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Fundamentals of Advanced Mathematics 1

Fundamentals of Advanced Mathematics 1
Categories, Algebraic Structures, Linear and Homological Algebra

by Henri Bourles

  • Publisher : Elsevier
  • Release : 2017-07-10
  • Pages : 268
  • ISBN : 0081021127
  • Language : En, Es, Fr & De
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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

Fundamentals of Advanced Mathematics

by Miansen Wang,Fred Brauer

  • Publisher : Unknown Publisher
  • Release : 2005
  • Pages : 390
  • ISBN : 9787040154849
  • Language : En, Es, Fr & De
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Fundamentals of Advanced Mathematics V3

Fundamentals of Advanced Mathematics V3
A Book

by Henri Bourles

  • Publisher : Elsevier
  • Release : 2019-10-11
  • Pages : 424
  • ISBN : 0081023863
  • Language : En, Es, Fr & De
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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: 3. Structures

Fundamentals of Advanced Mathematics: 3. Structures
A Book

by Henri Bourles

  • Publisher : Unknown Publisher
  • Release : 2017
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Fundamentals of Advanced Mathematics 2

Fundamentals of Advanced Mathematics 2
Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves

by Henri Bourles

  • Publisher : Elsevier
  • Release : 2018-02-03
  • Pages : 360
  • ISBN : 0081023855
  • Language : En, Es, Fr & De
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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

Fundamentals for Advanced Mathematics

Fundamentals for Advanced Mathematics
A Book

by Abraham M. Glicksman,Harry D. Ruderman

  • Publisher : Unknown Publisher
  • Release : 1964
  • Pages : 651
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Solutions for Fundamentals for Advanced Mathematics

Solutions for Fundamentals for Advanced Mathematics
A Book

by Abraham M. Glicksman,Harry D. Ruderman

  • Publisher : Unknown Publisher
  • Release : 1964
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Fundamentals of Mathematical Reasoning

Fundamentals of Mathematical Reasoning
A Transition to Advanced Mathematics

by Mike Daven,Lee Fothergill

  • Publisher : Createspace Independent Pub
  • Release : 2011-08-01
  • Pages : 88
  • ISBN : 9781456398736
  • Language : En, Es, Fr & De
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The book provides a transition to advanced mathematics. This is a complete workbook including all supporting content and explanation. Additional resources (PowerPoint, sample assignments) are available to instructors.

Fundamentals of Advanced Mathematics

Fundamentals of Advanced Mathematics
A Book

by Alberto D. Yazon

  • Publisher : Arcler Press
  • Release : 2019-11
  • Pages : 257
  • ISBN : 9781773614045
  • Language : En, Es, Fr & De
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Fundamentals of Advanced Mathematics explains the basic fundamentals of mathematics by introducing it to the readers. It further goes on to explain algebra and the basic math related to it and elaborate on the number theory and number system. Also discussed in the book are the relations and functions, the use of proportional logic, the graph theory and the mathematical induction and recursion and the various theorems and logics related to it. The book also delves upon the cardinal system. It gives some solved examples and the questions to be practiced in the later halves of the chapters.

Proofs and Fundamentals

Proofs and Fundamentals
A First Course in Abstract Mathematics

by Ethan D. Bloch

  • Publisher : Springer Science & Business Media
  • Release : 2013-12-01
  • Pages : 424
  • ISBN : 1461221307
  • Language : En, Es, Fr & De
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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.

Advanced Calculus: Fundamentals of Mathematics

Advanced Calculus: Fundamentals of Mathematics
A Book

by Carlos Polanco

  • Publisher : Bentham Science Publishers
  • Release : 2019-07-31
  • Pages : 212
  • ISBN : 9811415072
  • Language : En, Es, Fr & De
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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.

Nurturing Reflective Learners in Mathematics

Nurturing Reflective Learners in Mathematics
A Book

by Berinderjeet Kaur

  • Publisher : World Scientific
  • Release : 2013
  • Pages : 319
  • ISBN : 981447276X
  • Language : En, Es, Fr & De
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This annual volume focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reflection among students and teachers in mathematics classrooms. Published jointly with the Association of Mathematics Educators in Singapore.

Catalog of Copyright Entries. Third Series

Catalog of Copyright Entries. Third Series
1964: January-June

by Library of Congress. Copyright Office

  • Publisher : Unknown Publisher
  • Release : 1967
  • Pages : 1292
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)

Advanced Dictionary of Mathematics Formulas

Advanced Dictionary of Mathematics Formulas
A Book

by Rajesh Thakur Kumar

  • Publisher : Prabhat Prakashan Pvt Limited
  • Release : 2021-01-02
  • Pages : 290
  • ISBN : 9788184301328
  • Language : En, Es, Fr & De
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Mathematics is called the queen of all subjects but it is also thought to be one of the dreadful subject. Here is a Dictionary that goes beyond a mere listing of words and definations. This unique work has more than 2000 mathematical terms, designed as a time-saving reference work for students of all classes. Hundreds of examples and how to solve the problem of a particular type in almost every branch of mathematics has been its additional beauty. This vast fund of information will also enable the general reader to understand a particular mathematical concept, or to extend his own knowledge of mathematics. The coverage of terms is broad, from elementary terms in algebra, arithmetic through calculus, basic terms in 2-D and 3-Dimension geometry, advanced calculus, differential equations to the vector algebra and matrices, statics, dynamics and LPP. To make the understanding of concept clear more than 200 mathematical diagrams have been used. Apart from that, ample examples have been given to give in depth knowledge to students.

