An Invitation To Abstract Mathematics
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An Invitation To Abstract Mathematics
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Author : Béla Bajnok
language : en
Publisher: Springer Nature
Release Date : 2020-10-27
An Invitation To Abstract Mathematics written by Béla Bajnok and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-27 with Mathematics categories.
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
An Invitation To Abstract Algebra
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Author : Steven J. Rosenberg
language : en
Publisher:
Release Date : 2022
An Invitation To Abstract Algebra written by Steven J. Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
A Primer Of Abstract Mathematics
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Author : Robert B. Ash
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-02
A Primer Of Abstract Mathematics written by Robert B. Ash and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Mathematics categories.
The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formally but also to think intuitively about what is going on and to describe that process clearly and cogently in ordinary English. Ash tries to aid intuition by keeping proofs short and as informal as possible and using concrete examples as illustration. Thus, it is an ideal textbook for an audience with limited experience in formalism and abstraction. A number of expository innovations are included, for example, an informal development of set theory which teaches students all the basic results for algebra in one chapter.
An Introduction To Abstract Mathematics
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Author : Robert J. Bond
language : en
Publisher: Waveland Press
Release Date : 2007-08-24
An Introduction To Abstract Mathematics written by Robert J. Bond and has been published by Waveland Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-24 with Mathematics categories.
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.
An Invitation To Abstract Algebra
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Author : Steven J. Rosenberg
language : en
Publisher: CRC Press
Release Date : 2021-12-22
An Invitation To Abstract Algebra written by Steven J. Rosenberg and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-22 with Mathematics categories.
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout. The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois’ achievement in understanding how we can—and cannot—represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks—period. This book is offered as a manual to a new way of thinking. The author’s aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Introductory Concepts For Abstract Mathematics
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Author : Kenneth E. Hummel
language : en
Publisher: CRC Press
Release Date : 2000-03-23
Introductory Concepts For Abstract Mathematics written by Kenneth E. Hummel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-23 with Mathematics categories.
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.
Topology
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Author : K. Parthasarathy
language : en
Publisher: Springer Nature
Release Date : 2022-07-09
Topology written by K. Parthasarathy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-09 with Mathematics categories.
This book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré–Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk–Ulam theorem and the Lusternik–Schnirelmann–Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
Introduction To Abstract Mathematics
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Author : John F. Lucas
language : en
Publisher: Rowman & Littlefield
Release Date : 1990
Introduction To Abstract Mathematics written by John F. Lucas and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive strategies in the context of a variety of elementary mathematical situations. No background beyond single-variable calculus is presumed.
Bridge To Abstract Mathematics
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Author : Ralph W. Oberste-Vorth
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31
Bridge To Abstract Mathematics written by Ralph W. Oberste-Vorth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Education categories.
A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.
Introduction To Abstract Mathematics
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Author : Theodore A. Bick
language : en
Publisher:
Release Date : 1971
Introduction To Abstract Mathematics written by Theodore A. Bick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.