A Transition To Abstract Mathematics

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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.

A Transition to Abstract Mathematics

Author : Randall Maddox
Publisher : Academic Press
ISBN 13 : 0080922716
Total Pages : 384 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis A Transition to Abstract Mathematics by : Randall Maddox

Download or read book A Transition to Abstract Mathematics written by Randall Maddox and published by Academic Press. This book was released on 2008-10-13 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. A Transition to Abstract Mathematics teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction Explains identification of techniques and how they are applied in the specific problem Illustrates how to read written proofs with many step by step examples Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter

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.

An Elementary Transition to Abstract Mathematics

Author : Gove Effinger
Publisher : CRC Press
ISBN 13 : 1000702278
Total Pages : 260 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 260 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.

Mathematical Thinking and Writing

Author : Randall Maddox
Publisher : Academic Press
ISBN 13 : 0124649769
Total Pages : 324 pages
Book Rating : 4.1/5 (246 download)

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Book Synopsis Mathematical Thinking and Writing by : Randall Maddox

Download or read book Mathematical Thinking and Writing written by Randall Maddox and published by Academic Press. This book was released on 2002 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.

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.

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.

A Transition to Mathematics with Proofs

Author : Michael J. Cullinane
Publisher : Jones & Bartlett Publishers
ISBN 13 : 1449627781
Total Pages : 367 pages
Book Rating : 4.4/5 (496 download)

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Book Synopsis A Transition to Mathematics with Proofs by : Michael J. Cullinane

Download or read book A Transition to Mathematics with Proofs written by Michael J. Cullinane and published by Jones & Bartlett Publishers. This book was released on 2013 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.

Foundations of Abstract Mathematics

Author : David C. Kurtz
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Foundations of Abstract Mathematics by : David C. Kurtz

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.

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

Mathematical Proofs

Author : Gary Chartrand
Publisher : Pearson Educacion
ISBN 13 : 9780321782519
Total Pages : 400 pages
Book Rating : 4.7/5 (825 download)

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Book Synopsis Mathematical Proofs by : Gary Chartrand

Download or read book Mathematical Proofs written by Gary Chartrand and published by Pearson Educacion. This book was released on 2013 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.

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.

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.

A Transition to Advanced Mathematics

Author : Douglas Smith
Publisher : Cengage Learning
ISBN 13 : 9780495562023
Total Pages : 416 pages
Book Rating : 4.5/5 (62 download)

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Book Synopsis A Transition to Advanced Mathematics by : Douglas Smith

Download or read book A Transition to Advanced Mathematics written by Douglas Smith and published by Cengage Learning. This book was released on 2010-06-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Basic Abstract Algebra

Author : Robert B. Ash
Publisher : Courier Corporation
ISBN 13 : 0486318117
Total Pages : 432 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Basic Abstract Algebra by : Robert B. Ash

Download or read book Basic Abstract Algebra written by Robert B. Ash and published by Courier Corporation. This book was released on 2013-06-17 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

Abstract Algebra

Author : William Paulsen
Publisher : CRC Press
ISBN 13 : 1498719775
Total Pages : 619 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Abstract Algebra by : William Paulsen

Download or read book Abstract Algebra written by William Paulsen and published by CRC Press. This book was released on 2016-02-10 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use. This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered. This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area. Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics. This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.

Discovering Group Theory

Author : Tony Barnard
Publisher : CRC Press
ISBN 13 : 1315405768
Total Pages : 286 pages
Book Rating : 4.3/5 (154 download)

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Book Synopsis Discovering Group Theory by : Tony Barnard

Download or read book Discovering Group Theory written by Tony Barnard and published by CRC Press. This book was released on 2016-12-19 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.