A Formal Background to Mathematics

A Formal Background to Mathematics
Logic, Sets and Numbers

by R. E. Edwards

  • Publisher : Springer Science & Business Media
  • Release : 2013-12-18
  • Pages : 935
  • ISBN : 1461299845
  • Language : En, Es, Fr & De
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ยง1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).

Fundamentals of mathematics from an advanced viewpoint. 3. Geometry and geometric analysis

Fundamentals of mathematics from an advanced viewpoint. 3. Geometry and geometric analysis
A Book

by Ervand G. Kogbetliantz

  • Publisher : Unknown Publisher
  • Release : 1969
  • Pages : 354
  • ISBN : 9780677004556
  • Language : En, Es, Fr & De
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Theoretical Foundations

Theoretical Foundations
A Book

by Anonim

  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 2019-06-03
  • Pages : 548
  • ISBN : 3110814641
  • Language : En, Es, Fr & De
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Mathematics and Philosophy

Mathematics and Philosophy
A Book

by Daniel Parrochia

  • Publisher : John Wiley & Sons
  • Release : 2018-05-24
  • Pages : 352
  • ISBN : 1119527791
  • Language : En, Es, Fr & De
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This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cube, trisection of the angle...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to inspire philosophers (Descartes, Leibniz, Hegel, Husserl, etc.). However, from a certain level of complexity, the mathematicians themselves became philosophers (a movement that begins with Wronsky and Clifford, and continues until Grothendieck).

Fundamentals of Mathematics from an Advanced Viewpoint

Fundamentals of Mathematics from an Advanced Viewpoint
Algebra and analysis: determinants, equations, logarithms

by Ervand George Kogbetliantz

  • Publisher : Unknown Publisher
  • Release : 1968
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Advanced Mathematics for Engineering Aspirants

Advanced Mathematics for Engineering Aspirants
Vol. 1 of 4: Complete Study Material for Engineering Entrances

by Dr Vibhav Kumar Sachan

  • Publisher : Unknown Publisher
  • Release : 2020-05-06
  • Pages : 450
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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It is no doubt that engineering has always been one of the most sought-after career opportunities for aspirants, driving them towards a rigorous preparation in order to crack any engineering entrance exams. "Advanced Mathematics for Engineering Aspirants " is a Sachan Series of our best-in-class objective study guides in sync with class 11th and 12th syllabus to enable aspirants towards an effective preparation along with their school studies. It is divided into 20 chapters, accompanying complete text material and practice exercises, along with workbook exercises coupled with each theory. It is housed with more than 10000 MCQs and a brilliant collection of previous years' solved papers of different Engineering Entrances Examination in developed and developing Countries. The fundamental concepts and principles behind Mathematics are explained in a simple, easy- to- understand manner. Each chapter contains a large number of solved example or problem which will help the students in problem solving. This text book "Advanced Mathematics for Engineering Aspirants- Vol. 1 of 4" is organized into Six Chapters. Chapter -1: Sets, Relations and FunctionsChapter- 2: Basic AlgebraChapter -3: TrigonometryChapter-4: Combinatorics and Mathematical InductionChapter-5: Binomial Theorem, Sequences and SeriesChapter-6: Two Dimensional Analytical GeometryThe "Advanced Mathematics for Engineering Aspirants" has designed to help students learn the basics of mathematics that they are supposed to understand upon entering Intermediate school, as well as the fundamental lessons within Algebra, Geometry, and Statistics that students typically learn in 11th and 12th grade. Table of Contents (TOC) sets, fundamentals of relation and function, sequence and Series, complex Numbers, inequalities and Quadratic equation, Permutation and Combination, mathematical Induction, Binomial Theorem, Trigonometric Functions and equations, properties of Triangles, heights and Distances, Cartesian system of Rectangular coordinates, straight Line and pair of straight Lines, circle, Parabola, Ellipse, Hyperbola, introduction to three Dimensional (3D) Geometry, introduction to limits and derivatives, mathematical Reasoning, statistics, fundamentals of probability, Salient Features-Comprehensive Coverage of Sets, Relations & Functions, Basic Algebra, Trigonometry, Combinatorics & Mathematical Induction, Binomial Theorem, Sequences & Series and Two Dimensional Analytical Geometry. -Each chapter contains a large number of solved example or objective type's problem which will help the students in problem solving of Mathematics.-Clear perception of the various problems with a large number of neat, well drawn and illustrative diagrams. -Simple Language, easy- to- understand manner. Our sincere thanks are due to all Scientists, Engineers, Authors and Publishers, whose works and text have been the source of enlightenment, inspiration and guidance to us in presenting this small book. I will appreciate any suggestions from students and faculty members alike so that we can strive to make the text book more useful in the edition to come. Dr. V. K. Sachan