Bridge To Abstract Mathematics
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Bridge To Abstract Mathematics
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Author : Ronald P. Morash
language : en
Publisher:
Release Date : 1991
Bridge To Abstract Mathematics written by Ronald P. Morash and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content.
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.
Introductory Concepts For Abstract Mathematics
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Author : Kenneth E. Hummel
language : en
Publisher: CRC Press
Release Date : 2018-10-03
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 2018-10-03 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.
Linear Algebra As An Introduction To Abstract Mathematics
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Author : Isaiah Lankham
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-30
Linear Algebra As An Introduction To Abstract Mathematics written by Isaiah Lankham and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Mathematics categories.
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
Proofs And Fundamentals
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Proofs And Fundamentals written by Ethan D. Bloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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.
Sets Functions And Logic
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Author : Keith Devlin
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Sets Functions And Logic written by Keith Devlin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
Mathematical Bridges
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Author : Titu Andreescu
language : en
Publisher: Birkhäuser
Release Date : 2017-02-17
Mathematical Bridges written by Titu Andreescu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-17 with Mathematics categories.
Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.
Bridge To Abstract Mathematics
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Author : Ralph W. Oberste-Vorth
language : en
Publisher: American Mathematical Society
Release Date : 2020-02-20
Bridge To Abstract Mathematics written by Ralph W. Oberste-Vorth and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-20 with Mathematics 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.
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.
Introduction To Abstract Mathematics
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Author : T. A. Bick
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Introduction To Abstract Mathematics written by T. A. Bick and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.