Introductory Concepts For Abstract Mathematics

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Introductory Concepts for Abstract Mathematics

Author : Kenneth E. Hummel
Publisher : CRC Press
ISBN 13 : 1482285649
Total Pages : 345 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introductory Concepts for Abstract Mathematics by : Kenneth E. Hummel

Download or read book Introductory Concepts for Abstract Mathematics written by Kenneth E. Hummel and published by CRC Press. This book was released on 2018-10-03 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Abstract Mathematics

Author : Robert J. Bond
Publisher : Waveland Press
ISBN 13 : 1478608056
Total Pages : 344 pages
Book Rating : 4.4/5 (786 download)

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Book Synopsis An Introduction to Abstract Mathematics by : Robert J. Bond

Download or read book An Introduction to Abstract Mathematics written by Robert J. Bond and published by Waveland Press. This book was released on 2007-08-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Analysis

Author : Marvin E. Goldstein
Publisher : Courier Corporation
ISBN 13 : 0486799913
Total Pages : 256 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Introduction to Abstract Analysis by : Marvin E. Goldstein

Download or read book Introduction to Abstract Analysis written by Marvin E. Goldstein and published by Courier Corporation. This book was released on 2014-10-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise text prepares readers to pursue abstract analysis in the literature of pure mathematics. Detailed, easy-to-follow proofs and examples illustrate topics including real numbers, vector and metric spaces, infinite series, and other concepts. 1969 edition.

Linear Algebra as an Introduction to Abstract Mathematics

Author : Isaiah Lankham
Publisher : World Scientific Publishing Company
ISBN 13 : 9814723797
Total Pages : 208 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Linear Algebra as an Introduction to Abstract Mathematics by : Isaiah Lankham

Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bridge to Abstract Mathematics

Author : Ralph W. Oberste-Vorth
Publisher : American Mathematical Soc.
ISBN 13 : 0883857790
Total Pages : 232 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Bridge to Abstract Mathematics by : Ralph W. Oberste-Vorth

Download or read book Bridge to Abstract Mathematics written by Ralph W. Oberste-Vorth and published by American Mathematical Soc.. This book was released on 2012 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Algebra

Author : Jonathan D. H. Smith
Publisher : CRC Press
ISBN 13 : 9781420063721
Total Pages : 344 pages
Book Rating : 4.0/5 (637 download)

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Book Synopsis Introduction to Abstract Algebra by : Jonathan D. H. Smith

Download or read book Introduction to Abstract Algebra written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2016-04-19 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Introduction to Abstract Mathematics

Author : T. A. Bick
Publisher : Elsevier
ISBN 13 : 1483276597
Total Pages : 232 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Introduction to Abstract Mathematics by : T. A. Bick

Download or read book Introduction to Abstract Mathematics written by T. A. Bick and published by Elsevier. This book was released on 2014-05-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Invitation to Abstract Mathematics

Author : Béla Bajnok
Publisher : Springer Nature
ISBN 13 : 3030561747
Total Pages : 443 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok

Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Concepts of Modern Mathematics

Author : Ian Stewart
Publisher : Courier Corporation
ISBN 13 : 0486134954
Total Pages : 368 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Concepts of Modern Mathematics by : Ian Stewart

Download or read book Concepts of Modern Mathematics written by Ian Stewart and published by Courier Corporation. This book was released on 2012-05-23 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Proofs and Fundamentals

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
ISBN 13 : 1461221307
Total Pages : 434 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Proofs and Fundamentals by : Ethan D. Bloch

Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Book of Abstract Algebra

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486474178
Total Pages : 402 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Abstract Algebra by : Charles C Pinter

Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

An Elementary Transition to Abstract Mathematics

Author : Gove Effinger
Publisher : CRC Press
ISBN 13 : 1000701816
Total Pages : 293 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis An Elementary Transition to Abstract Mathematics by : Gove Effinger

Download or read book An Elementary Transition to Abstract Mathematics written by Gove Effinger and published by CRC Press. This book was released on 2019-11-05 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials. Features: The material is presented in many short chapters, so that one concept at a time can be absorbed by the student. Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student’s transition by working with familiar concepts. Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns. A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.

Mathematics for Physicists

Author : Alexander Altland
Publisher : Cambridge University Press
ISBN 13 : 1108651151
Total Pages : 723 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Mathematics for Physicists by : Alexander Altland

Download or read book Mathematics for Physicists written by Alexander Altland and published by Cambridge University Press. This book was released on 2019-02-14 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.

Introduction to Abstract Mathematics

Author : John F. Lucas
Publisher : Rowman & Littlefield
ISBN 13 : 9780912675732
Total Pages : 400 pages
Book Rating : 4.6/5 (757 download)

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Book Synopsis Introduction to Abstract Mathematics by : John F. Lucas

Download or read book Introduction to Abstract Mathematics written by John F. Lucas and published by Rowman & Littlefield. This book was released on 1990 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Passage to Abstract Mathematics

Author : Mark E. Watkins
Publisher : Pearson
ISBN 13 : 9780321738639
Total Pages : 0 pages
Book Rating : 4.7/5 (386 download)

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Book Synopsis Passage to Abstract Mathematics by : Mark E. Watkins

Download or read book Passage to Abstract Mathematics written by Mark E. Watkins and published by Pearson. This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses. The text covers logic, proof, numbers, sets, induction, functions, cardinality, and more-material which instructors of upper-level courses often presume their students have already mastered but is generally missing from lower-level courses. This streamlined text can realistically be covered in a semester. The authors resisted the temptation to include topics that are covered in the advanced courses for which this course is a prerequisite. The text assumes students have taken at least two semesters of calculus. Occasionally, the authors also refer to multivariable calculus and linear algebra, but these are not essential to the understanding of the text.

Mathematical Concepts

Author : Jürgen Jost
Publisher : Springer
ISBN 13 : 331920436X
Total Pages : 312 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematical Concepts by : Jürgen Jost

Download or read book Mathematical Concepts written by Jürgen Jost and published by Springer. This book was released on 2015-09-10 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning.

Fundamental Concepts of Abstract Algebra

Author : Gertrude Ehrlich
Publisher : Courier Corporation
ISBN 13 : 0486291863
Total Pages : 352 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Fundamental Concepts of Abstract Algebra by : Gertrude Ehrlich

Download or read book Fundamental Concepts of Abstract Algebra written by Gertrude Ehrlich and published by Courier Corporation. This book was released on 2013-05-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. It offers numerous examples, definitions, theorems, proofs, and practice exercises. 1991 edition.