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:

Download or read book Foundations for Advanced Mathematics written by Carol Avelsgaard and published by Scott Foresman & Company. This book was released on 1990 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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

Download or read book Practical Foundations of Mathematics written by Paul Taylor and published by Cambridge University Press. This book was released on 1999-05-13 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.

Download or read book Advanced Mathematics written by Martin Perkins and published by . This book was released on 1982 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Bridge to Advanced Mathematics written by Dennis Sentilles and published by Courier Corporation. This book was released on 2013-05-20 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

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

Download or read book Starting Advanced Mathematics written by Hugh Neill and published by Cambridge University Press. This book was released on 2002-03-14 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting Advanced Mathematics is a self-study guide for students who will be continuing their study of Mathematics after GCSE either to AS/A level or as part of the International Baccalaureate. It will enable students to consolidate the basic algebra and trigonometry skills that they will require during their study of advanced Mathematics. Other GCSE formulae and results that they may require during their post 16 studies are included for reference. The book is also a valuable revision aid for Higher Tier GCSE students who need more practice in Algebra and Trigonometry.

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.

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)

Download or read book Foundations of p adic Teichmuller Theory written by Shinichi Mochizuki and published by American Mathematical Soc.. This book was released on 2014-01-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p-adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of p-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis. Features: Presents a systematic treatment of the moduli space of curves from the point of view of p-adic Galois representations.Treats the analog of Serre-Tate theory for hyperbolic curves.Develops a p-adic analog of Fuchsian and Bers uniformization theories.Gives a systematic treatment of a "nonabelian example" of p-adic Hodge theory. Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Download or read book Foundations for Advanced Mathematics written by Ann Xavier and published by . This book was released on 1993-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Download or read book Foundations of Applied Mathematics Volume I written by Jeffrey Humpherys and published by SIAM. This book was released on 2017-07-07 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

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 766 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.

Download or read book A Transition to Advanced Mathematics written by Douglas Smith and published by Cengage Learning. This book was released on 2010-06-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.