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.
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.
Download or read book Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 209 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.
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 257 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.
Download or read book Introduction to the Theory of Abstract Algebras written by Richard S Pierce and published by Courier Corporation. This book was released on 2015-01-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Suitable for introductory graduate-level courses and independent study, this text presents the basic definitions of the theory of abstract algebra. Following introductory material, each of four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Problems and a bibliography supplement the text. "--
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
Download or read book Bridge to Abstract Mathematics written by Ralph W. Oberste-Vorth and published by American Mathematical Society. This book was released on 2020-02-20 with total page 254 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.
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.
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 330 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.
Download or read book Passage to Abstract Mathematics written by Mark E Watkins and published by . This book was released on 2020-08-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Passage to Abstract Mathematics helps students progress from a facility with computational procedures to an understanding of abstract mathematical concepts. Students develop their ability in mathematical communication through reading proofs, constructing proofs, and writing proofs in correct mathematical language. Concise, practical, and highly valuable, the text is ideal for students who have taken lower-division mathematics courses and need the tools requisite to study more advanced, abstract mathematics. The text features material that instructors of upper-level courses in set theory, analysis, topology, and modern algebra presume students have already learned by the time they enter advanced courses. It places emphasis on complete and correct definitions, as well as expressing mathematics in correct syntax. The core material consists of the first five closely knit chapters: Logic, Numbers, Sets, Functions, and Induction. To support active and continuous learning, exercises are embedded within the text material immediately following a definition or theorem. The explanatory comments, hints to solutions, and thought-provoking questions that appear within brackets throughout the text all serve to deepen the student's understanding of the material. In the second edition, the chapter entitled Functions precedes the chapter entitled Induction, and select material has been clarified or corrected. Number theoretic digressions such as Euclid's Algorithm and the Chinese Remainder Theorem have been deleted.
Download or read book Concepts in Abstract Algebra written by Charles Lanski and published by American Mathematical Soc.. This book was released on with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.).
Download or read book Introduction to Abstract Algebra written by Benjamin Fine and published by JHU Press. This book was released on 2014-07-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic
Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Download or read book A First Course in Abstract Mathematics written by Ali Mostafazadeh and published by . This book was released on 2013 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Abstract Mathematics written by David C. Kurtz and published by McGraw-Hill Companies. This book was released on 1992 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for the average to strong mathematics major taking a course called Transition to Higher Mathematics, Introduction to Proofs, or Fundamentals of Mathematics. It provides a transition to topics covered in advanced mathematics and covers logic, proofs and sets and emphasizes two important mathematical activities - finding examples of objects with specified properties and writing proofs.
Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
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.
