# Search Results for "a-transition-to-advanced-mathematics"

## A Transition to Advanced Mathematics

**Author**: Douglas Smith,Maurice Eggen,Richard St. Andre**Publisher:**Cengage Learning**ISBN:**1285463269**Category:**Mathematics**Page:**448**View:**4725

A TRANSITION TO ADVANCED MATHEMATICS helps students to bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th 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. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

## Introduction to Mathematical Proofs, Second Edition

*A Transition to Advanced Mathematics, Second Edition*

**Author**: Charles Roberts**Publisher:**CRC Press**ISBN:**1482246880**Category:**Mathematics**Page:**414**View:**9759

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.

## A Transition to Advanced Mathematics

*A Survey Course*

**Author**: William Johnston,Alex McAllister**Publisher:**Oxford University Press**ISBN:**9780199718665**Category:**Mathematics**Page:**768**View:**9448

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.

## Mathematical Proofs

*A Transition to Advanced Mathematics*

**Author**: Gary Chartrand,Albert D. Polimeni,Ping Zhang**Publisher:**Addison-Wesley Longman**ISBN:**N.A**Category:**Mathematics**Page:**365**View:**9079

Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.

## A Transition to Advanced Mathematics, A Survey Course

*Mathematics, Mathematics*

**Author**: CTI Reviews**Publisher:**Cram101 Textbook Reviews**ISBN:**1467211028**Category:**Education**Page:**29**View:**9484

Facts101 is your complete guide to A Transition to Advanced Mathematics, A Survey Course. In this book, you will learn topics such as Number Theory, Real Analysis, Probability and Statistics, and Graph Theory plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

## Mathematical Proofs, A Transition to Advanced Mathematics

**Author**: CTI Reviews**Publisher:**Cram101 Textbook Reviews**ISBN:**1467298212**Category:**Education**Page:**37**View:**7758

Facts101 is your complete guide to Mathematical Proofs, A Transition to Advanced Mathematics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

## A Transition to Advanced Mathematics

*Mathematics, Mathematics*

**Author**: CTI Reviews**Publisher:**Cram101 Textbook Reviews**ISBN:**1467210846**Category:**Education**Page:**42**View:**483

Facts101 is your complete guide to A Transition to Advanced Mathematics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

## Elementary Point-Set Topology

*A Transition to Advanced Mathematics*

**Author**: Andre L. Yandl,Adam Bowers**Publisher:**Courier Dover Publications**ISBN:**0486811018**Category:**Mathematics**Page:**256**View:**2754

In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

## Mathematical Proofs: Pearson New International Edition

*A Transition to Advanced Mathematics*

**Author**: Gary Chartrand,Albert D. Polimeni,Ping Zhang**Publisher:**Pearson Higher Ed**ISBN:**1292052341**Category:**Mathematics**Page:**424**View:**2342

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book 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. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

## Discovering Group Theory

*A Transition to Advanced Mathematics*

**Author**: Tony Barnard,Hugh Neill**Publisher:**CRC Press**ISBN:**1315405768**Category:**Mathematics**Page:**231**View:**4596

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. ? Features Full proofs with all details clearly laid out and explained Reader-friendly conversational style Complete solutions to all exercises Focus on deduction, helping students learn how to construct proofs "Asides" to the reader, providing overviews and connections "What you should know" reviews at the end of each chapter

## A Discrete Transition to Advanced Mathematics

**Author**: Bettina Richmond,Thomas Richmond**Publisher:**American Mathematical Soc.**ISBN:**0821847899**Category:**Mathematics**Page:**424**View:**8482

As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last three chapters address topics such as continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio, and may be used for independent reading assignments. The treatment of sequences may be used to introduce epsilon-delta proofs. The selection of topics provides flexibility for the instructor in a course designed to spark the interest of students through exciting material while preparing them for subsequent proof-based courses.

## The Mathematical Method

*A Transition to Advanced Mathematics*

**Author**: Murray Eisenberg**Publisher:**Pearson College Division**ISBN:**9780131270022**Category:**Mathematics**Page:**350**View:**6355

This text includes an eclectic blend of math: number theory, analysis, and algebra, with logic as an extra.

## A Transition to Mathematics with Proofs

**Author**: Michael J Cullinane**Publisher:**Jones & Bartlett Publishers**ISBN:**1449627781**Category:**Mathematics**Page:**354**View:**7452

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.

## A Transition to Abstract Mathematics

*Learning Mathematical Thinking and Writing*

**Author**: Randall Maddox**Publisher:**Academic Press**ISBN:**0080922716**Category:**Mathematics**Page:**384**View:**8970

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

## Student Solutions Manual for A Transition to Abstract Mathematics

**Author**: Randall Maddox**Publisher:**Academic Press**ISBN:**0123748887**Category:**Science**Page:**78**View:**3806

Student Solutions Manual for A Transition to Abstract Mathematics

## Das BUCH der Beweise

**Author**: Martin Aigner,Günter M. Ziegler**Publisher:**Springer-Verlag**ISBN:**3662064545**Category:**Mathematics**Page:**247**View:**5893

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

## Advanced Calculus

*A Transition to Analysis, Student Solutions Manual (e-only)*

**Author**: Joseph B. Dence,Thomas P. Dence**Publisher:**Academic Press**ISBN:**0123846978**Category:**Mathematics**Page:**116**View:**2047

Advanced Calculus

## The keys to advanced mathematics

*recurrent themes in abstract reasoning*

**Author**: Daniel Solow**Publisher:**Books Unlimited**ISBN:**9780964451902**Category:**Mathematics**Page:**476**View:**3222

Here is a unique book that reduces the time & frustration involved in learning virtually every college-level undergraduate mathematics course & is as appropriate for freshman as it is for seniors. Standard textbooks teach specific subject matter, but this book explains for the first time the underlying thinking processes used in all of these courses. This book is therefore suitable as a supplement & as a reference for all of the following courses: discrete mathematics, linear algebra, abstract algebra, real analysis, transition-to-advanced math courses, courses on proofs & mathematical reasoning, & many more. There is currently no book on the market like this. You will not be able to keep this book on the shelf, but do not take our word for it -- Ask the head of your math department about this book. Distributed by BookMasters Distribution Center, P.O. Box 388, 1444 St. Route 42, Ashland, OH 44805. Phone (800) 247-6553, FAX (419) 281-6883.

## Visualize This!

**Author**: Nathan Yau**Publisher:**John Wiley & Sons**ISBN:**3527760229**Category:**Statistics / Graphic methods / Data processing**Page:**422**View:**7409

A guide on how to visualise and tell stories with data, providing practical design tips complemented with step-by-step tutorials.

## The Elements of Advanced Mathematics

**Author**: Steven G. Krantz**Publisher:**CRC Press**ISBN:**9780849384912**Category:**Mathematics**Page:**176**View:**3110

Clearly written and easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material.