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Author: William E. Kline
Publisher:
Published: 1975
Total Pages: 583
ISBN-13: 9780278469198
DOWNLOAD EBOOKDownload 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:
Author: Henri Bourles
Publisher: Elsevier
Published: 2017-07-10
Total Pages: 268
ISBN-13: 0081021127
DOWNLOAD EBOOKThis 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 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
Author: Martin Perkins
Publisher:
Published: 1982
Total Pages: 580
ISBN-13: 9780713512724
DOWNLOAD EBOOKDownload 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:
Author: Carol Avelsgaard
Publisher: Scott Foresman & Company
Published: 1990
Total Pages: 325
ISBN-13: 9780673381521
DOWNLOAD EBOOKDownload 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:
Author: Peter Fletcher
Publisher:
Published: 1992
Total Pages: 0
ISBN-13: 9780534983864
DOWNLOAD EBOOKDownload or read book Foundations of Higher Mathematics written by Peter Fletcher and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Paul Taylor
Publisher: Cambridge University Press
Published: 1999-05-13
Total Pages: 590
ISBN-13: 9780521631075
DOWNLOAD EBOOKThis 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 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.
Author: Henri Bourles
Publisher: Elsevier
Published: 2018-02-03
Total Pages: 360
ISBN-13: 0081023855
DOWNLOAD EBOOKThe 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 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
Author: Dennis Sentilles
Publisher: Courier Corporation
Published: 2013-05-20
Total Pages: 416
ISBN-13: 0486277585
DOWNLOAD EBOOKThis 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 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.
Author: Stephen Siklos
Publisher:
Published: 2020-10-09
Total Pages: 180
ISBN-13: 9781013293832
DOWNLOAD EBOOKThis new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Download or read book Advanced Problems in Mathematics written by Stephen Siklos and published by . This book was released on 2020-10-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Author: Shinichi Mochizuki
Publisher: American Mathematical Soc.
Published: 2014-01-06
Total Pages: 529
ISBN-13: 1470412268
DOWNLOAD EBOOKThis 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 of p-adic Teichmüller Theory written by Shinichi Mochizuki and published by American Mathematical Soc.. This book was released on 2014-01-06 with total page 529 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.
