Proof by : Neil R. Nicholson

Download or read book A Transition to Proof written by Neil R. Nicholson and published by CRC Press. This book was released on 2019-03-21 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

Advanced Mathematics

Author : John H. Saxon, Jr.
Publisher : Saxon Pub
ISBN 13 : 9781565771277
Total Pages : pages
Book Rating : 4.7/5 (712 download)

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Book Synopsis Advanced Mathematics by : John H. Saxon, Jr.

Download or read book Advanced Mathematics written by John H. Saxon, Jr. and published by Saxon Pub. This book was released on 1999-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Saxon math programs produce confident students who are not only able to correctly compute, but also to apply concepts to new situations. These materials gently develop concepts, and the practice of those concepts is extended over a considerable period of time. This is called "incremental development and continual review." Material is introduced in easily understandable pieces (increments), allowing students to grasp one facet of a concept before the next one is introduced. Both facets are then practiced together until another one is introduced. This feature is combined with continual review in every lesson throughout the year. Topics are never dropped but are increased in complexity and practiced every day, providing the time required for concepts to become totally familiar. Advanced Mathematics, second edition is made up of five instructional components: Introduction of the New Increment, Examples with complete Solutions, Practice of the Increment, Daily Problem Set, and Cumulative Tests. In Advanced Mathematics, topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis are interwoven to form a fully integrated text. A rigorous treatment of Euclidean geometry is also presented. Word problems are developed throughout the problem sets and become progressively more elaborate. With this practice, students will be able to solve challenging problems such as rate problems and work problems involving abstract quantities. A graphing calculator is used to graph functions and perform data analysis. Conceptually-oriented problems that prepare students for college entrance exams (such as the ACT and SAT) are included in the problem sets. This set contains a student text, answer key and test forms. A solutions manual is sold separately. Grade 11.

A Transition to Advanced Mathematics

Author : William Johnston
Publisher : Oxford University Press
ISBN 13 : 9780199718665
Total Pages : 768 pages
Book Rating : 4.7/5 (186 download)

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Book Synopsis A Transition to Advanced Mathematics by : William Johnston

Download or read book A Transition to Advanced Mathematics written by William Johnston and published by Oxford University Press. This book was released on 2009-07-27 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.