Abstract Calculus

Author : Francisco Javier Garcia-Pacheco
Publisher : CRC Press
Page : 396 pages
File Size : 46,7 Mb
Release : 2021-09-08
Category : Mathematics
ISBN : 9781000432268

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Abstract Calculus by Francisco Javier Garcia-Pacheco Pdf

Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing PhDs in pure mathematics but junior and senior researchers in basically any field of mathematics and theoretical physics will also be interested. Any calculus text for undergraduate students majoring in engineering, mathematics or physics deals with the classical concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the exact same topics, but from a categorical perspective, making the classification of topological modules as the main category involved. Features Suitable for PhD candidates and researchers Requires prerequisites in set theory, general topology, and abstract algebra, but is otherwise self-contained Dr. Francisco Javier García-Pacheco is a full professor and Director of the Departmental Section of Mathematics at the College of Engineering of the University of Cádiz, Spain.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 42,7 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

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.

Author : I. N. Herstein
Publisher : Macmillan College
Page : 322 pages
File Size : 45,7 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015049346839

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Abstract Algebra by I. N. Herstein Pdf

Author : Dan Saracino
Publisher : Waveland Press
Page : 320 pages
File Size : 52,8 Mb
Release : 2008-09-02
Category : Mathematics
ISBN : 9781478610137

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Abstract Algebra by Dan Saracino Pdf

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

Author : Werner Kluge
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 43,5 Mb
Release : 2005-02-18
Category : Computers
ISBN : 9783540211464

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Abstract Computing Machines by Werner Kluge Pdf

The book emphasizes the design of full-fledged, fully normalizing lambda calculus machinery, as opposed to the just weakly normalizing machines.

Author : Qun Lin
Publisher : World Scientific
Page : 109 pages
File Size : 49,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812704580

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Free Calculus by Qun Lin Pdf

This book provides a fascinating account of the accumulated knowledge of the mechanisms by which plants regulate their patterning. This is an exciting subject based on a novel endeavor, not least due to the rapid progress made in recent years in the diverse fields of genetics, molecular biology, microscopy, inter- and intracellular signaling, as well as our intimate knowledge of model plants (such as Arabidopsis). This book is unique in that it provides, in one volume, comprehensive information on all the main organs of flowering plants. There is no other book similar to this, written by a single author, that has been published in the last 10 years. The book contains updated information on the differentiation of the plant organs with respect to structure and molecular genetics, and the methodologies employed to investigate plant patterning are described in detail. Extensively illustrated with numerous figures, many of which are in color, the book will appeal to three main groups of readers: novices interested in plant patterning; plant biologists requiring a comprehensive understanding of differentiation in flowering plants; and graduate students in advanced courses.

Author : T. A. Bick
Publisher : Elsevier
Page : 232 pages
File Size : 55,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483276595

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Introduction to Abstract Mathematics by T. A. Bick Pdf

Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.

Author : Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 367 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881913

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Parabolicity, Volterra Calculus, and Conical Singularities by Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze Pdf

Partial differential equations constitute an integral part of mathematics. They lie at the interface of areas as diverse as differential geometry, functional analysis, or the theory of Lie groups and have numerous applications in the applied sciences. A wealth of methods has been devised for their analysis. Over the past decades, operator algebras in connection with ideas and structures from geometry, topology, and theoretical physics have contributed a large variety of particularly useful tools. One typical example is the analysis on singular configurations, where elliptic equations have been studied successfully within the framework of operator algebras with symbolic structures adapted to the geometry of the underlying space. More recently, these techniques have proven to be useful also for studying parabolic and hyperbolic equations. Moreover, it turned out that many seemingly smooth, noncompact situations can be handled with the ideas from singular analysis. The three papers at the beginning of this volume highlight this aspect. They deal with parabolic equations, a topic relevant for many applications. The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed. It is shown how timelike infinity can be treated as a conical singularity.

Author : Kenneth E. Hummel
Publisher : CRC Press
Page : 345 pages
File Size : 41,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285642

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Introductory Concepts for Abstract Mathematics by Kenneth E. Hummel Pdf

Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.

Author : Richard A. Silverman
Publisher : Courier Corporation
Page : 320 pages
File Size : 51,9 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486318592

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Essential Calculus with Applications by Richard A. Silverman Pdf

Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician. The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables. Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

Author : Charles Lanski
Publisher : American Mathematical Soc.
Page : 564 pages
File Size : 55,6 Mb
Release : 2024-06-02
Category : Mathematics
ISBN : 0821874284

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Concepts in Abstract Algebra by Charles Lanski Pdf

The style and structure of CONCEPTS IN ABSTRACT ALGEBRA is designed to help students learn the core concepts and associated techniques in algebra deeply and well. Providing a fuller and richer account of material than time allows in a lecture, this text presents interesting examples of sufficient complexity so that students can see the concepts and results used in a nontrivial setting. Author Charles Lanski gives students the opportunity to practice by offering many exercises that require the use and synthesis of the techniques and results. Both readable and mathematically interesting, the text also helps students learn the art of constructing mathematical arguments. Overall, students discover how mathematics proceeds and how to use techniques that mathematicians actually employ. This book is included in the Brooks/Cole Series in Advanced Mathematics (Series Editor: Paul Sally, Jr.).

Author : Robert J. Bond,William J. Keane
Publisher : Waveland Press
Page : 344 pages
File Size : 49,5 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9781478608059

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An Introduction to Abstract Mathematics by Robert J. Bond,William J. Keane Pdf

Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.

Author : Anonim
Publisher : Unknown
Page : 788 pages
File Size : 45,7 Mb
Release : 1878
Category : Medicine
ISBN : HARVARD:32044103093647

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The Monthly Abstract of Medical Science by Anonim Pdf

Author : Carlos Polanco
Publisher : Bentham Science Publishers
Page : 141 pages
File Size : 44,8 Mb
Release : 2021-09-01
Category : Mathematics
ISBN : 9789814998796

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Exterior Calculus: Theory and Cases by Carlos Polanco Pdf

Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem. This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions. Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. 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 exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.

Author : Alejandro Uribe A.,Daniel A. Visscher
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 48,7 Mb
Release : 2020-05-21
Category : Education
ISBN : 9781470452704

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Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics by Alejandro Uribe A.,Daniel A. Visscher Pdf

This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.